From 318cf5f11287d18d5391673046950696777f1936 Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Sat, 28 Mar 2026 15:08:22 +0000
Subject: [PATCH 01/24] add PSGD PRO, fix existing PSGD

---
 README.md              |   2 +-
 heavyball/__init__.py  |  76 +++++++++++++++++++++++++
 heavyball/chainable.py | 116 +++++++++++++++++++++++++++++++++++++++
 heavyball/utils.py     | 122 +++++++++++++++++++++++++++++++++--------
 4 files changed, 291 insertions(+), 25 deletions(-)

diff --git a/README.md b/README.md
index e45eefe..d9ba71f 100644
--- a/README.md
+++ b/README.md
@@ -70,7 +70,7 @@ Muon, MuonLaProp, OrthoLaProp, LaPropOrtho
 SOAP, PaLMSOAP, PrecondScheduleSOAP, PrecondSchedulePaLMSOAP, SOAPNAdam, SOAPAdEMAMix, ForeachSOLP
 
 **PSGD (Kronecker):**
-PSGDKron, CachedPSGDKron, DelayedPSGD, CachedDelayedPSGDKron, PurePSGD, NewtonPSGDKron, NewtonHybrid2PSGDKron
+PSGDPRO, PSGDKron, CachedPSGDKron, DelayedPSGD, CachedDelayedPSGDKron, PurePSGD, NewtonPSGDKron, NewtonHybrid2PSGDKron
 
 `Newton`-PSGD requires a closure passed to `step()`.
 
diff --git a/heavyball/__init__.py b/heavyball/__init__.py
index e8c3eaf..784cfc1 100644
--- a/heavyball/__init__.py
+++ b/heavyball/__init__.py
@@ -1023,6 +1023,82 @@ class NewtonHybrid2PSGDKron(ForeachCachedNewtonPSGD):
     hvp_interval = 2
 
 
+class PSGDPRO(C.BaseOpt):
+    """
+    PSGD with Q0.5EQ1.5 (PRO/Procrustes) preconditioner update.
+    Solve-free alternative to standard PSGD-Kron (EQ method).
+    Reference: https://github.com/lixilinx/psgd_torch
+    """
+
+    cached: bool = False
+    exp_avg_input: bool = True
+
+    def __init__(
+        self,
+        params,
+        lr=0.001,
+        beta=None,
+        betas=(0.9, 0.999),
+        weight_decay=0.0,
+        preconditioner_update_probability=C.use_default,
+        max_size_triangular=2048,
+        min_ndim_triangular=2,
+        memory_save_mode=None,
+        momentum_into_precond_update=True,
+        warmup_steps: int = 0,
+        merge_dims: bool = False,
+        split: bool = False,
+        foreach: bool = True,
+        q_dtype="float32",
+        stochastic_schedule: bool = False,
+        storage_dtype: str = "float32",
+        mars: bool = False,
+        caution: bool = False,
+        mars_gamma: float = 0.0025,
+        cached: Optional[bool] = C.use_default,
+        exp_avg_input: Optional[bool] = C.use_default,
+        gradient_clipping: C.str_or_fn = C.use_default,
+        update_clipping: C.str_or_fn = C.use_default,
+        precond_grad_accum: bool = False,
+        lower_bound_beta: float = 0.9,
+        dampening: float = 2**-13,
+        precond_update_power_iterations: int = 2,
+        precond_init_scale=None,
+        precond_init_scale_scale: float = 1,
+        precond_init_scale_power: Optional[float] = None,
+        precond_lr: float = 0.1,
+        compile_step: bool = C.use_default,
+        promote: bool = C.use_default,
+        ecc: str | None = None,
+        param_ecc: str | None = None,
+        **kwargs,
+    ):
+        cached = C.default(cached, self.cached)
+        exp_avg_input = C.default(exp_avg_input, self.exp_avg_input)
+        update_clipping = C.default(update_clipping, utils.trust_region_clip_)
+
+        params, defaults = C._build_defaults(locals())
+        defaults["store_triu_as_line"] = False
+        defaults["inverse_free"] = False
+
+        self.precond_schedule = C.default(
+            defaults.pop("preconditioner_update_probability"), utils.precond_update_prob_schedule()
+        )
+
+        super().__init__(
+            params,
+            defaults,
+            foreach,
+            gradient_clipping,
+            update_clipping,
+            False,
+            fns=(
+                *(C.exp_avg,) * exp_avg_input,
+                functools.partial(C.scale_by_psgd_pro, cached=cached),
+            ),
+        )
+
+
 class ForeachPSGDLRA(C.BaseOpt):
     """
     Originally from Evan Walters and Omead Pooladzandi, 2024
diff --git a/heavyball/chainable.py b/heavyball/chainable.py
index eca7ea7..0df6279 100644
--- a/heavyball/chainable.py
+++ b/heavyball/chainable.py
@@ -792,6 +792,27 @@ def _init_psgd_kron(state, group, update, grad, param, cached: bool = False, pro
     state["Q_cache"] = [torch.empty_like(q) for q in Q]
 
 
+def _init_psgd_pro_kron(state, group, update, grad, param, cached: bool = False, prob: Optional[callable] = None):
+    Q = utils.init_Q_exprs(
+        grad,
+        group["precond_init_scale"],
+        group["precond_init_scale_scale"],
+        group["precond_init_scale_power"],
+        group["max_size_triangular"],
+        group["min_ndim_triangular"],
+        group["memory_save_mode"],
+        None,
+        None,
+        dtype=getattr(torch, group["q_dtype"]),
+    )
+    state["Q"] = Q
+    state["running_lower_bound"] = [torch.zeros((1,), device=q.device, dtype=torch.float64) for q in Q]
+    state["step"] = torch.zeros((), device=param.device, dtype=torch.float64)
+    if not cached:
+        return
+    state["Q_cache"] = [torch.empty_like(q) for q in Q]
+
+
 def _init_psgd_lra(state, group, update, grad, param, cached: bool = False, prob: Optional[callable] = None):
     state["U"], state["V"], state["d"] = utils.init_lra(
         grad,
@@ -1094,6 +1115,56 @@ def _update_psgd_precond(
     return None
 
 
+def _update_psgd_pro_precond(
+    cached,
+    Q_cache,
+    group,
+    param,
+    grad,
+    Q,
+    running_lower_bound,
+    step,
+    prob: Optional[callable] = None,
+) -> None:
+    if prob is None:
+        prob = utils.precond_update_prob_schedule()
+
+    if not group["is_preconditioning"]:
+        return
+
+    utils.psgd_pro_update_precond(
+        grad,
+        group["precond_lr"],
+        Q,
+        running_lower_bound,
+        group["lower_bound_beta"],
+        group["precond_update_power_iterations"],
+        group["dampening"],
+    )
+
+    if isinstance(prob, float):
+        float_prob = prob
+    else:
+        float_prob = prob(group["step"])
+    group["is_cached"] = should_use_cache = cached and float_prob < 0.5
+
+    if not should_use_cache or not cached:
+        return
+
+    for i, (c_, q_) in enumerate(zip(Q_cache, Q)):
+        if c_ is None:
+            c_ = (
+                torch.empty_like(q_)
+                if q_.ndim == 1
+                else torch.empty(q_.shape[0], q_.shape[0], device=q_.device, dtype=q_.dtype)
+            )
+            Q_cache[i] = c_
+        if q_.ndim == 2:
+            torch.matmul(q_.T, q_, out=c_)
+        else:
+            torch.mul(q_, q_, out=c_)
+
+
 def _cached_psgd_precond_grad(group, update, Q, Q_cache, grad):
     kwargs = {"ea": update, "caution": group["caution"], "grad": grad}
     if group.get("is_cached", False) and Q_cache[0] is not None:
@@ -1297,6 +1368,51 @@ def update_by_delayed_psgd(
     raise SkipUpdate from None
 
 
+@needs_full_param
+@SqueezeGrad
+@PrecondGradAccumGuard
+@general_guard("Q", "Q_cache", "running_lower_bound", "step", init_fn=_init_psgd_pro_kron, skip_first=False)
+@no_state_no_foreach
+def scale_by_psgd_pro(
+    group,
+    update,
+    grad,
+    param,
+    update_to_precond,
+    Q,
+    Q_cache,
+    running_lower_bound: List[Tensor],
+    step: Tensor,
+    cached: bool = False,
+    prob: Optional[callable] = None,
+):
+    _update_psgd_pro_precond(cached, Q_cache, group, param, update_to_precond, Q, running_lower_bound, step, prob)
+    return _cached_psgd_precond_grad(group, update, Q, Q_cache, grad)
+
+
+@needs_full_param
+@SqueezeGrad
+@PrecondGradAccumGuard
+@general_guard("Q", "Q_cache", "running_lower_bound", "step", init_fn=_init_psgd_pro_kron, skip_first=False)
+@no_state_no_foreach
+def update_by_psgd_pro(
+    group,
+    update,
+    grad,
+    param,
+    update_to_precond,
+    Q,
+    Q_cache,
+    running_lower_bound: List[Tensor],
+    step: Tensor,
+    cached: bool = False,
+    prob: Optional[callable] = None,
+):
+    _update_psgd_pro_precond(cached, Q_cache, group, param, update_to_precond, Q, running_lower_bound, step, prob)
+    _fused_cached_psgd_precond_grad(group, update, param, update, Q, Q_cache)
+    raise SkipUpdate from None
+
+
 def palm_beta2(state, group, update, grad, param):
     beta2 = 1 - group["step"] ** -group["beta2_scale"]
     group["betas"] = (utils.get_beta1(group), beta2)
diff --git a/heavyball/utils.py b/heavyball/utils.py
index f935fca..984cf17 100644
--- a/heavyball/utils.py
+++ b/heavyball/utils.py
@@ -2525,9 +2525,10 @@ def lra_precond(U: Tensor, V: Tensor, d: Tensor, g: Tensor):
 
 @decorator_knowngood
 def dampen_grad(g: Tensor, damp: float = 2**-13):
-    # https://github.com/lixilinx/psgd_torch/blob/1943e66596111e78157ca1b72b31c1dfdf0653ef/preconditioned_stochastic_gradient_descent.py#L50
+    # https://github.com/lixilinx/psgd_torch/blob/89b4cead31b7ad1494c4cf4dc39f4cbf920ff14d/psgd.py
     v = torch.randn_like(g)
-    return v, g + damp * g.abs().mean() * v
+    damping = damp + torch.finfo(g.dtype).eps * g.abs()
+    return v, g + damping * v
 
 
 @decorator_knowngood
@@ -2768,6 +2769,44 @@ def max_singular_value(A: Tensor, max_svd: int = 0, use_cholesky: bool = False,
     return max_singular_value_power_iter(A, None, iterations=power_iter)
 
 
+@decorator_knowngood
+def max_eigenvalue_spd(A_outer: Tensor, power_iter: int = 4) -> Tensor:
+    """Power iteration for the largest eigenvalue of a symmetric positive (semi)definite matrix.
+    Exploits A = A^T: A^T A = A^2, so v -> A^T(Av) = v -> A(Av), saving a transpose.
+    Uses x @ A.mT (gemm transB=true) for faster BLAS dispatch than A.mv(x)."""
+    if A_outer.ndim < 2:
+        return A_outer.max()
+    x_norm, max_idx = A_outer.norm(dim=1).max(dim=0)
+    x_norm = promote(x_norm)
+
+    def _inner():
+        x = A_outer.index_select(0, max_idx).flatten().contiguous()
+        A = stochastic_round_(A_outer / x_norm)
+        x = x / x_norm
+
+        def _mv(x):
+            return promote((x.to(A.dtype) @ A.mT) @ A.mT)
+
+        for _ in range(power_iter):
+            x = F.normalize(_mv(x), dim=0)
+        return (x @ _mv(x)).to(x_norm.dtype).sqrt() * x_norm
+
+    return cond(x_norm > 0, _inner, lambda: x_norm.squeeze().clone()).squeeze()
+
+
+@decorator_knowngood
+def procrustes_step(Q: Tensor, max_step_size: float = 1 / 8) -> None:
+    R = (Q.T - Q).contiguous()
+    R_norm = max_singular_value(R, power_iter=2) + torch.finfo(R.dtype).smallest_normal
+    R = R / R_norm
+    RQ = R @ Q
+    RRQ = R @ RQ
+    tr_RQ = RQ.diagonal().sum()
+    tr_RRQ = RRQ.diagonal().sum()
+    a = torch.where(tr_RRQ < 0, torch.clamp(-tr_RQ / tr_RRQ, max=max_step_size), max_step_size)
+    Q.add_(a * (RQ + 0.5 * a * RRQ))
+
+
 @decorator_knowngood
 def clamped_max_singular_value(
     A: Tensor, min: float, max_svd: int = 0, use_cholesky: bool = False, power_iter: int = 16
@@ -2927,22 +2966,11 @@ def _chebychef_coeff(degree: int, device, eps: float = 1e-8):
     return coeff0.float(), coeffs.float()
 
 
-@decorator_knowngood
-def _psgd_default_preconditioner_grad(
-    terms: List[Tuple[Tensor, Tensor]],
-    Q: List[Tensor],
-) -> List[Tensor]:
-    out = []
-    for q, (x, y) in zip(Q, terms):
-        x = promote(x)
-        y = promote(y)
-        update = x - y
-        if q.ndim < 2:
-            update = promote(q) * update
-        else:
-            update = (promote(q) @ update).triu()
-        out.append(update)
-    return out
+def _update_lb(ell: Tensor, lb_state: Tensor, beta: Tensor) -> Tensor:
+    ell = promote(ell)
+    ell = ell.maximum(promote(lb_state) + (ell - promote(lb_state)) * (1 - beta))
+    copy_stochastic_(lb_state, ell)
+    return ell
 
 
 @decorator
@@ -2965,15 +2993,61 @@ def psgd_update_precond(
     precond_lr, beta2, lower_bount_beta = scalar_guard(precond_lr, beta2, lower_bount_beta, G)
 
     A, conjB = psgd_calc_A_and_conjB(G, Q, V)
-    terms = [(compiled_einsum(exprG, A, A), compiled_einsum(exprG, conjB, conjB)) for exprG in exprGs]
-    del A, conjB, V
-    updates = _psgd_default_preconditioner_grad(terms, Q)
-    _psgd_precond_update_(
-        updates, oq, running_lower_bound, lower_bount_beta, precond_lr, store_triu_as_line, power_iter
-    )
+    del V
+
+    for oq_i, q, exprG, lb_state in zip(oq, Q, exprGs, running_lower_bound):
+        term1 = promote(compiled_einsum(exprG, A, A))
+        term2 = promote(compiled_einsum(exprG, conjB, conjB))
+
+        if q.ndim < 2:
+            ell = _update_lb((term1 + term2).max(), lb_state, lower_bount_beta)
+            update = promote(q) * (term1 - term2)
+        else:
+            ell = _update_lb(max_eigenvalue_spd(term1 + term2, power_iter=power_iter), lb_state, lower_bount_beta)
+            update = (term1 - term2).triu() @ promote(q)
+            if store_triu_as_line:
+                update = triu_to_line([update])[0][1]
+
+        real_oq = oq_i[1] if isinstance(oq_i, tuple) else oq_i
+        copy_stochastic_(real_oq, promote(real_oq) - update / ell * precond_lr)
     return None
 
 
+@decorator
+def psgd_pro_update_precond(
+    G: Tensor,
+    precond_lr: float,
+    Q: List[Tensor],
+    running_lower_bound: List[Tensor],
+    lower_bount_beta: float,
+    power_iter: int,
+    dampening: float,
+) -> None:
+    """Update Kronecker product preconditioner Q with Q0.5EQ1.5 (PRO) method."""
+    psgd_balance_Q(Q)
+    exprGs = calcG_expr(ndim_tuple(Q), G.ndim)
+    precond_lr, lower_bount_beta = scalar_guard(precond_lr, lower_bount_beta, G)
+
+    damping = dampening + torch.finfo(G.dtype).eps * G.abs()
+    Pg = psgd_precond_grad(G + damping * torch.randn_like(G), Q)
+
+    total_numel = G.numel()
+    for q, exprG, lb_state in zip(Q, exprGs, running_lower_bound):
+        term1 = promote(compiled_einsum(exprG, Pg, Pg))
+        q_ = promote(q)
+
+        if q.ndim < 2:
+            term2 = total_numel / max(1, q.numel())
+            ell = _update_lb(term1.max() + term2, lb_state, lower_bount_beta)
+            copy_stochastic_(q, q_ - q_ * (term1 - term2) / ell * precond_lr)
+        else:
+            term2 = total_numel / q.shape[0]
+            ell = _update_lb(max_eigenvalue_spd(term1, power_iter=power_iter) + term2, lb_state, lower_bount_beta)
+            copy_stochastic_(q, q_ - (term1 @ q_ - term2 * q_) / ell * precond_lr)
+            procrustes_step(q)
+    del Pg
+
+
 @decorator_knowngood
 def bf16_matmul(x: Tensor, y: Tensor):
     return (promote(x) @ promote(y)).to(x.dtype)

From 450d1b2276f07dbc6a86b17cf86c23de08f0cfb8 Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Sat, 28 Mar 2026 17:04:34 +0000
Subject: [PATCH 02/24] add HyperBallAdamW, MuonAdamW

---
 heavyball/__init__.py  |  84 +++++++++++++++++++++++++++++-
 heavyball/chainable.py | 113 ++++++++++++++++++++++++++++++++++++++---
 heavyball/utils.py     |  46 ++++++++++++++---
 3 files changed, 227 insertions(+), 16 deletions(-)

diff --git a/heavyball/__init__.py b/heavyball/__init__.py
index 784cfc1..379acd6 100644
--- a/heavyball/__init__.py
+++ b/heavyball/__init__.py
@@ -303,6 +303,86 @@ def __init__(
         )
 
 
+class HyperBallAdamW(C.BaseOpt):
+    def __init__(
+        self,
+        params,
+        lr=0.0025,
+        betas=(0.9, 0.99),
+        eps=1e-8,
+        weight_decay=0,
+        warmup_steps=0,
+        foreach: bool = True,
+        storage_dtype: str = "float32",
+        mars: bool = False,
+        caution: bool = False,
+        mars_gamma: float = 0.0025,
+        gradient_clipping: C.str_or_fn = C.use_default,
+        update_clipping: C.str_or_fn = C.use_default,
+        palm: bool = C.use_default,
+        beta2_scale: float = 0.8,
+        compile_step: bool = C.use_default,
+        promote: bool = C.use_default,
+        ecc: str | None = None,
+        param_ecc: str | None = None,
+        **kwargs,
+    ):
+        params, defaults = C._build_defaults(locals())
+        super().__init__(
+            params,
+            defaults,
+            foreach,
+            gradient_clipping,
+            update_clipping,
+            palm,
+            fns=(C.scale_by_exp_avg_sq, C.route(
+                (lambda p: p.ndim >= 2, C.update_by_hyperball),
+                default=C.apply_update,
+            )),
+        )
+
+
+class MuonAdamW(C.BaseOpt):
+    def __init__(
+        self,
+        params,
+        lr=0.0025,
+        betas=(0.9, 0.99),
+        eps=1e-8,
+        weight_decay=0,
+        warmup_steps=0,
+        foreach: bool = True,
+        storage_dtype: str = "float32",
+        mars: bool = False,
+        caution: bool = False,
+        mars_gamma: float = 0.0025,
+        gradient_clipping: C.str_or_fn = C.use_default,
+        update_clipping: C.str_or_fn = C.use_default,
+        palm: bool = C.use_default,
+        beta2_scale: float = 0.8,
+        nesterov: bool = True,
+        compile_step: bool = C.use_default,
+        promote: bool = C.use_default,
+        ecc: str | None = None,
+        param_ecc: str | None = None,
+        **kwargs,
+    ):
+        params, defaults = C._build_defaults(locals())
+        ema = C.nesterov_ema if nesterov else C.exp_avg
+        super().__init__(
+            params,
+            defaults,
+            foreach,
+            gradient_clipping,
+            update_clipping,
+            palm,
+            fns=(C.route(
+                (lambda p: p.ndim >= 2, (ema, C.orthogonalize_update)),
+                default=C.scale_by_adam,
+            ),),
+        )
+
+
 class ForeachSFAdamW(C.ScheduleFree):
     def __init__(
         self,
@@ -951,7 +1031,7 @@ def __init__(
         precond_grad_accum: bool = False,
         lower_bound_beta: float = 0.9,  # 0.0 recovers pre-2.0.0 PSGD
         inverse_free: bool = C.use_default,
-        dampening: float = 2**-13,
+        dampening: float = 1e-9,
         precond_update_power_iterations: int = 2,
         # expert parameters
         precond_init_scale=None,
@@ -1061,7 +1141,7 @@ def __init__(
         update_clipping: C.str_or_fn = C.use_default,
         precond_grad_accum: bool = False,
         lower_bound_beta: float = 0.9,
-        dampening: float = 2**-13,
+        dampening: float = 1e-9,
         precond_update_power_iterations: int = 2,
         precond_init_scale=None,
         precond_init_scale_scale: float = 1,
diff --git a/heavyball/chainable.py b/heavyball/chainable.py
index 0df6279..dc16ce0 100644
--- a/heavyball/chainable.py
+++ b/heavyball/chainable.py
@@ -85,20 +85,94 @@ def __repr__(self):
         return f"{self.__class__.__name__}({self.fn}, transform_idx={self.transform_idx})"
 
 
-class Branch:
+def _enforce_uniform_skip(results):
+    skips = [skip for _, skip, _ in results]
+    if not skips:
+        return False
+    if all(skips):
+        return True
+    if not any(skips):
+        return False
+    raise ValueError("All branches must uniformly skip or not skip updates")
+
+
+def _normalize_chain(fns):
+    if fns is None:
+        return None
+    return fns if isinstance(fns, (list, tuple)) else (fns,)
+
+
+class Parallel:
     def __init__(self, branches: List[List[callable]], merge_fn: callable):
         self.branches = branches
         self.merge_fn = merge_fn
 
     def __call__(self, state, group, update, grad, param):
-        outputs = []
+        results = []
         for branch in self.branches:
             branch_update = [torch.clone(u, memory_format=torch.preserve_format) for u in update]
-            branch_update, skip_update = _inner_chain(state, group, branch_update, grad, param, *branch)
-            if skip_update:
-                raise ValueError("Branches should not skip updates")
-            outputs.append(branch_update)
-        return self.merge_fn(outputs)
+            u, skip = _inner_chain(state, group, branch_update, grad, param, *branch)
+            results.append((u, skip, None))
+        if _enforce_uniform_skip(results):
+            raise SkipUpdate from None
+        return self.merge_fn([u for u, _, _ in results])
+
+
+class Route:
+    """Route params by predicate through different fn chains.
+
+    Takes arbitrary (predicate, fns) pairs. Each param is assigned to the first
+    matching route; unmatched params use the default chain (None = passthrough).
+    All routes must uniformly either skip or not skip updates.
+    """
+
+    def __init__(self, *routes, default=None):
+        self.routes = [(pred, _normalize_chain(fns)) for pred, fns in routes]
+        self.default = _normalize_chain(default)
+
+    def __call__(self, state, group, update, grad, param):
+        buckets = {}
+        assigned = set()
+        for j, (pred, _) in enumerate(self.routes):
+            for i, p in enumerate(param):
+                if i not in assigned and pred(p):
+                    buckets.setdefault(j, []).append(i)
+                    assigned.add(i)
+        default_idx = [i for i in range(len(param)) if i not in assigned]
+
+        def _sel(lst, idx):
+            return [lst[i] for i in idx]
+
+        caution = group["caution"]
+        results = []
+
+        all_chains = [(buckets.get(j), fns) for j, (_, fns) in enumerate(self.routes)]
+        if default_idx:
+            all_chains.append((default_idx, self.default))
+
+        for idx, fns in all_chains:
+            if not idx:
+                continue
+            group["caution"] = caution
+            if fns is not None:
+                u, skip = _inner_chain(state, group, _sel(update, idx), _sel(grad, idx), _sel(param, idx), *fns)
+            else:
+                u, skip = _sel(update, idx), False
+            results.append((u, skip, idx))
+
+        if _enforce_uniform_skip(results):
+            raise SkipUpdate from None
+
+        out = [None] * len(param)
+        for u_list, _, idx in results:
+            if u_list is not None:
+                for i, u in zip(idx, u_list):
+                    out[i] = u
+        return out
+
+
+def route(*routes, default=None):
+    return Route(*routes, default=default)
 
 
 def _zero_guard(state, key, ref, dtype):
@@ -405,6 +479,12 @@ def identity(state, group, update, grad, param):
     return update
 
 
+@no_state
+def apply_update(group, update, grad, param):
+    utils.update_param_(param, update, group["lr"], group["weight_decay"], caution=group["caution"], grad=grad)
+    raise SkipUpdate from None
+
+
 @zero_guard("exp_avg")
 @no_state
 def weight_decay_to_ema(group, update, grad, param, exp_avg):
@@ -867,6 +947,18 @@ def nesterov_ema(group, updates, grads, params, momentum):  # equivalent to Grok
     return utils.nesterov_ema(momentum, updates, utils.get_beta1(group))
 
 
+def _store_init_norm(state, group, update, grad, param):
+    state["init_norm"] = param.float().norm()
+
+
+@needs_full_param
+@general_guard("init_norm", init_fn=_store_init_norm, skip_first=False)
+@no_state
+def update_by_hyperball(group, update, grad, param, init_norm):
+    utils.hyperball_step_(param, update, init_norm, group["lr"], group["weight_decay"], group["caution"], grad)
+    raise SkipUpdate from None
+
+
 def _store_std(state, group, update, grad, param):
     state["init_std"] = torch.std(param)
 
@@ -1616,9 +1708,14 @@ def _walk_fns(obj):
             stack.append(cur.fn)
         elif isinstance(cur, functools.partial):
             stack.append(cur.func)
-        elif isinstance(cur, Branch):
+        elif isinstance(cur, Parallel):
             for branch in cur.branches:
                 stack.extend(branch)
+        elif isinstance(cur, Route):
+            for _, fns in cur.routes:
+                stack.extend(fns)
+            if cur.default is not None:
+                stack.extend(cur.default)
         elif isinstance(cur, _Iterable) and not isinstance(cur, (str, bytes, bytearray)):
             stack.extend(cur)
 
diff --git a/heavyball/utils.py b/heavyball/utils.py
index 984cf17..7cb8675 100644
--- a/heavyball/utils.py
+++ b/heavyball/utils.py
@@ -1504,7 +1504,7 @@ def _finite_differences_hvp(self, closure):
                 p.vector = torch.randn_like(p)
                 p.orig = p.data.clone()
                 # scale taken from https://github.com/lixilinx/psgd_torch/blob/1943e66596111e78157ca1b72b31c1dfdf0653ef/preconditioned_stochastic_gradient_descent.py#L2161
-                stochastic_add_(p.data, p.vector, torch.finfo(p.dtype).eps ** 0.5)
+                stochastic_add_(p.data, p.vector, torch.finfo(torch.float32).eps ** 0.5)
 
         with torch.enable_grad():
             closure()
@@ -1514,7 +1514,7 @@ def _finite_differences_hvp(self, closure):
         for group in self.param_groups:
             for p, g in self.split_p_and_g_in_group(group, skip_none=True, raw=True):
                 p.grad = grads.pop(0)
-                stochastic_add_divide_(g, p.grad, -1, torch.finfo(p.dtype).eps ** 0.5)
+                stochastic_add_divide_(g, p.grad, -1, torch.finfo(torch.float32).eps ** 0.5)
                 p.hessian_vector = g
                 p.data.copy_(p.orig)
                 del p.orig
@@ -2524,10 +2524,9 @@ def lra_precond(U: Tensor, V: Tensor, d: Tensor, g: Tensor):
 
 
 @decorator_knowngood
-def dampen_grad(g: Tensor, damp: float = 2**-13):
-    # https://github.com/lixilinx/psgd_torch/blob/89b4cead31b7ad1494c4cf4dc39f4cbf920ff14d/psgd.py
+def dampen_grad(g: Tensor, damp: float = 1e-9):
     v = torch.randn_like(g)
-    damping = damp + torch.finfo(g.dtype).eps * g.abs()
+    damping = damp + torch.finfo(torch.float32).eps * g.abs()
     return v, g + damping * v
 
 
@@ -3028,7 +3027,7 @@ def psgd_pro_update_precond(
     exprGs = calcG_expr(ndim_tuple(Q), G.ndim)
     precond_lr, lower_bount_beta = scalar_guard(precond_lr, lower_bount_beta, G)
 
-    damping = dampening + torch.finfo(G.dtype).eps * G.abs()
+    damping = dampening + torch.finfo(torch.float32).eps * G.abs()
     Pg = psgd_precond_grad(G + damping * torch.randn_like(G), Q)
 
     total_numel = G.numel()
@@ -3693,6 +3692,41 @@ def caution(g, update):
     return _compilable_cautioning(g, update)
 
 
+@decorator_knowngood
+def _compilable_hyperball_(
+    p: List[Tensor],
+    u: List[Tensor],
+    init_norm: List[Tensor],
+    lr: Tensor,
+    decay: float,
+    caution: bool,
+    g: List[Tensor],
+):
+    for op, u_, n_, g_ in zip(p, u, init_norm, g):
+        u_ = promote(u_.view_as(op))
+        p_ = promote(op)
+        if decay != 0:
+            u_ = u_ + p_ * decay
+        if caution:
+            u_ = _compilable_cautioning(promote(g_), u_)
+        u_norm = u_.norm()
+        u_norm = u_norm.clamp(min=1e-12)
+        u_ = u_ / u_norm
+        p_ = p_ - lr * u_ * n_
+        p_norm = p_.norm()
+        p_norm = p_norm.clamp(min=1e-12)
+        p_ = p_ * (n_ / p_norm)
+        copy_stochastic_(op, p_)
+
+
+def hyperball_step_(param, update, init_norm, lr, decay, caution, grad):
+    param, update, init_norm, grad = list_guard(param, update, init_norm, grad)
+    lr = scalar_guard(lr, param[0])
+    if not caution:
+        grad = [None] * len(param)
+    _compilable_hyperball_(param, update, init_norm, lr, decay, caution, grad)
+
+
 def _inner_precond_update_prob_schedule(
     n: int, max_prob: float = 1.0, min_prob: float = 0.03, decay: float = 0.999, flat_start: float = 1000
 ):

From bff2265ee7cef70d6eebb4dd376233afbd9cd177 Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Sat, 28 Mar 2026 18:13:56 +0000
Subject: [PATCH 03/24] rename everything

---
 README.md                          |  20 +--
 docs/benchmark.md                  |   4 +-
 docs/heavyball2.md                 |   4 +-
 examples/branched_optimizer.py     |   4 +-
 examples/ddp_training.py           |   6 +-
 examples/ecc_bf16.py               |   6 +-
 examples/fsdp_training.py          |   8 +-
 heavyball/__init__.py              | 235 ++++++++++-------------------
 heavyball/chainable.py             |  40 ++---
 heavyball/utils.py                 |  29 ++--
 scripts/migrate_optimizer_state.py |   2 +-
 test/test_ademamix.py              |   6 +-
 test/test_chainable_cpu.py         |  50 +++---
 test/test_cpu_features.py          |  10 +-
 test/test_distributed.py           |  19 +--
 test/test_ecc.py                   |  82 +++++-----
 test/test_foreach.py               |  18 +--
 test/test_memory_leak.py           |   2 +-
 test/test_merge.py                 |   2 +-
 test/test_migrate_cli.py           |   6 +-
 test/test_optimizer_cpu_smoke.py   |   2 +-
 test/test_param_ecc_compile.py     |   2 +-
 test/test_toy_training.py          |  14 +-
 test/utils.py                      |  12 +-
 24 files changed, 241 insertions(+), 342 deletions(-)

diff --git a/README.md b/README.md
index d9ba71f..56b5359 100644
--- a/README.md
+++ b/README.md
@@ -55,29 +55,25 @@ training, and SAM.
 <summary>Full list</summary>
 
 **First-order:**
-AdamW, NAdam, RMSprop, ADOPT, ForeachAdEMAMix, LaProp, SignLaProp, SGD, Scion, UnscaledAdamW, ForeachAdamC, SUDSAdamW
+AdamW, NAdam, RMSprop, ADOPT, AdEMAMix, LaProp, SignLaProp, SGD, Scion, UnscaledAdamW, AdamC, SUDSAdamW
 
 **Schedule-Free:**
-SFAdamW, PaLMSFAdamW
+SFAdamW
 
 Schedule-Free optimizers override `.eval()` and `.train()` to swap between training and evaluation parameter states.
 Call `opt.eval()` before validation and `opt.train()` before resuming training.
 
 **Orthogonal:**
-Muon, MuonLaProp, OrthoLaProp, LaPropOrtho
+Muon, MuonAdamW, MuonLaProp, HyperBallAdamW, OrthoLaProp, LaPropOrtho
 
 **Shampoo-based (SOAP):**
-SOAP, PaLMSOAP, PrecondScheduleSOAP, PrecondSchedulePaLMSOAP, SOAPNAdam, SOAPAdEMAMix, ForeachSOLP
+SOAP, SOAPNAdam, SOAPAdEMAMix, SOLP
 
 **PSGD (Kronecker):**
-PSGDPRO, PSGDKron, CachedPSGDKron, DelayedPSGD, CachedDelayedPSGDKron, PurePSGD, NewtonPSGDKron, NewtonHybrid2PSGDKron
-
-`Newton`-PSGD requires a closure passed to `step()`.
+PSGDKron, PSGDPRO
 
 **PSGD (Low-Rank):**
-PSGDLRA, DelayedPSGDLRA, NewtonPSGDLRA, NewtonHybrid2PSGDLRA
-
-`Newton`-PSGD requires a closure passed to `step()`.
+PSGDLRA
 
 **SAM:**
 SAMWrapper, MSAMLaProp
@@ -169,11 +165,11 @@ def graft(outputs, eps=1e-8):
 
 class GraftedAdam(C.BaseOpt):
     def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8,
-                 weight_decay=0, warmup_steps=0, foreach=True):
+                 weight_decay=0, warmup_steps=0, multi_tensor=True):
         defaults = dict(lr=lr, betas=betas, eps=eps, weight_decay=weight_decay,
                         warmup_steps=warmup_steps)
         branch = C.Branch(branches=[[C.scale_by_adam], [C.identity]], merge_fn=graft)
-        super().__init__(params, defaults, foreach, fns=(branch,))
+        super().__init__(params, defaults, multi_tensor, fns=(branch,))
 ```
 
 Custom optimizers that inherit from `BaseOpt` get ECC, MARS, caution, clipping, warmup, and stochastic rounding
diff --git a/docs/benchmark.md b/docs/benchmark.md
index 398b051..5fdb320 100644
--- a/docs/benchmark.md
+++ b/docs/benchmark.md
@@ -56,9 +56,9 @@ reinforcing the need for diagnostic rather than purely comparative evaluation.
 | Optimizer      | Cautious¹ | Mars² | Success | Attempts | Avg Runtime (s) |
 |:---------------|:----------|:------|:--------|:---------|:----------------|
 | PSGDKron       | No        | No    | 77.0%   | 73.2     | 8240            |
-| NewtonPSGDKron | No        | No    | 77.0%   | 80.5     | 9052            |
+| PSGDKron (Newton) | No     | No    | 77.0%   | 80.5     | 9052            |
 | AdamW          | Yes       | No    | 75.7%   | 61.2     | 8072            |
-| ForeachSOAP    | No        | No    | 72.5%   | 77.9     | 7827            |
+| SOAP           | No        | No    | 72.5%   | 77.9     | 7827            |
 | AdamW          | No        | No    | 72.3%   | 107.8    | 10029           |
 | MuonLaProp     | No        | No    | 68.2%   | 82.7     | 10141           |
 | RMSprop        | No        | No    | 55.6%   | 114.4    | 10725           |
diff --git a/docs/heavyball2.md b/docs/heavyball2.md
index 5660cb1..7bc8555 100644
--- a/docs/heavyball2.md
+++ b/docs/heavyball2.md
@@ -4,7 +4,7 @@
 
 * First‑class SAM via `SAMWrapper` (closure‑based)
 * More robust checkpoint/restore with HeavyBall‑internal state
-* New optimizers: `SGD`, `ForeachAdamC`, `MSAMLaProp`
+* New optimizers: `SGD`, `AdamC`, `MSAMLaProp`
 * Overhauled chainable pipeline: indexed transforms, branching, internal gradient‑accumulation, and `SqueezeGrad`
 * Faster, more accurate code paths
 * New `heavyball.helpers` with Optuna‑compatible samplers and utilities
@@ -18,7 +18,7 @@
 * `SAMWrapper` applies sharpness‑aware minimization to any HeavyBall optimizer while preserving the wrapped step logic;
   requires a closure
 * `SGD` built on the chainable internals
-* `ForeachAdamC`, a ["corrected version of Adam"](https://arxiv.org/abs/2506.02285) with weight decay normalized by the
+* `AdamC`, a ["corrected version of Adam"](https://arxiv.org/abs/2506.02285) with weight decay normalized by the
   maximum LR
 * `MSAMLaProp` built on top of [Momentum‑SAM](https://arxiv.org/abs/2401.12033)
 * Chainable pipeline:
diff --git a/examples/branched_optimizer.py b/examples/branched_optimizer.py
index b8a2795..001f107 100644
--- a/examples/branched_optimizer.py
+++ b/examples/branched_optimizer.py
@@ -29,7 +29,7 @@ def __init__(
         eps: float = 1e-8,
         weight_decay: float = 1e-4,
         warmup_steps: int = 0,
-        foreach: bool = True,
+        multi_tensor: bool = True,
     ):
         defaults = dict(
             lr=lr,
@@ -39,7 +39,7 @@ def __init__(
             warmup_steps=warmup_steps,
         )
         branch = C.Branch(branches=[[C.scale_by_adam], [C.identity]], merge_fn=_graft)
-        super().__init__(params, defaults, foreach, fns=(branch,))
+        super().__init__(params, defaults, multi_tensor, fns=(branch,))
 
 
 def main(epochs: int = 20, batch_size: int = 256, subset_size: int = 4096):
diff --git a/examples/ddp_training.py b/examples/ddp_training.py
index dc27092..bc39932 100644
--- a/examples/ddp_training.py
+++ b/examples/ddp_training.py
@@ -2,8 +2,8 @@
 
 Launch with torchrun:
     torchrun --nproc_per_node=2 examples/ddp_training.py
-    torchrun --nproc_per_node=2 examples/ddp_training.py --opt ForeachSOAP
-    torchrun --nproc_per_node=2 examples/ddp_training.py --opt ForeachMuon --lr 0.01
+    torchrun --nproc_per_node=2 examples/ddp_training.py --opt SOAP
+    torchrun --nproc_per_node=2 examples/ddp_training.py --opt Muon --lr 0.01
 
 All HeavyBall optimizers work transparently with DDP
 """
@@ -38,7 +38,7 @@ def make_model():
 
 def main():
     parser = argparse.ArgumentParser()
-    parser.add_argument("--opt", default="ForeachAdamW")
+    parser.add_argument("--opt", default="AdamW")
     parser.add_argument("--epochs", type=int, default=5)
     parser.add_argument("--batch-size", type=int, default=256)
     parser.add_argument("--lr", type=float, default=1e-3)
diff --git a/examples/ecc_bf16.py b/examples/ecc_bf16.py
index 1b8d1bf..7effd5d 100644
--- a/examples/ecc_bf16.py
+++ b/examples/ecc_bf16.py
@@ -19,11 +19,11 @@
 CONFIGS = {
     "naive_fp32": lambda p: NaiveAdamW(p, lr=LR, betas=BETAS, eps=EPS, state_dtype=torch.float32),
     "naive_bf16": lambda p: NaiveAdamW(p, lr=LR, betas=BETAS, eps=EPS, state_dtype=torch.bfloat16),
-    "heavyball_fp32": lambda p: heavyball.ForeachAdamW(p, lr=LR, betas=BETAS, eps=EPS, storage_dtype="float32"),
-    "heavyball_bf16": lambda p: heavyball.ForeachAdamW(
+    "heavyball_fp32": lambda p: heavyball.AdamW(p, lr=LR, betas=BETAS, eps=EPS, storage_dtype="float32"),
+    "heavyball_bf16": lambda p: heavyball.AdamW(
         p, lr=LR, betas=BETAS, eps=EPS, weight_decay=0, storage_dtype="bfloat16"
     ),
-    "ecc_bf16+8": lambda p: heavyball.ForeachAdamW(p, lr=LR, betas=BETAS, eps=EPS, weight_decay=0, ecc="bf16+8"),
+    "ecc_bf16+8": lambda p: heavyball.AdamW(p, lr=LR, betas=BETAS, eps=EPS, weight_decay=0, ecc="bf16+8"),
 }
 
 COLORS = {
diff --git a/examples/fsdp_training.py b/examples/fsdp_training.py
index 375d0e8..06087de 100644
--- a/examples/fsdp_training.py
+++ b/examples/fsdp_training.py
@@ -2,8 +2,8 @@
 
 Launch with torchrun:
     torchrun --nproc_per_node=2 examples/fsdp_training.py
-    torchrun --nproc_per_node=2 examples/fsdp_training.py --opt ForeachSOAP
-    torchrun --nproc_per_node=2 examples/fsdp_training.py --opt ForeachMuon --lr 0.01
+    torchrun --nproc_per_node=2 examples/fsdp_training.py --opt SOAP
+    torchrun --nproc_per_node=2 examples/fsdp_training.py --opt Muon --lr 0.01
 
 Shape-aware optimizers (SOAP, Muon, PSGD, Scion, etc.) auto-detect FSDP-flattened
 params and restore original shapes. No manual intervention needed.
@@ -11,7 +11,7 @@
 For non-FSDP parallelism backends, capture shapes before wrapping:
     shapes = heavyball.capture_param_shapes(model)
     model = your_wrapper(model)
-    opt = heavyball.ForeachSOAP(model.parameters(), lr=3e-3, orig_shapes=shapes)
+    opt = heavyball.SOAP(model.parameters(), lr=3e-3, orig_shapes=shapes)
 """
 
 import argparse
@@ -44,7 +44,7 @@ def make_model():
 
 def main():
     parser = argparse.ArgumentParser()
-    parser.add_argument("--opt", default="ForeachAdamW")
+    parser.add_argument("--opt", default="AdamW")
     parser.add_argument("--epochs", type=int, default=5)
     parser.add_argument("--batch-size", type=int, default=256)
     parser.add_argument("--lr", type=float, default=1e-3)
diff --git a/heavyball/__init__.py b/heavyball/__init__.py
index 379acd6..476aac0 100644
--- a/heavyball/__init__.py
+++ b/heavyball/__init__.py
@@ -16,7 +16,7 @@ def __init__(
         beta=0.9,
         weight_decay=0,
         warmup_steps=0,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -30,10 +30,10 @@ def __init__(
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
-        super().__init__(params, defaults, foreach, gradient_clipping, update_clipping, fns=(C.heavyball_momentum,))
+        super().__init__(params, defaults, multi_tensor, gradient_clipping, update_clipping, fns=(C.heavyball_momentum,))
 
 
-class ForeachAdamW(C.BaseOpt):
+class AdamW(C.BaseOpt):
     def __init__(
         self,
         params,
@@ -42,7 +42,7 @@ def __init__(
         eps=1e-8,
         weight_decay=0,
         warmup_steps=0,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -58,10 +58,10 @@ def __init__(
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
-        super().__init__(params, defaults, foreach, gradient_clipping, update_clipping, palm, fns=(C.update_by_adam,))
+        super().__init__(params, defaults, multi_tensor, gradient_clipping, update_clipping, palm, fns=(C.update_by_adam,))
 
 
-class ForeachNAdam(C.BaseOpt):
+class NAdam(C.BaseOpt):
     def __init__(
         self,
         params,
@@ -72,7 +72,7 @@ def __init__(
         momentum_decay: float = 4e-3,
         decoupled_weight_decay: bool = False,
         warmup_steps=0,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -88,10 +88,10 @@ def __init__(
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
-        super().__init__(params, defaults, foreach, gradient_clipping, update_clipping, palm, fns=(C.update_by_nadam,))
+        super().__init__(params, defaults, multi_tensor, gradient_clipping, update_clipping, palm, fns=(C.update_by_nadam,))
 
 
-class ForeachAdEMAMix(C.BaseOpt):
+class AdEMAMix(C.BaseOpt):
     def __init__(
         self,
         params,
@@ -103,7 +103,7 @@ def __init__(
         beta3_warmup: Optional[int] = None,
         alpha_warmup: Optional[int] = None,
         warmup_steps=0,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -120,7 +120,7 @@ def __init__(
             raise ValueError("AdEMAMix expects betas with three coefficients.")
 
         params, defaults = C._build_defaults(locals())
-        super().__init__(params, defaults, foreach, gradient_clipping, update_clipping, fns=(C.update_by_ademamix,))
+        super().__init__(params, defaults, multi_tensor, gradient_clipping, update_clipping, fns=(C.update_by_ademamix,))
 
 
 class UnscaledAdamW(C.BaseOpt):
@@ -132,7 +132,7 @@ def __init__(
         eps=1e-8,
         weight_decay=0,
         warmup_steps=0,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -149,7 +149,7 @@ def __init__(
     ):
         params, defaults = C._build_defaults(locals())
         super().__init__(
-            params, defaults, foreach, gradient_clipping, update_clipping, palm, fns=(C.scale_by_unscaled_adam,)
+            params, defaults, multi_tensor, gradient_clipping, update_clipping, palm, fns=(C.scale_by_unscaled_adam,)
         )
 
 
@@ -162,7 +162,7 @@ def __init__(
         eps=1e-8,
         weight_decay=0,
         warmup_steps=0,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -179,7 +179,7 @@ def __init__(
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
-        super().__init__(params, defaults, foreach, gradient_clipping, update_clipping, palm, fns=(C.scale_by_suds,))
+        super().__init__(params, defaults, multi_tensor, gradient_clipping, update_clipping, palm, fns=(C.scale_by_suds,))
 
 
 class Scion(C.BaseOpt):
@@ -191,7 +191,7 @@ def __init__(
         eps: float = 1e-8,
         weight_decay: float = 0,
         warmup_steps: int = 0,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -222,11 +222,11 @@ def __init__(
         defaults.pop("momentum", None)
 
         super().__init__(
-            params, defaults, foreach, gradient_clipping, update_clipping, fns=(C.exp_avg, C.scion_auto_norm)
+            params, defaults, multi_tensor, gradient_clipping, update_clipping, fns=(C.exp_avg, C.scion_auto_norm)
         )
 
 
-class ForeachAdamC(C.BaseOpt):
+class AdamC(C.BaseOpt):
     def __init__(
         self,
         params,
@@ -236,7 +236,7 @@ def __init__(
         weight_decay=0,
         max_lr: float | None = None,
         warmup_steps=0,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -258,10 +258,10 @@ def __init__(
             max_lr = lr
 
         params, defaults = C._build_defaults(locals())
-        super().__init__(params, defaults, foreach, gradient_clipping, update_clipping, palm, fns=(C.update_by_adamc,))
+        super().__init__(params, defaults, multi_tensor, gradient_clipping, update_clipping, palm, fns=(C.update_by_adamc,))
 
 
-class ForeachRMSprop(C.BaseOpt):
+class RMSprop(C.BaseOpt):
     """
     Debiased RMSprop (not torch.optim.RMSprop)
     """
@@ -276,7 +276,7 @@ def __init__(
         warmup_steps=0,
         r=0.0,
         weight_lr_power=2.0,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -295,7 +295,7 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            foreach,
+            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -312,7 +312,7 @@ def __init__(
         eps=1e-8,
         weight_decay=0,
         warmup_steps=0,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -331,7 +331,7 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            foreach,
+            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -351,7 +351,7 @@ def __init__(
         eps=1e-8,
         weight_decay=0,
         warmup_steps=0,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -372,7 +372,7 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            foreach,
+            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -383,7 +383,7 @@ def __init__(
         )
 
 
-class ForeachSFAdamW(C.ScheduleFree):
+class SFAdamW(C.ScheduleFree):
     def __init__(
         self,
         params,
@@ -394,7 +394,7 @@ def __init__(
         warmup_steps=0,
         r=0.0,
         weight_lr_power=2.0,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -413,7 +413,7 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            foreach,
+            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -432,7 +432,7 @@ def __init__(
         warmup_steps=0,
         r=0.0,
         weight_lr_power=2.0,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -452,7 +452,7 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            foreach,
+            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -460,11 +460,7 @@ def __init__(
         )
 
 
-class PaLMForeachSFAdamW(ForeachSFAdamW):
-    palm: bool = True
-
-
-class ForeachADOPT(C.BaseOpt):
+class ADOPT(C.BaseOpt):
     def __init__(
         self,
         params,
@@ -473,7 +469,7 @@ def __init__(
         eps=1e-8,
         weight_decay=0,
         warmup_steps=0,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -489,10 +485,10 @@ def __init__(
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
-        super().__init__(params, defaults, foreach, gradient_clipping, update_clipping, palm, fns=(C.update_by_adopt,))
+        super().__init__(params, defaults, multi_tensor, gradient_clipping, update_clipping, palm, fns=(C.update_by_adopt,))
 
 
-class ForeachMuon(C.BaseOpt):
+class Muon(C.BaseOpt):
     def __init__(
         self,
         params,
@@ -501,7 +497,7 @@ def __init__(
         eps=1e-8,
         weight_decay=0,
         warmup_steps=0,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -530,7 +526,7 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            foreach,
+            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -538,7 +534,7 @@ def __init__(
         )
 
 
-class ForeachLaProp(C.BaseOpt):
+class LaProp(C.BaseOpt):
     def __init__(
         self,
         params,
@@ -547,7 +543,7 @@ def __init__(
         eps=1e-8,
         weight_decay=0,
         warmup_steps=0,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -563,7 +559,7 @@ def __init__(
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
-        super().__init__(params, defaults, foreach, gradient_clipping, update_clipping, palm, fns=(C.update_by_laprop,))
+        super().__init__(params, defaults, multi_tensor, gradient_clipping, update_clipping, palm, fns=(C.update_by_laprop,))
 
 
 class MuonLaProp(C.BaseOpt):
@@ -575,7 +571,7 @@ def __init__(
         eps=1e-8,
         weight_decay=0,
         warmup_steps=0,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -594,7 +590,7 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            foreach,
+            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -602,9 +598,9 @@ def __init__(
         )
 
 
-class ForeachSOAP(C.BaseOpt):
+class SOAP(C.BaseOpt):
     """
-    ForeachSOAP
+    SOAP
 
     Sources:
         Baseline SOAP:
@@ -632,7 +628,7 @@ def __init__(
         correct_bias: bool = True,
         warmup_steps: int = 0,
         split: bool = False,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         mars: bool = False,
         caution: bool = False,
         mars_gamma: float = 0.0025,
@@ -664,7 +660,7 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            foreach,
+            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,  #
@@ -672,7 +668,7 @@ def __init__(
         )
 
 
-class ForeachSOAPNAdam(C.BaseOpt):
+class SOAPNAdam(C.BaseOpt):
     use_precond_schedule: bool = False
 
     def __init__(
@@ -691,7 +687,7 @@ def __init__(
         correct_bias: bool = True,
         warmup_steps: int = 0,
         split: bool = False,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         mars: bool = False,
         caution: bool = False,
         mars_gamma: float = 0.0025,
@@ -725,7 +721,7 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            foreach,
+            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -733,7 +729,7 @@ def __init__(
         )
 
 
-class ForeachSOAPAdEMAMix(C.BaseOpt):
+class SOAPAdEMAMix(C.BaseOpt):
     use_precond_schedule: bool = False
 
     def __init__(
@@ -752,7 +748,7 @@ def __init__(
         correct_bias: bool = True,
         warmup_steps: int = 0,
         split: bool = False,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         mars: bool = False,
         caution: bool = False,
         mars_gamma: float = 0.0025,
@@ -787,7 +783,7 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            foreach,
+            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -795,7 +791,7 @@ def __init__(
         )
 
 
-class ForeachSignLaProp(C.BaseOpt):
+class SignLaProp(C.BaseOpt):
     def __init__(
         self,
         params,
@@ -804,7 +800,7 @@ def __init__(
         eps=1e-8,
         weight_decay=0,
         warmup_steps=0,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -823,7 +819,7 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            foreach,
+            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -831,9 +827,9 @@ def __init__(
         )
 
 
-class ForeachSOLP(C.BaseOpt):
+class SOLP(C.BaseOpt):
     """
-    ForeachSOLP
+    SOLP
 
     Sources:
         Baseline SOAP:
@@ -861,7 +857,7 @@ def __init__(
         correct_bias: bool = True,
         warmup_steps: int = 0,
         split: bool = False,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         mars: bool = False,
         caution: bool = False,
         mars_gamma: float = 0.0025,
@@ -892,7 +888,7 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            foreach,
+            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,  #
@@ -900,20 +896,6 @@ def __init__(
         )
 
 
-class PaLMForeachSOAP(ForeachSOAP):
-    use_precond_schedule: bool = False
-    palm: bool = True
-
-
-class PrecondScheduleForeachSOAP(ForeachSOAP):
-    use_precond_schedule: bool = True
-
-
-class PrecondSchedulePaLMForeachSOAP(ForeachSOAP):
-    use_precond_schedule: bool = True
-    palm: bool = True
-
-
 class OrthoLaProp(C.BaseOpt):
     def __init__(
         self,
@@ -923,7 +905,7 @@ def __init__(
         eps=1e-8,
         weight_decay=0,
         warmup_steps=0,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -942,7 +924,7 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            foreach,
+            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -959,7 +941,7 @@ def __init__(
         eps=1e-8,
         weight_decay=0,
         warmup_steps=0,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -978,7 +960,7 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            foreach,
+            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -986,7 +968,7 @@ def __init__(
         )
 
 
-class ForeachPSGDKron(C.BaseOpt):
+class PSGDKron(C.BaseOpt):
     """
     Originally from Evan Walters and Omead Pooladzandi, 2024
     Modified under Creative Commons Attribution 4.0 International
@@ -1014,7 +996,7 @@ def __init__(
         merge_dims: bool = False,
         split: bool = False,
         store_triu_as_line: bool = True,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         q_dtype="float32",
         stochastic_schedule: bool = False,
         storage_dtype: str = "float32",
@@ -1067,7 +1049,7 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            foreach,
+            multi_tensor,
             gradient_clipping,
             update_clipping,
             False,  #
@@ -1078,31 +1060,6 @@ def __init__(
         )
 
 
-class ForeachPurePSGD(ForeachPSGDKron):
-    exp_avg_input: bool = False
-
-
-class ForeachCachedDelayedPSGDKron(ForeachPSGDKron):
-    delayed: bool = True
-    cached: bool = True
-
-
-class ForeachCachedPSGDKron(ForeachPSGDKron):
-    cached: bool = True
-
-
-class ForeachDelayedPSGD(ForeachPSGDKron):
-    delayed: bool = True
-
-
-class ForeachCachedNewtonPSGD(ForeachCachedPSGDKron):
-    hessian_approx = True
-
-
-class NewtonHybrid2PSGDKron(ForeachCachedNewtonPSGD):
-    hvp_interval = 2
-
-
 class PSGDPRO(C.BaseOpt):
     """
     PSGD with Q0.5EQ1.5 (PRO/Procrustes) preconditioner update.
@@ -1128,7 +1085,7 @@ def __init__(
         warmup_steps: int = 0,
         merge_dims: bool = False,
         split: bool = False,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         q_dtype="float32",
         stochastic_schedule: bool = False,
         storage_dtype: str = "float32",
@@ -1155,7 +1112,7 @@ def __init__(
     ):
         cached = C.default(cached, self.cached)
         exp_avg_input = C.default(exp_avg_input, self.exp_avg_input)
-        update_clipping = C.default(update_clipping, utils.trust_region_clip_)
+        update_clipping = C.default(update_clipping, None)
 
         params, defaults = C._build_defaults(locals())
         defaults["store_triu_as_line"] = False
@@ -1168,7 +1125,7 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            foreach,
+            multi_tensor,
             gradient_clipping,
             update_clipping,
             False,
@@ -1179,14 +1136,14 @@ def __init__(
         )
 
 
-class ForeachPSGDLRA(C.BaseOpt):
+class PSGDLRA(C.BaseOpt):
     """
     Originally from Evan Walters and Omead Pooladzandi, 2024
     Modified under Creative Commons Attribution 4.0 International
     Source available at https://github.com/evanatyourservice/kron_torch/blob/97a2b5ee8a1a4c29e4780bbf6c521e545189eff9/kron_torch/kron.py
 
-    Note: `foreach=True` (default) uses a single global low-rank approximation shared across all
-    parameters, while `foreach=False` fits an independent per-parameter LRA. These are different
+    Note: `multi_tensor=True` (default) uses a single global low-rank approximation shared across all
+    parameters, while `multi_tensor=False` fits an independent per-parameter LRA. These are different
     algorithms and will produce different results.
     """
 
@@ -1203,7 +1160,7 @@ def __init__(
         momentum_into_precond_update=True,
         rank: Optional[int] = None,
         warmup_steps: int = 0,
-        foreach: bool = True,  # True: global LRA across all params. False: independent per-param LRA.
+        multi_tensor: bool = True,  # True: global LRA across all params. False: independent per-param LRA.
         q_dtype="float32",
         stochastic_schedule: bool = False,
         storage_dtype: str = "float32",
@@ -1251,7 +1208,7 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            foreach,
+            multi_tensor,
             gradient_clipping,
             update_clipping,
             False,  #
@@ -1259,18 +1216,6 @@ def __init__(
         )
 
 
-class ForeachDelayedPSGDLRA(ForeachPSGDLRA):
-    delayed: bool = True
-
-
-class ForeachNewtonPSGDLRA(ForeachPSGDLRA):
-    hessian_approx = True
-
-
-class NewtonHybrid2PSGDLRA(ForeachNewtonPSGDLRA):
-    hvp_interval = 2
-
-
 class SplitOpt(utils.StatefulOptimizer):
     """
     Delegates different parameter groups to different underlying optimizers.
@@ -1291,7 +1236,7 @@ def __init__(self, specs):
                 all_params.extend(params)
         if not self.optimizers:
             raise ValueError("No optimizers created")
-        super().__init__(all_params, {}, foreach=True)
+        super().__init__(all_params, {}, multi_tensor=True)
 
     def _step(self, group):
         pass
@@ -1322,7 +1267,7 @@ class SAMWrapper(torch.optim.Optimizer):
     def __init__(
         self,
         params,
-        wrapped_optimizer: Union[utils.StatefulOptimizer, Type[utils.StatefulOptimizer]] = ForeachAdamW,
+        wrapped_optimizer: Union[utils.StatefulOptimizer, Type[utils.StatefulOptimizer]] = AdamW,
         ball: float = 0.1,
     ):
         params = list(params)
@@ -1366,31 +1311,5 @@ def zero_grad(self, set_to_none: bool = True):
         self.wrapped_optimizer.zero_grad(set_to_none=set_to_none)
 
 
-PalmForEachSoap = PaLMForeachSOAP
-PaLMSOAP = PaLMForeachSOAP
-PaLMSFAdamW = PaLMForeachSFAdamW
-SOAP = ForeachSOAP
-SOAPAdEMAMix = ForeachSOAPAdEMAMix
-SOAPNAdam = ForeachSOAPNAdam
-SFAdamW = ForeachSFAdamW
-LaProp = ForeachLaProp
-ADOPT = ForeachADOPT
-RMSprop = ForeachRMSprop
-PrecondScheduleSOAP = PrecondScheduleForeachSOAP
-PrecondSchedulePaLMSOAP = PrecondSchedulePaLMForeachSOAP
-PSGDKron = ForeachPSGDKron
-AdamW = ForeachAdamW
-NAdam = ForeachNAdam
-PurePSGD = ForeachPurePSGD
-DelayedPSGD = ForeachDelayedPSGD
-CachedPSGDKron = ForeachCachedPSGDKron
-CachedDelayedPSGDKron = ForeachCachedDelayedPSGDKron
-Muon = ForeachMuon
-SignLaProp = ForeachSignLaProp
-DelayedPSGDLRA = ForeachDelayedPSGDLRA
-PSGDLRA = ForeachPSGDLRA
-NewtonPSGDLRA = ForeachNewtonPSGDLRA
-NewtonPSGDKron = ForeachCachedNewtonPSGD
-
 capture_param_shapes = utils.capture_param_shapes
 __all__ = [k for k, v in globals().items() if isinstance(v, type) and issubclass(v, torch.optim.Optimizer)]
diff --git a/heavyball/chainable.py b/heavyball/chainable.py
index dc16ce0..6dbf1f9 100644
--- a/heavyball/chainable.py
+++ b/heavyball/chainable.py
@@ -374,7 +374,7 @@ def __call__(self, state, group, update, grad, param, *args, **kwargs):
         return self.fn(group, update, grad, param, *args, **kwargs)
 
 
-class NoStateNoForeach(FunctionTransform):
+class NoStateNoMultiTensor(FunctionTransform):
     def __call__(self, state, group, update, grad, param, *args, **kwargs):
         updates = []
         skip_update = False
@@ -446,8 +446,8 @@ def no_state(fn):
     return NoState(fn)
 
 
-def no_state_no_foreach(fn):
-    return NoStateNoForeach(fn)
+def no_state_no_multi_tensor(fn):
+    return NoStateNoMultiTensor(fn)
 
 
 class SkipUpdate(ValueError):
@@ -699,7 +699,7 @@ def orthogonalize_grad_to_param(group, update, grad, param):
 @copy_guard(2, "z")
 @no_state
 def update_by_schedule_free(group, update, grad, param, z):
-    # Compute weight_sum once per step, not per param in no-foreach mode.
+    # Compute weight_sum once per step, not per param in no-multi_tensor mode.
     if group.get("_sf_step") != group["step"]:
         weight = abs(group["lr"]) ** group["weight_lr_power"] * max(group["step"], 1) ** group["r"]
         group["weight_sum"] = group.get("weight_sum", 0) + weight
@@ -779,7 +779,7 @@ def update_by_adopt(group, update, grad, param, exp_avg, exp_avg_sq):
 
 @needs_full_param
 @zero_guard("exp_avg", "exp_avg_sq", "fisher_approx")
-@no_state_no_foreach
+@no_state_no_multi_tensor
 def scale_by_suds(group, update, grad, param, exp_avg, exp_avg_sq, fisher_approx):
     if group["step"] == 1:
         utils.copy_stochastic_(fisher_approx, update / update.norm().clamp(min=1e-8))
@@ -924,7 +924,7 @@ def precond_schedule(group, prob: Union[callable, float, None] = None, name: str
 
 
 @needs_full_param
-@no_state_no_foreach
+@no_state_no_multi_tensor
 def orthogonalize_update(group, update, grad, param, scale_mode: str = "scale"):  # explore scale_mode="graft"
     if update.dim() < 2:
         return update
@@ -1352,7 +1352,7 @@ def update_by_delayed_psgd_lra(group, update, grad, param, update_to_precond, U,
 @SqueezeGrad
 @PrecondGradAccumGuard
 @general_guard("Q", "Q_cache", "velocity", "running_lower_bound", "step", init_fn=_init_psgd_kron, skip_first=False)
-@no_state_no_foreach
+@no_state_no_multi_tensor
 def scale_by_psgd(
     group,
     update,
@@ -1375,7 +1375,7 @@ def scale_by_psgd(
 @SqueezeGrad
 @PrecondGradAccumGuard
 @general_guard("Q", "Q_cache", "velocity", "running_lower_bound", "step", init_fn=_init_psgd_kron, skip_first=False)
-@no_state_no_foreach
+@no_state_no_multi_tensor
 def scale_by_delayed_psgd(
     group,
     update,
@@ -1404,7 +1404,7 @@ def scale_by_delayed_psgd(
 @SqueezeGrad
 @PrecondGradAccumGuard
 @general_guard("Q", "Q_cache", "velocity", "running_lower_bound", "step", init_fn=_init_psgd_kron, skip_first=False)
-@no_state_no_foreach
+@no_state_no_multi_tensor
 def update_by_psgd(
     group,
     update,
@@ -1440,7 +1440,7 @@ def global_clip(group, update, grad, param, clip_fn: Optional[callable] = None):
 @SqueezeGrad
 @PrecondGradAccumGuard
 @general_guard("Q", "Q_cache", "velocity", "running_lower_bound", "step", init_fn=_init_psgd_kron, skip_first=False)
-@no_state_no_foreach
+@no_state_no_multi_tensor
 def update_by_delayed_psgd(
     group,
     update,
@@ -1464,7 +1464,7 @@ def update_by_delayed_psgd(
 @SqueezeGrad
 @PrecondGradAccumGuard
 @general_guard("Q", "Q_cache", "running_lower_bound", "step", init_fn=_init_psgd_pro_kron, skip_first=False)
-@no_state_no_foreach
+@no_state_no_multi_tensor
 def scale_by_psgd_pro(
     group,
     update,
@@ -1486,7 +1486,7 @@ def scale_by_psgd_pro(
 @SqueezeGrad
 @PrecondGradAccumGuard
 @general_guard("Q", "Q_cache", "running_lower_bound", "step", init_fn=_init_psgd_pro_kron, skip_first=False)
-@no_state_no_foreach
+@no_state_no_multi_tensor
 def update_by_psgd_pro(
     group,
     update,
@@ -1745,14 +1745,14 @@ class ChainOpt(utils.StatefulOptimizer):
         "eps": 1e-8,
     }
 
-    def __init__(self, params, defaults, foreach: bool, *fns):
+    def __init__(self, params, defaults, multi_tensor: bool, *fns):
         orig = defaults.pop("orig_shapes", None)
         self._orig_shapes = (
             {k: _ShapeInfo(v) if isinstance(v, tuple) else v for k, v in orig.items()} if orig is not None else None
         )
         base = self.global_defaults.copy()
         base.update({k: v for k, v in defaults.items() if v is not use_default})
-        super().__init__(params, base, foreach)
+        super().__init__(params, base, multi_tensor)
         self.fns = fns
         self.register_load_state_dict_post_hook(ChainOpt._restore_ecc_dtypes)
         self._init_param_ecc()
@@ -1854,7 +1854,7 @@ def _step(self, group):
         if "prev_lr" in group and group["prev_lr"] != group["lr"]:
             utils.warn_once(
                 f"Learning rate changed between steps. This is an experimental feature and "
-                f"only supported with foreach=True (currently foreach={group['foreach']})."
+                f"only supported with multi_tensor=True (currently multi_tensor={group['multi_tensor']})."
             )
             group["base_lr"] = group["lr"]
 
@@ -1890,7 +1890,7 @@ def _step_inner(self, group):
         group["step"] = state["step"] = step = step + 1
         group["prev_lr"] = group["lr"] = group["base_lr"] * step / max(step, group["warmup_steps"] + 1)
 
-        if not group["foreach"] or len(p) == 1:
+        if not group["multi_tensor"] or len(p) == 1:
             for param, grad in zip(p, g):
                 chain(self.state_, group, [grad], [param], *self.fns)
                 group["caution"] = caution
@@ -1936,6 +1936,7 @@ def default(a, b):
     scale_by_laprop.get_fn(): update_by_laprop,  #
     scale_by_adopt.get_fn(): update_by_adopt,  #
     scale_by_ademamix.get_fn(): update_by_ademamix,  #
+    scale_by_psgd_pro.get_fn(): update_by_psgd_pro,  #
 }
 _scale_to_update_map_inv = {
     update_by_delayed_psgd.get_fn(): scale_by_delayed_psgd,  #
@@ -1947,6 +1948,7 @@ def default(a, b):
     update_by_laprop.get_fn(): scale_by_laprop,  #
     update_by_adopt.get_fn(): scale_by_adopt,  #
     update_by_ademamix.get_fn(): scale_by_ademamix,  #
+    update_by_psgd_pro.get_fn(): scale_by_psgd_pro,  #
 }
 
 
@@ -1961,7 +1963,7 @@ class BaseOpt(ChainOpt):
     promote: bool = False
     Whether to promote the gradients to fp32 before applying the optimizer
     Improves update quality for low-precision parameters, but increases costs
-    Compiling the optimizer step would reduce memory and compute. Alternatively, `foreach=False` decreases memory at the cost of runtime
+    Compiling the optimizer step would reduce memory and compute. Alternatively, `multi_tensor=False` decreases memory at the cost of runtime
 
     gradient_clipping: str_or_fn = None
     The function to use for clipping the incoming gradients, before any other transformations.
@@ -1983,7 +1985,7 @@ def __init__(
         self,
         params,
         defaults,
-        foreach: bool = True,
+        multi_tensor: bool = True,
         gradient_clipping: str_or_fn = None,
         update_clipping: str_or_fn = None,
         palm: bool = use_default,
@@ -2031,7 +2033,7 @@ def __init__(
         if default(update_clipping, self.update_clipping) is not None:
             fns = fns + (apply_to_idx(update_clipping, 2),)
 
-        super().__init__(params, defaults, foreach, *fns)
+        super().__init__(params, defaults, multi_tensor, *fns)
 
 
 class ScheduleFree(BaseOpt):
diff --git a/heavyball/utils.py b/heavyball/utils.py
index 7cb8675..0eab0be 100644
--- a/heavyball/utils.py
+++ b/heavyball/utils.py
@@ -1305,13 +1305,13 @@ class StatefulOptimizer(torch.optim.Optimizer):
         "hessian_approx",
     )
 
-    def __init__(self, params, defaults, foreach: bool = True, use_ema: bool = False):
+    def __init__(self, params, defaults, multi_tensor: bool = True, use_ema: bool = False):
         for attr in self._INSTANCE_ATTRS:
             if attr in defaults:
                 val = defaults.pop(attr)
                 if val is not use_default:
                     setattr(self, attr, val)
-        super().__init__(params, {**defaults, "foreach": foreach})
+        super().__init__(params, {**defaults, "multi_tensor": multi_tensor})
         self.use_ema = use_ema
         self.mapping = {}
         self.mapping_inverse = {}
@@ -2151,7 +2151,7 @@ def _compilable_update_(
     caution: bool,
     g: List[Optional[Tensor]],
 ):
-    for i, (u_, g_, p_) in enumerate(zip(u, g, p)):  # lr is data-dependent -> can't compile a foreach
+    for i, (u_, g_, p_) in enumerate(zip(u, g, p)):  # lr is data-dependent -> can't compile a multi-tensor op
         u_ = promote(u_.view_as(p_))
         p32_ = promote(p_)
         if caution:
@@ -2620,7 +2620,7 @@ def multi_flatten(*xs: Tuple[List[Tensor], int]):
 
 
 @decorator_knowngood
-def dampen_multiple(g: List[Tensor], damp: float = 2**-13):
+def dampen_multiple(g: List[Tensor], damp: float = 1e-9):
     vs = []
     gs = []
     for g_ in g:
@@ -2631,8 +2631,7 @@ def dampen_multiple(g: List[Tensor], damp: float = 2**-13):
 
 
 def casted_einsum(expr: str, *args: Tensor) -> Tensor:
-    md = min_dtype(args)
-    return compiled_einsum(expr, *[a.to(md) for a in args]).to(args[-1].dtype)
+    return compiled_einsum(expr, *[promote(a) for a in args]).to(args[-1].dtype)
 
 
 @decorator_knowngood
@@ -3012,7 +3011,7 @@ def psgd_update_precond(
     return None
 
 
-@decorator
+@decorator_knowngood
 def psgd_pro_update_precond(
     G: Tensor,
     precond_lr: float,
@@ -3548,9 +3547,8 @@ def precond_grad_cached_(
 ):
     if caution:
         ea = _compilable_cautioning(grad, ea)
-    md = min_dtype(list(cached_q) + [ea])
-    args = [q.to(md) for q in cached_q]
-    args = args + [ea.to(md)]
+    args = [promote(q) for q in cached_q]
+    args = args + [promote(ea)]
     expr = cached_precond_grad_expr(ndim_tuple(cached_q), ea.ndim)
     new = compiled_einsum(expr, *args)
     if cast:
@@ -3591,16 +3589,18 @@ def psgd_precond_grad(
     grad: Optional[Tensor] = None,
     store_triu_as_line: bool = False,
     symmetric_output: bool = False,
+    cast: bool = True,
 ):
     if caution:
         ea = _compilable_cautioning(grad, ea)
     if store_triu_as_line:
         preconds = line_to_triu(preconds, symmetric_output)
-    md = min_dtype(list(preconds) + [ea])
-    args = [q.to(md) for q in preconds]
+    args = [promote(q) for q in preconds]
     expr = precond_grad_expr(ndim_tuple(args), ea.ndim)
-    new = compiled_einsum(expr, *[a for a in args for _ in (0, 1)], ea.to(md))
-    return new.to(ea.dtype)
+    new = compiled_einsum(expr, *[a for a in args for _ in (0, 1)], promote(ea))
+    if cast:
+        return new.to(ea.dtype)
+    return new
 
 
 @decorator_knowngood
@@ -3622,6 +3622,7 @@ def _compilable_fused_psgd_precond_grad(
         grad=grad,
         store_triu_as_line=store_triu_as_line,
         symmetric_output=symmetric_output,
+        cast=False,
     )
     update_param_(param, precond, lr, decay, caution=False, grad=grad)
 
diff --git a/scripts/migrate_optimizer_state.py b/scripts/migrate_optimizer_state.py
index fb9f6e2..1eef0aa 100644
--- a/scripts/migrate_optimizer_state.py
+++ b/scripts/migrate_optimizer_state.py
@@ -234,7 +234,7 @@ def migrate(
     ),
     optimizer_class: str = typer.Argument(
         ...,
-        help="Optimizer class to instantiate (e.g., heavyball.ForeachAdamW)",
+        help="Optimizer class to instantiate (e.g., heavyball.AdamW)",
     ),
     state_key: str = typer.Option(
         "optimizer",
diff --git a/test/test_ademamix.py b/test/test_ademamix.py
index 847a290..49e53de 100644
--- a/test/test_ademamix.py
+++ b/test/test_ademamix.py
@@ -101,7 +101,7 @@ def test_ademamix_matches_reference_math():
     alpha_warmup = 4
 
     param = torch.nn.Parameter(initial.clone())
-    optimizer = heavyball.ForeachAdEMAMix(
+    optimizer = heavyball.AdEMAMix(
         [param],
         lr=lr,
         betas=betas,
@@ -110,7 +110,7 @@ def test_ademamix_matches_reference_math():
         alpha=alpha,
         beta3_warmup=beta3_warmup,
         alpha_warmup=alpha_warmup,
-        foreach=False,
+        multi_tensor=False,
     )
 
     for grad in grads:
@@ -149,7 +149,7 @@ def test_soap_ademamix_projects_gradients_into_eigenbasis():
     torch.manual_seed(7)
 
     param = torch.nn.Parameter(torch.randn(2, 2))
-    optimizer = heavyball.ForeachSOAPAdEMAMix([param], lr=0.01, foreach=False)
+    optimizer = heavyball.SOAPAdEMAMix([param], lr=0.01, multi_tensor=False)
 
     # First call initializes the SOAP preconditioner state without applying an update.
     param.grad = torch.randn_like(param)
diff --git a/test/test_chainable_cpu.py b/test/test_chainable_cpu.py
index 124cbe4..6612028 100644
--- a/test/test_chainable_cpu.py
+++ b/test/test_chainable_cpu.py
@@ -70,46 +70,36 @@ def state_fn(_x):
 # Optimizers whose chains are purely elementwise must NOT need gather
 _EXPECT_NO_GATHER = {
     "SGD",
-    "ForeachAdamW",
-    "ForeachNAdam",
-    "ForeachAdEMAMix",
+    "AdamW",
+    "NAdam",
+    "AdEMAMix",
     "UnscaledAdamW",
-    "ForeachAdamC",
-    "ForeachRMSprop",
-    "ForeachSFAdamW",
-    "ForeachADOPT",
-    "ForeachLaProp",
-    "PaLMForeachSFAdamW",
+    "AdamC",
+    "RMSprop",
+    "SFAdamW",
+    "ADOPT",
+    "LaProp",
 }
 
 # Optimizers whose chains use shape-dependent or global-reduction ops must need gather
 _EXPECT_GATHER = {
-    "ForeachSOAP",
-    "ForeachSOAPNAdam",
-    "ForeachSOAPAdEMAMix",
-    "ForeachSOLP",
-    "ForeachMuon",
+    "SOAP",
+    "SOAPNAdam",
+    "SOAPAdEMAMix",
+    "SOLP",
+    "Muon",
     "MuonLaProp",
     "OrthoLaProp",
     "LaPropOrtho",
-    "ForeachPSGDKron",
-    "ForeachPurePSGD",
-    "ForeachCachedPSGDKron",
-    "ForeachDelayedPSGD",
-    "ForeachCachedDelayedPSGDKron",
-    "ForeachCachedNewtonPSGD",
-    "NewtonHybrid2PSGDKron",
-    "ForeachPSGDLRA",
-    "ForeachDelayedPSGDLRA",
-    "ForeachNewtonPSGDLRA",
-    "NewtonHybrid2PSGDLRA",
+    "PSGDKron",
+    "PSGDLRA",
+    "PSGDPRO",
     "SUDSAdamW",
     "Scion",
-    "ForeachSignLaProp",
+    "SignLaProp",
     "MSAMLaProp",
-    "PaLMForeachSOAP",
-    "PrecondScheduleForeachSOAP",
-    "PrecondSchedulePaLMForeachSOAP",
+    "HyperBallAdamW",
+    "MuonAdamW",
 }
 
 _SKIP_INSTANTIATE = {"SplitOpt", "SAMWrapper"}
@@ -120,7 +110,7 @@ def state_fn(_x):
 @pytest.mark.parametrize("opt_name", _ALL_OPTS)
 def test_needs_gather_flag(opt_name):
     params = [torch.nn.Parameter(torch.randn(4, 4))]
-    extra = {"max_lr": 0.0025} if opt_name == "ForeachAdamC" else {}
+    extra = {"max_lr": 0.0025} if opt_name == "AdamC" else {}
     opt = getattr(heavyball, opt_name)(params, lr=1e-3, **extra)
     if opt_name in _EXPECT_NO_GATHER:
         assert not opt._needs_gather, f"{opt_name} should be elementwise (no gather needed)"
diff --git a/test/test_cpu_features.py b/test/test_cpu_features.py
index e241f98..82ed343 100644
--- a/test/test_cpu_features.py
+++ b/test/test_cpu_features.py
@@ -44,9 +44,9 @@ def _make_batch(
 @pytest.mark.parametrize(
     "opt_name",
     [
-        "ForeachSOAP",
+        "SOAP",
         "Muon",
-        "ForeachAdamW",
+        "AdamW",
     ],
 )
 def test_selected_optimizers_run_on_cpu(opt_name: str) -> None:
@@ -92,8 +92,8 @@ def test_mars_flag_changes_behavior() -> None:
     model_a, data, target = _make_batch()
     model_b = deepcopy(model_a)
 
-    opt_a = heavyball.ForeachAdamW(model_a.parameters(), mars=False, warmup_steps=0)
-    opt_b = heavyball.ForeachAdamW(model_b.parameters(), mars=True, warmup_steps=0)
+    opt_a = heavyball.AdamW(model_a.parameters(), mars=False, warmup_steps=0)
+    opt_b = heavyball.AdamW(model_b.parameters(), mars=True, warmup_steps=0)
 
     init = [param.detach().clone() for param in model_a.parameters()]
 
@@ -112,7 +112,7 @@ def test_mars_flag_changes_behavior() -> None:
 
 def test_sam_wrapper_requires_closure() -> None:
     model = nn.Linear(4, 2)
-    base = heavyball.ForeachAdamW(model.parameters())
+    base = heavyball.AdamW(model.parameters())
     wrapper = heavyball.SAMWrapper(model.parameters(), wrapped_optimizer=base)
 
     with pytest.raises(ValueError):
diff --git a/test/test_distributed.py b/test/test_distributed.py
index 1b60e7b..1663f13 100644
--- a/test/test_distributed.py
+++ b/test/test_distributed.py
@@ -17,14 +17,13 @@
     pytest.mark.skipif(not torch.cuda.is_available(), reason="CUDA required"),
 ]
 
-_EXTRA_KWARGS = {"ForeachAdamC": {"max_lr": 0.0025}}
+_EXTRA_KWARGS = {"AdamC": {"max_lr": 0.0025}}
 _MODEL_SEED = 42
 _DATA_SEED = 0xABCD
 
 # LRA builds one preconditioner over all grads, under FSDP each rank only has a subset
 _FSDP_SKIP = {
-    "ForeachPSGDLRA": "LRA preconditioner scope differs under FSDP",
-    "ForeachDelayedPSGDLRA": "LRA preconditioner scope differs under FSDP",
+    "PSGDLRA": "LRA preconditioner scope differs under FSDP",
 }
 
 # torch.compile(dynamic=False) specializes on list length → different kernels per rank
@@ -39,16 +38,14 @@
 _INTEGRATION_OPTS = [
     n
     for n in [
-        "ForeachAdamW",
-        "ForeachSOAP",
-        "ForeachMuon",
-        "ForeachPSGDKron",
-        "ForeachPurePSGD",
+        "AdamW",
+        "SOAP",
+        "Muon",
+        "PSGDKron",
         "Scion",
-        "ForeachLaProp",
+        "LaProp",
         "MuonLaProp",
-        "ForeachSOAPNAdam",
-        "ForeachCachedPSGDKron",
+        "SOAPNAdam",
     ]
     if n in REPRESENTATIVE_OPTS and n not in _FSDP_SKIP
 ]
diff --git a/test/test_ecc.py b/test/test_ecc.py
index 97c0eab..1dd7364 100644
--- a/test/test_ecc.py
+++ b/test/test_ecc.py
@@ -14,13 +14,13 @@
 ULP_MODES = ["bf16+8", "bf16+16", "fp16+8", "fp16+16"]
 
 _OPTIMIZERS = [
-    (heavyball.ForeachAdamW, 5e-2, {}),
-    (heavyball.ForeachADOPT, 5e-2, {}),
-    (heavyball.ForeachNAdam, 1e-2, {}),
-    (heavyball.ForeachLaProp, 5e-2, {}),
-    (heavyball.ForeachAdEMAMix, 5e-2, {"betas": (0.9, 0.999, 0.9999)}),
-    (heavyball.ForeachRMSprop, 1e-2, {}),
-    (heavyball.PaLMForeachSFAdamW, 1e-2, {}),
+    (heavyball.AdamW, 5e-2, {}),
+    (heavyball.ADOPT, 5e-2, {}),
+    (heavyball.NAdam, 1e-2, {}),
+    (heavyball.LaProp, 5e-2, {}),
+    (heavyball.AdEMAMix, 5e-2, {"betas": (0.9, 0.999, 0.9999)}),
+    (heavyball.RMSprop, 1e-2, {}),
+    (heavyball.SFAdamW, 1e-2, {}),
 ]
 
 
@@ -125,12 +125,12 @@ def test_ecc_convergence(opt_cls, lr, extra_kw, mode):
 def test_param_ecc_convergence(combined):
     set_torch()
     data, target = _problem()
-    m0, o0 = _model_opt(heavyball.PaLMForeachSFAdamW, 16, 8, 1e-2)
+    m0, o0 = _model_opt(heavyball.SFAdamW, 16, 8, 1e-2)
     losses_base = _train(m0, o0, data, target, 200)
     kw = {"param_ecc": "bf16+8"}
     if combined:
         kw["ecc"] = "bf16+8"
-    m1, o1 = _model_opt(heavyball.PaLMForeachSFAdamW, 16, 8, 1e-2, **kw)
+    m1, o1 = _model_opt(heavyball.SFAdamW, 16, 8, 1e-2)
     losses_ecc = _train(m1, o1, data, target, 200)
     p = list(m1.parameters())[0]
     assert p.dtype == torch.bfloat16
@@ -148,7 +148,7 @@ def test_state_layout_and_invariants(mode):
     cfg = ECCConfig(mode)
     torch.manual_seed(42)
     model = nn.Linear(32, 16, bias=False, device="cuda")
-    opt = heavyball.ForeachAdamW(model.parameters(), lr=1e-2, ecc=mode)
+    opt = heavyball.AdamW(model.parameters(), lr=1e-2, ecc=mode)
     x = torch.randn(4, 32, device="cuda")
     for _ in range(3):
         model(x).sum().backward()
@@ -174,7 +174,7 @@ def test_ademamix_three_vars():
     set_torch()
     torch.manual_seed(42)
     model = nn.Linear(64, 32, bias=False, device="cuda")
-    opt = heavyball.ForeachAdEMAMix(model.parameters(), lr=5e-2, betas=(0.9, 0.999, 0.9999), ecc="bf16+8")
+    opt = heavyball.AdEMAMix(model.parameters(), lr=5e-2, betas=(0.9, 0.999, 0.9999), ecc="bf16+8")
     x = torch.randn(4, 64, device="cuda")
     for _ in range(10):
         model(x).sum().backward()
@@ -193,7 +193,7 @@ def test_ademamix_three_vars():
 
 def test_combined_ecc_dtypes():
     set_torch()
-    m, o = _model_opt(heavyball.PaLMForeachSFAdamW, 32, 16, 1e-2, ecc="bf16+16", param_ecc="bf16+8")
+    m, o = _model_opt(heavyball.SFAdamW, 32, 16, 1e-2, ecc="bf16+16", param_ecc="bf16+8")
     data, target = _problem(in_dim=32, out_dim=16, n=8)
     _train(m, o, data, target, 100)
     p = list(m.parameters())[0]
@@ -211,7 +211,7 @@ def test_shapes_and_bias():
     set_torch()
     torch.manual_seed(42)
     model = nn.Sequential(nn.Linear(32, 16, bias=True), nn.Linear(16, 4, bias=False)).cuda()
-    opt = heavyball.ForeachAdamW(model.parameters(), lr=1e-2, ecc="bf16+8")
+    opt = heavyball.AdamW(model.parameters(), lr=1e-2, ecc="bf16+8")
     data, target = torch.randn(16, 32, device="cuda"), torch.randn(16, 4, device="cuda")
     losses = _train(model, opt, data, target, 50)
     for p in model.parameters():
@@ -225,9 +225,9 @@ def test_shapes_and_bias():
 def test_foreach_false():
     set_torch()
     data, target = _problem(in_dim=32, out_dim=4, n=16)
-    m_fe, o_fe = _model_opt(heavyball.ForeachAdamW, 32, 4, 1e-2, ecc="bf16+8", foreach=True)
+    m_fe, o_fe = _model_opt(heavyball.AdamW, 32, 4, 1e-2, ecc="bf16+8", multi_tensor=True)
     losses_fe = _train(m_fe, o_fe, data, target, 50)
-    m_nf, o_nf = _model_opt(heavyball.ForeachAdamW, 32, 4, 1e-2, ecc="bf16+8", foreach=False)
+    m_nf, o_nf = _model_opt(heavyball.AdamW, 32, 4, 1e-2, ecc="bf16+8", multi_tensor=False)
     losses_nf = _train(m_nf, o_nf, data, target, 50)
     assert losses_nf[-1] < losses_nf[0] * 0.5
     assert 0.3 < losses_nf[-1] / max(losses_fe[-1], 1e-12) < 3.0
@@ -239,7 +239,7 @@ def test_param_groups():
     set_torch()
     torch.manual_seed(42)
     m1, m2 = nn.Linear(16, 8, bias=False, device="cuda"), nn.Linear(8, 4, bias=False, device="cuda")
-    opt = heavyball.ForeachAdamW(
+    opt = heavyball.AdamW(
         [
             {"params": m1.parameters(), "ecc": "bf16+8"},
             {"params": m2.parameters()},
@@ -261,7 +261,7 @@ def test_zero_gradients():
     set_torch()
     torch.manual_seed(42)
     p = nn.Parameter(torch.randn(16, 8, device="cuda"))
-    opt = heavyball.ForeachAdamW([p], lr=1e-2, ecc="bf16+8")
+    opt = heavyball.AdamW([p], lr=1e-2, ecc="bf16+8")
     for _ in range(10):
         p.grad = torch.zeros_like(p)
         opt.step()
@@ -276,10 +276,10 @@ def test_state_save_restore():
 
     set_torch()
     data, target = _problem()
-    m, o = _model_opt(heavyball.PaLMForeachSFAdamW, 16, 8, 1e-2, ecc="bf16+8")
+    m, o = _model_opt(heavyball.SFAdamW, 16, 8, 1e-2, ecc="bf16+8")
     _train(m, o, data, target, 10)
     sd_opt, sd_model = deepcopy(o.state_dict()), deepcopy(m.state_dict())
-    m2, o2 = _model_opt(heavyball.PaLMForeachSFAdamW, 16, 8, 1e-2, ecc="bf16+8")
+    m2, o2 = _model_opt(heavyball.SFAdamW, 16, 8, 1e-2, ecc="bf16+8")
     m2.load_state_dict(sd_model)
     o2.load_state_dict(sd_opt)
     losses_after = _train(m2, o2, data, target, 10)
@@ -302,7 +302,7 @@ def _measure_peak(cls, n, lr, ecc=None, param_ecc=None, steps=3):
         kw["ecc"] = ecc
     if param_ecc:
         kw["param_ecc"] = param_ecc
-    opt = cls([p], lr=lr, **kw)
+    opt = cls([p], lr=lr)
 
     for _ in range(steps):
         p.grad = torch.randn_like(p)
@@ -326,9 +326,9 @@ def _measure_peak(cls, n, lr, ecc=None, param_ecc=None, steps=3):
 @pytest.mark.parametrize(
     "cls,lr",
     [
-        (heavyball.ForeachAdamW, 1e-3),
-        (heavyball.PaLMForeachSFAdamW, 1e-2),
-        (heavyball.ForeachRMSprop, 1e-2),
+        (heavyball.AdamW, 1e-3),
+        (heavyball.SFAdamW, 1e-2),
+        (heavyball.RMSprop, 1e-2),
     ],
     ids=["AdamW", "SFAdamW", "RMSprop"],
 )
@@ -346,7 +346,7 @@ def test_ecc_peak_memory(cls, lr, mode):
 @pytest.mark.parametrize("combined", [False, True], ids=["param_only", "state+param"])
 def test_param_ecc_peak_memory(combined):
     n = 2**24
-    cls, lr = heavyball.PaLMForeachSFAdamW, 1e-2
+    cls, lr = heavyball.SFAdamW, 1e-2
     pre_base, peak_base = _measure_peak(cls, n, lr)
     ecc = "bf16+8" if combined else None
     pre_ecc, peak_ecc = _measure_peak(cls, n, lr, ecc=ecc, param_ecc="bf16+8")
@@ -357,7 +357,7 @@ def test_param_ecc_peak_memory(combined):
 def test_ecc_live_path_nonzero_correction():
     set_torch()
     data, target = _problem()
-    m, o = _model_opt(heavyball.ForeachAdamW, 16, 8, 5e-2, ecc="bf16+8")
+    m, o = _model_opt(heavyball.AdamW, 16, 8, 5e-2, ecc="bf16+8")
     _train(m, o, data, target, 20)
     p = list(m.parameters())[0]
     st, ecc_keys = _ecc_keys(o, p)
@@ -369,7 +369,7 @@ def test_ecc_live_path_nonzero_correction():
 
 def test_lerp_returns_valid_fp32():
     set_torch()
-    m, o = _model_opt(heavyball.ForeachAdamW, 16, 8, 5e-2, ecc="bf16+8")
+    m, o = _model_opt(heavyball.AdamW, 16, 8, 5e-2, ecc="bf16+8")
     data, target = _problem()
     _train(m, o, data, target, 10)
     p = list(m.parameters())[0]
@@ -398,7 +398,7 @@ def test_param_ecc_merge_dims():
         nn.Flatten(),
         nn.Linear(64, 8, bias=False),
     ).cuda()
-    opt = heavyball.ForeachSOAP(model.parameters(), lr=1e-3, param_ecc="bf16+8")
+    opt = heavyball.SOAP(model.parameters(), lr=1e-3, param_ecc="bf16+8")
     conv_p = list(model.parameters())[0]
     assert conv_p.dtype == torch.bfloat16
     st = _flat_state(opt, conv_p)
@@ -417,7 +417,7 @@ def test_param_ecc_merge_dims():
 
 def test_param_ecc_dtype_at_construction():
     set_torch()
-    m, o = _model_opt(heavyball.PaLMForeachSFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
+    m, o = _model_opt(heavyball.SFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
     p = list(m.parameters())[0]
     assert p.dtype == torch.bfloat16, "param should be bf16 immediately after construction"
     st = _flat_state(o, p)
@@ -431,11 +431,11 @@ def test_param_ecc_save_restore():
 
     set_torch()
     data, target = _problem()
-    m, o = _model_opt(heavyball.PaLMForeachSFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
+    m, o = _model_opt(heavyball.SFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
     _train(m, o, data, target, 10)
     sd_opt, sd_model = deepcopy(o.state_dict()), deepcopy(m.state_dict())
 
-    m2, o2 = _model_opt(heavyball.PaLMForeachSFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
+    m2, o2 = _model_opt(heavyball.SFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
     m2.load_state_dict(sd_model)
     o2.load_state_dict(sd_opt)
     p2 = list(m2.parameters())[0]
@@ -452,7 +452,7 @@ def test_param_ecc_partial_state_restore():
 
     set_torch()
     data, target = _problem()
-    m, o = _model_opt(heavyball.PaLMForeachSFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
+    m, o = _model_opt(heavyball.SFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
     _train(m, o, data, target, 10)
     sd_opt = deepcopy(o.state_dict())
     sd_model = deepcopy(m.state_dict())
@@ -460,7 +460,7 @@ def test_param_ecc_partial_state_restore():
         for idx_state in param_state.values():
             if isinstance(idx_state, dict):
                 idx_state.pop("param::ecc", None)
-    m2, o2 = _model_opt(heavyball.PaLMForeachSFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
+    m2, o2 = _model_opt(heavyball.SFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
     m2.load_state_dict(sd_model)
     o2.load_state_dict(sd_opt)
     st2 = _flat_state(o2, list(m2.parameters())[0])
@@ -478,12 +478,12 @@ def test_param_ecc_empty_state_restore():
 
     set_torch()
     data, target = _problem()
-    m, o = _model_opt(heavyball.PaLMForeachSFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
+    m, o = _model_opt(heavyball.SFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
     _train(m, o, data, target, 10)
     sd_opt = deepcopy(o.state_dict())
     sd_model = deepcopy(m.state_dict())
     sd_opt["state"] = {}
-    m2, o2 = _model_opt(heavyball.PaLMForeachSFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
+    m2, o2 = _model_opt(heavyball.SFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
     m2.load_state_dict(sd_model)
     o2.load_state_dict(sd_opt)
     p2 = list(m2.parameters())[0]
@@ -508,7 +508,7 @@ def test_param_ecc_merged_view_partial_restore():
         nn.Flatten(),
         nn.Linear(64, 8, bias=False),
     ).cuda()
-    opt = heavyball.ForeachSOAP(model.parameters(), lr=1e-3, param_ecc="bf16+8")
+    opt = heavyball.SOAP(model.parameters(), lr=1e-3, param_ecc="bf16+8")
     data = torch.randn(4, 3, 8, 8, device="cuda")
     target = torch.randn(4, 8, device="cuda")
     conv_p = list(model.parameters())[0]
@@ -529,7 +529,7 @@ def test_param_ecc_merged_view_partial_restore():
         nn.Flatten(),
         nn.Linear(64, 8, bias=False),
     ).cuda()
-    opt2 = heavyball.ForeachSOAP(model2.parameters(), lr=1e-3, param_ecc="bf16+8")
+    opt2 = heavyball.SOAP(model2.parameters(), lr=1e-3, param_ecc="bf16+8")
     model2.load_state_dict(sd_model)
     opt2.load_state_dict(sd_opt)
     conv_p2 = list(model2.parameters())[0]
@@ -549,7 +549,7 @@ def test_param_ecc_merged_view_partial_restore():
 def test_optimizer_kwargs_not_in_param_groups():
     set_torch()
     p = torch.nn.Parameter(torch.randn(4, 4, device="cuda"))
-    o = heavyball.ForeachAdamW([p], lr=1e-3, compile_step=True, promote=True)
+    o = heavyball.AdamW([p], lr=1e-3, compile_step=True, promote=True)
     assert o.compile_step is True
     assert o.promote is True
     assert "compile_step" not in o.param_groups[0]
@@ -564,7 +564,7 @@ def test_param_ecc_load_order_model_before_optimizer():
 
     set_torch()
     data, target = _problem()
-    m, o = _model_opt(heavyball.PaLMForeachSFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
+    m, o = _model_opt(heavyball.SFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
     _train(m, o, data, target, 10)
     sd_opt = deepcopy(o.state_dict())
     sd_model = deepcopy(m.state_dict())
@@ -573,7 +573,7 @@ def test_param_ecc_load_order_model_before_optimizer():
             if isinstance(idx_state, dict):
                 idx_state.pop("param::ecc", None)
     # model-first: load model, then optimizer
-    m2, o2 = _model_opt(heavyball.PaLMForeachSFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
+    m2, o2 = _model_opt(heavyball.SFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
     m2.load_state_dict(sd_model)
     o2.load_state_dict(sd_opt)
     p2 = list(m2.parameters())[0]
@@ -594,7 +594,7 @@ def test_param_ecc_load_order_optimizer_before_model():
 
     set_torch()
     data, target = _problem()
-    m, o = _model_opt(heavyball.PaLMForeachSFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
+    m, o = _model_opt(heavyball.SFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
     _train(m, o, data, target, 10)
     sd_opt = deepcopy(o.state_dict())
     sd_model = deepcopy(m.state_dict())
@@ -603,7 +603,7 @@ def test_param_ecc_load_order_optimizer_before_model():
             if isinstance(idx_state, dict):
                 idx_state.pop("param::ecc", None)
     # optimizer-first: load optimizer, then model
-    m2, o2 = _model_opt(heavyball.PaLMForeachSFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
+    m2, o2 = _model_opt(heavyball.SFAdamW, 16, 8, 1e-2, param_ecc="bf16+8")
     o2.load_state_dict(sd_opt)
     m2.load_state_dict(sd_model)
     p2 = list(m2.parameters())[0]
diff --git a/test/test_foreach.py b/test/test_foreach.py
index de3fa2a..06dd9f4 100644
--- a/test/test_foreach.py
+++ b/test/test_foreach.py
@@ -57,12 +57,12 @@ def test_foreach(
     losses = [[], []]
 
     for i in range(total_runs):
-        for foreach in [True, False]:
-            lss, pk = losses[int(foreach)], peaks[int(foreach)]
+        for multi_tensor in [True, False]:
+            lss, pk = losses[int(multi_tensor)], peaks[int(multi_tensor)]
             torch.manual_seed(0x2131290)
 
             model = nn.Sequential(*[nn.Linear(size, size) for _ in range(depth)]).cuda()
-            o = get_optim(opt, model.parameters(), lr=1e-3, foreach=foreach)
+            o = get_optim(opt, model.parameters(), lr=1e-3, multi_tensor=multi_tensor)
 
             clean()
 
@@ -92,17 +92,17 @@ def test_foreach(
         cutoff = warmup_runs * iterations
         losses = [loss_list[cutoff:] for loss_list in losses]
 
-    for peak_no_foreach, peak_foreach in zip(*peaks):
-        assert peak_no_foreach < peak_foreach
+    for peak_single, peak_multi in zip(*peaks):
+        assert peak_single < peak_multi
 
-    # no-foreach LRA is a different optimizer (per-parameter LRA vs global LRA),
+    # single-tensor LRA is a different optimizer (per-parameter LRA vs global LRA),
     # so we only check that both converge, not that they match.
     if "LRA" in opt.__name__:
         return
 
-    for loss_no_foreach, loss_foreach in zip(*losses):
-        if torch.isnan(loss_no_foreach) and torch.isnan(loss_foreach):
+    for loss_single, loss_multi in zip(*losses):
+        if torch.isnan(loss_single) and torch.isnan(loss_multi):
             continue
 
         # increase error tolerance for PSGD, as we have different RNGs -> expected differences
-        assert torch.allclose(loss_no_foreach, loss_foreach, rtol=0.01 if "PSGD" in opt.__name__ else 1e-5)
+        assert torch.allclose(loss_single, loss_multi, rtol=0.01 if "PSGD" in opt.__name__ else 1e-5)
diff --git a/test/test_memory_leak.py b/test/test_memory_leak.py
index f7088dc..f6c6f50 100644
--- a/test/test_memory_leak.py
+++ b/test/test_memory_leak.py
@@ -34,7 +34,7 @@ def forward(self, x):
 
 
 def test_memory(
-    opt: str = "NewtonHybrid2PSGDKron",
+    opt: str = "PSGDKron",
     size: int = 64,
     depth: int = 2,
     mars: bool = False,
diff --git a/test/test_merge.py b/test/test_merge.py
index 90bafb2..d1a660f 100644
--- a/test/test_merge.py
+++ b/test/test_merge.py
@@ -18,7 +18,7 @@ def forward(self, inp):
         return self.weight.mean() * inp
 
 
-@pytest.mark.parametrize("opt", ["ForeachPSGDKron"])
+@pytest.mark.parametrize("opt", ["PSGDKron"])
 @pytest.mark.parametrize("size", [(16, 16, 16, 16), (4, 4, 4, 4), (512, 1, 128), (32128, 768)])
 @pytest.mark.parametrize("merge,split", [(False, False), (True, False), (True, True)])
 def test_merge(
diff --git a/test/test_migrate_cli.py b/test/test_migrate_cli.py
index 1554d09..7507289 100644
--- a/test/test_migrate_cli.py
+++ b/test/test_migrate_cli.py
@@ -130,7 +130,7 @@ def test_cli_migrates_legacy_checkpoint(runner, tmp_path):
                     "eps": 1e-8,
                     "weight_decay": 0.0,
                     "warmup_steps": 0,
-                    "foreach": True,
+                    "multi_tensor": True,
                     "storage_dtype": "float32",
                     "mars": False,
                     "caution": False,
@@ -139,7 +139,7 @@ def test_cli_migrates_legacy_checkpoint(runner, tmp_path):
                     "update_clipping": "use_default",
                     "palm": "use_default",
                     "beta2_scale": 0.8,
-                    "__class__": "heavyball.ForeachAdamW",
+                    "__class__": "heavyball.AdamW",
                 }
             ],
         }
@@ -148,7 +148,7 @@ def test_cli_migrates_legacy_checkpoint(runner, tmp_path):
 
         result = runner.invoke(
             migrate_script.app,
-            [str(checkpoint_path), "heavyball.ForeachAdamW", "--output", str(output_path)],
+            [str(checkpoint_path), "heavyball.AdamW", "--output", str(output_path)],
         )
 
         assert result.exit_code == 0, result.stderr or result.stdout
diff --git a/test/test_optimizer_cpu_smoke.py b/test/test_optimizer_cpu_smoke.py
index 9a9fa68..80b82c7 100644
--- a/test/test_optimizer_cpu_smoke.py
+++ b/test/test_optimizer_cpu_smoke.py
@@ -31,7 +31,7 @@ def _optimizer_params():
                 )
             )
             continue
-        if name == "ForeachSOAPNAdam":
+        if name == "SOAPNAdam":
             params.append(
                 pytest.param(
                     name,
diff --git a/test/test_param_ecc_compile.py b/test/test_param_ecc_compile.py
index 7182344..e6fc4ce 100644
--- a/test/test_param_ecc_compile.py
+++ b/test/test_param_ecc_compile.py
@@ -70,7 +70,7 @@ def _train_linear(compile_mode, rne=False, steps=50):
     try:
         with ctx:
             model = torch.nn.Linear(64, 32, bias=False, device="cuda")
-            opt = heavyball.ForeachAdamW(model.parameters(), lr=1e-2, param_ecc="bf16+8")
+            opt = heavyball.AdamW(model.parameters(), lr=1e-2, param_ecc="bf16+8")
             data = torch.randn(32, 64, device="cuda")
             target = torch.randn(32, 32, device="cuda")
             for _ in range(steps):
diff --git a/test/test_toy_training.py b/test/test_toy_training.py
index 08859c5..0e2e83a 100644
--- a/test/test_toy_training.py
+++ b/test/test_toy_training.py
@@ -23,7 +23,7 @@ def _flatten_tensors(tensors: Iterable[torch.Tensor]):
 
 
 EXTRA_KWARGS = {
-    "ForeachAdamC": {"max_lr": 0.0025},
+    "AdamC": {"max_lr": 0.0025},
 }
 
 
@@ -62,15 +62,15 @@ def toy_training_results(request):
 
     sig = inspect.signature(optimizer_cls.__init__)
     kwargs = dict(EXTRA_KWARGS.get(optimizer_name, {}))
-    if "foreach" in sig.parameters:
-        kwargs["foreach"] = True
+    if "multi_tensor" in sig.parameters:
+        kwargs["multi_tensor"] = True
 
     if optimizer_name == "SAMWrapper":
         inner_kwargs = {}
-        inner_sig = inspect.signature(heavyball.ForeachAdamW.__init__)
-        if "foreach" in inner_sig.parameters:
-            inner_kwargs["foreach"] = True
-        inner_optimizer = heavyball.ForeachAdamW(param_list, **inner_kwargs)
+        inner_sig = inspect.signature(heavyball.AdamW.__init__)
+        if "multi_tensor" in inner_sig.parameters:
+            inner_kwargs["multi_tensor"] = True
+        inner_optimizer = heavyball.AdamW(param_list, **inner_kwargs)
         optimizer = optimizer_cls(param_list, wrapped_optimizer=inner_optimizer, **kwargs)
     else:
         optimizer = optimizer_cls(param_list, **kwargs)
diff --git a/test/utils.py b/test/utils.py
index 800c2fc..906526a 100644
--- a/test/utils.py
+++ b/test/utils.py
@@ -13,17 +13,11 @@
 #   AdEMAMix variants require 3 betas, SplitOpt requires dict param specs,
 #   SAMWrapper and Newton variants require closures
 _SKIP_GET_OPTIM = {
-    "ForeachAdEMAMix",
-    "ForeachSOAPAdEMAMix",
+    "AdEMAMix",
+    "SOAPAdEMAMix",
     "SOAPAdEMAMix",
     "SplitOpt",
     "SAMWrapper",
-    "ForeachCachedNewtonPSGD",
-    "NewtonHybrid2PSGDKron",
-    "ForeachNewtonPSGDLRA",
-    "NewtonHybrid2PSGDLRA",
-    "NewtonPSGDLRA",
-    "NewtonPSGDKron",
 }
 
 
@@ -40,7 +34,7 @@ def _fn_key(f):
 def _deduplicate_by_chain(names):
     """Keep one optimizer per unique chain of functions.
 
-    Two optimizers that differ only by foreach=True/False have identical
+    Two optimizers that differ only by multi_tensor=True/False have identical
     chains and test the same code paths — keep whichever appears first.
     """
     seen = set()

From 4c9ac161d345f8403801b9922527db048350c40a Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Sat, 28 Mar 2026 18:34:58 +0000
Subject: [PATCH 04/24] higher psgd precision

---
 heavyball/utils.py | 30 +++++++++++-------------------
 1 file changed, 11 insertions(+), 19 deletions(-)

diff --git a/heavyball/utils.py b/heavyball/utils.py
index 0eab0be..1114b4b 100644
--- a/heavyball/utils.py
+++ b/heavyball/utils.py
@@ -2363,7 +2363,7 @@ def init_Q_exprs(
 
 @decorator_knowngood
 def psgd_balance_Q(Q):
-    norms = [promote(q.norm(float("inf"))).log() for q in Q]
+    norms = [promote(q.abs().max()).log() for q in Q]
     geometric_mean = sum([n for n in norms]) / len(Q)
     for q, n in zip(Q, norms):
         q *= (geometric_mean - n).exp()
@@ -2726,7 +2726,7 @@ def max_singular_value_cholesky(A: Tensor, max_abs: Optional[Tensor] = None):
     Adapted from @evanatyourservice
     """
     if max_abs is None:
-        max_abs = A.norm(float("inf")).clamp(min=1e-8)
+        max_abs = A.abs().max().clamp(min=1e-8)
 
     # cholesky uses random projection, but this uses topk -- topk is a warm start, which may converge to a biased result
     k = 2 ** math.ceil(math.log2(math.log2(min(A.shape))))  # next-largest-power-of-2 of log2-of-size
@@ -2794,15 +2794,16 @@ def _mv(x):
 
 @decorator_knowngood
 def procrustes_step(Q: Tensor, max_step_size: float = 1 / 8) -> None:
-    R = (Q.T - Q).contiguous()
+    Q_ = promote(Q)
+    R = (Q_.T - Q_).contiguous()
     R_norm = max_singular_value(R, power_iter=2) + torch.finfo(R.dtype).smallest_normal
     R = R / R_norm
-    RQ = R @ Q
+    RQ = R @ Q_
     RRQ = R @ RQ
     tr_RQ = RQ.diagonal().sum()
     tr_RRQ = RRQ.diagonal().sum()
     a = torch.where(tr_RRQ < 0, torch.clamp(-tr_RQ / tr_RRQ, max=max_step_size), max_step_size)
-    Q.add_(a * (RQ + 0.5 * a * RRQ))
+    copy_stochastic_(Q, Q_ + a * (RQ + 0.5 * a * RRQ))
 
 
 @decorator_knowngood
@@ -3031,7 +3032,7 @@ def psgd_pro_update_precond(
 
     total_numel = G.numel()
     for q, exprG, lb_state in zip(Q, exprGs, running_lower_bound):
-        term1 = promote(compiled_einsum(exprG, Pg, Pg))
+        term1 = compiled_einsum(exprG, Pg, Pg)
         q_ = promote(q)
 
         if q.ndim < 2:
@@ -3159,7 +3160,7 @@ def _psgd_precond_update_(
 
         q = promote(oq)
         if update.ndim < 2:
-            lb = update.norm(float("inf"))
+            lb = update.abs().max()
         else:
             lb = max_singular_value(update, power_iter=power_iter)
             update = promote(update)
@@ -3543,17 +3544,13 @@ def precond_grad_cached_(
     cached_q: List[Tensor],
     caution: bool = False,
     grad: Optional[Tensor] = None,
-    cast: bool = True,
 ):
     if caution:
         ea = _compilable_cautioning(grad, ea)
     args = [promote(q) for q in cached_q]
     args = args + [promote(ea)]
     expr = cached_precond_grad_expr(ndim_tuple(cached_q), ea.ndim)
-    new = compiled_einsum(expr, *args)
-    if cast:
-        return new.to(ea.dtype)
-    return new
+    return compiled_einsum(expr, *args)
 
 
 TriuOrLine = Union[List[Tensor], List[Tuple[Optional[List[int]], Tensor]]]
@@ -3561,7 +3558,7 @@ def precond_grad_cached_(
 
 @decorator_knowngood
 def _compilable_fused_precond_grad_cached_(ea: Tensor, param, lr, grad, decay, caution, cached_q: List[Tensor]):
-    precond = precond_grad_cached_(ea, cached_q, caution=caution, grad=grad, cast=False)
+    precond = precond_grad_cached_(ea, cached_q, caution=caution, grad=grad)
     update_param_(param, precond, lr, decay, caution=False)
 
 
@@ -3589,7 +3586,6 @@ def psgd_precond_grad(
     grad: Optional[Tensor] = None,
     store_triu_as_line: bool = False,
     symmetric_output: bool = False,
-    cast: bool = True,
 ):
     if caution:
         ea = _compilable_cautioning(grad, ea)
@@ -3597,10 +3593,7 @@ def psgd_precond_grad(
         preconds = line_to_triu(preconds, symmetric_output)
     args = [promote(q) for q in preconds]
     expr = precond_grad_expr(ndim_tuple(args), ea.ndim)
-    new = compiled_einsum(expr, *[a for a in args for _ in (0, 1)], promote(ea))
-    if cast:
-        return new.to(ea.dtype)
-    return new
+    return compiled_einsum(expr, *[a for a in args for _ in (0, 1)], promote(ea))
 
 
 @decorator_knowngood
@@ -3622,7 +3615,6 @@ def _compilable_fused_psgd_precond_grad(
         grad=grad,
         store_triu_as_line=store_triu_as_line,
         symmetric_output=symmetric_output,
-        cast=False,
     )
     update_param_(param, precond, lr, decay, caution=False, grad=grad)
 

From 8526f7b118ef16480ccea93b6c94ce9017b4f713 Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Sat, 28 Mar 2026 21:15:18 +0000
Subject: [PATCH 05/24] init compile step

---
 heavyball/chainable.py    | 27 +++++++++++--
 heavyball/utils.py        |  2 +
 test/test_compile_step.py | 83 +++++++++++++++++++++++++++++++++++++++
 3 files changed, 109 insertions(+), 3 deletions(-)
 create mode 100644 test/test_compile_step.py

diff --git a/heavyball/chainable.py b/heavyball/chainable.py
index 6dbf1f9..bdad159 100644
--- a/heavyball/chainable.py
+++ b/heavyball/chainable.py
@@ -1754,6 +1754,8 @@ def __init__(self, params, defaults, multi_tensor: bool, *fns):
         base.update({k: v for k, v in defaults.items() if v is not use_default})
         super().__init__(params, base, multi_tensor)
         self.fns = fns
+        if self.compile_step:
+            self._chain = torch.compile(self._chain, fullgraph=True)
         self.register_load_state_dict_post_hook(ChainOpt._restore_ecc_dtypes)
         self._init_param_ecc()
 
@@ -1890,17 +1892,36 @@ def _step_inner(self, group):
         group["step"] = state["step"] = step = step + 1
         group["prev_lr"] = group["lr"] = group["base_lr"] * step / max(step, group["warmup_steps"] + 1)
 
+        if isinstance(step, torch.Tensor):
+            _orig_floats = {}
+            for k, v in group.items():
+                if isinstance(v, float):
+                    _orig_floats[k] = v
+                    group[k] = torch.tensor(v, dtype=torch.float64, device=step.device)
+                elif isinstance(v, tuple) and any(isinstance(x, float) for x in v):
+                    _orig_floats[k] = v
+                    group[k] = tuple(
+                        torch.tensor(x, dtype=torch.float64, device=step.device) if isinstance(x, float) else x
+                        for x in v
+                    )
+
         if not group["multi_tensor"] or len(p) == 1:
             for param, grad in zip(p, g):
-                chain(self.state_, group, [grad], [param], *self.fns)
-                group["caution"] = caution
+                self._chain(group, [grad], [param], caution)
         else:
-            chain(self.state_, group, g, p, *self.fns)
+            self._chain(group, g, p, caution)
+
+        if isinstance(step, torch.Tensor):
+            group.update(_orig_floats)
 
         group["caution"] = caution
         group["lr"] = group["prev_lr"]
         group["step"] = None
 
+    def _chain(self, group, g, p, caution):
+        chain(self.state_, group, g, p, *self.fns)
+        group["caution"] = caution
+
 
 str_or_fn = Union[str, callable, None, Literal[use_default]]
 
diff --git a/heavyball/utils.py b/heavyball/utils.py
index 1114b4b..d0154b5 100644
--- a/heavyball/utils.py
+++ b/heavyball/utils.py
@@ -988,6 +988,8 @@ def scalar_guard(*args):
             out.append(torch.empty((), dtype=promote(ref.dtype), device=ref.device).fill_(x))
         elif isinstance(x, int):
             out.append(torch.empty((), dtype=torch.int64, device=ref.device).fill_(x))
+        elif isinstance(x, Tensor) and x.is_floating_point() and x.ndim == 0:
+            out.append(x.to(dtype=promote(ref.dtype)))
         else:
             out.append(x)
     if len(xs) == 1:
diff --git a/test/test_compile_step.py b/test/test_compile_step.py
new file mode 100644
index 0000000..14b8f80
--- /dev/null
+++ b/test/test_compile_step.py
@@ -0,0 +1,83 @@
+import inspect
+
+import pytest
+import torch
+
+import heavyball
+
+DEVICE = torch.device("cuda" if torch.cuda.is_available() else "cpu")
+
+EXTRA_KWARGS = {
+    "AdamC": {"max_lr": 0.01},
+}
+
+
+def _optimizer_params():
+    seen = set()
+    params = []
+    for name in heavyball.__all__:
+        if not hasattr(heavyball, name):
+            continue
+        obj = getattr(heavyball, name)
+        if not inspect.isclass(obj):
+            continue
+        if not issubclass(obj, torch.optim.Optimizer):
+            continue
+        ident = id(obj)
+        if ident in seen:
+            continue
+        seen.add(ident)
+        if name == "SplitOpt":
+            params.append(
+                pytest.param(name, obj, id=name, marks=pytest.mark.skip(reason="SplitOpt requires dict specs"))
+            )
+            continue
+        params.append(pytest.param(name, obj, id=name))
+    return params
+
+
+def _make_model():
+    return torch.nn.Sequential(
+        torch.nn.Linear(8, 16),
+        torch.nn.Tanh(),
+        torch.nn.Linear(16, 4),
+    ).to(DEVICE)
+
+
+def _run_steps(model, optimizer, n=5, seed=0xDEADBEEF):
+    torch.manual_seed(seed)
+    for _ in range(n):
+        def closure():
+            optimizer.zero_grad(set_to_none=True)
+            data = torch.randn(4, 8, device=DEVICE)
+            target = torch.randn(4, 4, device=DEVICE)
+            loss = torch.nn.functional.mse_loss(model(data), target)
+            loss.backward()
+            return loss
+
+        optimizer.step(closure)
+
+
+@pytest.mark.parametrize("opt_name,opt_cls", _optimizer_params())
+def test_compile_step_matches_eager(opt_name, opt_cls):
+    """compile_step=True must produce identical parameters to compile_step=False."""
+    sig = inspect.signature(opt_cls.__init__)
+    if "compile_step" not in sig.parameters:
+        pytest.skip("optimizer does not accept compile_step")
+
+    kwargs = dict(EXTRA_KWARGS.get(opt_name, {}))
+
+    torch.manual_seed(0xDEADBEEF)
+    model_ref = _make_model()
+    model_test = _make_model()
+    model_test.load_state_dict(model_ref.state_dict())
+
+    opt_ref = opt_cls(model_ref.parameters(), compile_step=False, **kwargs)
+    opt_test = opt_cls(model_test.parameters(), compile_step=True, **kwargs)
+
+    _run_steps(model_ref, opt_ref)
+    _run_steps(model_test, opt_test)
+
+    for p_ref, p_test in zip(model_ref.parameters(), model_test.parameters()):
+        diff = (p_ref.data - p_test.data).abs().max().item()
+        assert diff < 1e-5, f"compile_step diverged: max_diff={diff}"

From 89187c8a3ebc917250113b78cc5e4b0d7ec4ca5b Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Sun, 29 Mar 2026 17:54:59 +0000
Subject: [PATCH 06/24] compile step

---
 README.md                          |   4 +-
 examples/branched_optimizer.py     |   2 +-
 heavyball/__init__.py              |  32 +--
 heavyball/chainable.py             | 331 +++++++++++++----------------
 heavyball/utils.py                 | 101 ++-------
 scripts/migrate_optimizer_state.py |   2 +-
 test/test_chainable_cpu.py         |   2 +-
 test/test_compile_step.py          |   2 +-
 test/test_ecc.py                   |   4 +-
 test/test_migrate_cli.py           |   1 -
 test/test_stochastic_updates.py    |  58 -----
 test/test_stochastic_utils_cpu.py  |  16 +-
 test/test_utils_cpu.py             |  24 +--
 test/test_utils_property.py        |   3 +
 test/utils.py                      |   1 -
 15 files changed, 196 insertions(+), 387 deletions(-)
 delete mode 100644 test/test_stochastic_updates.py

diff --git a/README.md b/README.md
index 56b5359..e8bd664 100644
--- a/README.md
+++ b/README.md
@@ -153,7 +153,7 @@ opt = SOAP(model.parameters(), lr=3e-3, orig_shapes=shapes)
 ## Building Custom Optimizers
 
 Every built-in optimizer is a chain of `FunctionTransform`s, an API also available for building custom optimizers.
-`Branch` runs parallel transform paths with a merge function, which is useful for grafted optimizers or ensemble
+`Parallel` runs parallel transform paths with a merge function, which is useful for grafted optimizers or ensemble
 updates.
 
 ```python
@@ -168,7 +168,7 @@ class GraftedAdam(C.BaseOpt):
                  weight_decay=0, warmup_steps=0, multi_tensor=True):
         defaults = dict(lr=lr, betas=betas, eps=eps, weight_decay=weight_decay,
                         warmup_steps=warmup_steps)
-        branch = C.Branch(branches=[[C.scale_by_adam], [C.identity]], merge_fn=graft)
+        branch = C.Parallel(branches=[[C.scale_by_adam], [C.identity]], merge_fn=graft)
         super().__init__(params, defaults, multi_tensor, fns=(branch,))
 ```
 
diff --git a/examples/branched_optimizer.py b/examples/branched_optimizer.py
index 001f107..73aa271 100644
--- a/examples/branched_optimizer.py
+++ b/examples/branched_optimizer.py
@@ -38,7 +38,7 @@ def __init__(
             weight_decay=weight_decay,
             warmup_steps=warmup_steps,
         )
-        branch = C.Branch(branches=[[C.scale_by_adam], [C.identity]], merge_fn=_graft)
+        branch = C.Parallel(branches=[[C.scale_by_adam], [C.identity]], merge_fn=_graft)
         super().__init__(params, defaults, multi_tensor, fns=(branch,))
 
 
diff --git a/heavyball/__init__.py b/heavyball/__init__.py
index 476aac0..d760970 100644
--- a/heavyball/__init__.py
+++ b/heavyball/__init__.py
@@ -624,8 +624,6 @@ def __init__(
         max_precond_dim: int = 2048,  #
         merge_dims: bool = True,
         precondition_1d: bool = False,
-        normalize_grads: bool = False,
-        correct_bias: bool = True,
         warmup_steps: int = 0,
         split: bool = False,
         multi_tensor: bool = True,
@@ -639,7 +637,6 @@ def __init__(
         gradient_clipping: C.str_or_fn = C.use_default,
         update_clipping: C.str_or_fn = C.use_default,
         storage_dtype: str = "float32",
-        stochastic_schedule: bool = False,
         precond_grad_accum: bool = False,
         compile_step: bool = C.use_default,
         promote: bool = C.use_default,
@@ -683,8 +680,6 @@ def __init__(
         max_precond_dim: int = 2048,
         merge_dims: bool = True,
         precondition_1d: bool = False,
-        normalize_grads: bool = False,
-        correct_bias: bool = True,
         warmup_steps: int = 0,
         split: bool = False,
         multi_tensor: bool = True,
@@ -698,7 +693,6 @@ def __init__(
         gradient_clipping: C.str_or_fn = C.use_default,
         update_clipping: C.str_or_fn = C.use_default,
         storage_dtype: str = "float32",
-        stochastic_schedule: bool = False,
         precond_grad_accum: bool = False,
         momentum_decay: float = 4e-3,
         decoupled_weight_decay: bool = False,
@@ -744,8 +738,6 @@ def __init__(
         max_precond_dim: int = 2048,
         merge_dims: bool = True,
         precondition_1d: bool = False,
-        normalize_grads: bool = False,
-        correct_bias: bool = True,
         warmup_steps: int = 0,
         split: bool = False,
         multi_tensor: bool = True,
@@ -759,7 +751,6 @@ def __init__(
         gradient_clipping: C.str_or_fn = C.use_default,
         update_clipping: C.str_or_fn = C.use_default,
         storage_dtype: str = "float32",
-        stochastic_schedule: bool = False,
         precond_grad_accum: bool = False,
         alpha: float = 2.0,
         beta3_warmup: int | None = None,
@@ -853,8 +844,6 @@ def __init__(
         max_precond_dim: int = 2048,  #
         merge_dims: bool = True,
         precondition_1d: bool = False,
-        normalize_grads: bool = False,
-        correct_bias: bool = True,
         warmup_steps: int = 0,
         split: bool = False,
         multi_tensor: bool = True,
@@ -868,7 +857,6 @@ def __init__(
         gradient_clipping: C.str_or_fn = C.use_default,
         update_clipping: C.str_or_fn = C.use_default,
         storage_dtype: str = "float32",
-        stochastic_schedule: bool = False,
         compile_step: bool = C.use_default,
         promote: bool = C.use_default,
         ecc: str | None = None,
@@ -978,7 +966,6 @@ class PSGDKron(C.BaseOpt):
     delayed: bool = False
     cached: bool = False
     exp_avg_input: bool = True
-    quad: bool = False
 
     def __init__(
         self,
@@ -998,7 +985,6 @@ def __init__(
         store_triu_as_line: bool = True,
         multi_tensor: bool = True,
         q_dtype="float32",
-        stochastic_schedule: bool = False,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -1008,11 +994,9 @@ def __init__(
         exp_avg_input: Optional[bool] = C.use_default,
         gradient_clipping: C.str_or_fn = C.use_default,
         update_clipping: C.str_or_fn = C.use_default,  #
-        adaptive: bool = False,
-        ortho_method: Optional[str] = None,  # If None, no orthogonalization
+        ortho_method: Optional[str] = None,
         precond_grad_accum: bool = False,
-        lower_bound_beta: float = 0.9,  # 0.0 recovers pre-2.0.0 PSGD
-        inverse_free: bool = C.use_default,
+        lower_bound_beta: float = 0.9,
         dampening: float = 1e-9,
         precond_update_power_iterations: int = 2,
         # expert parameters
@@ -1034,11 +1018,6 @@ def __init__(
         cached = C.default(cached, self.cached)
         exp_avg_input = C.default(exp_avg_input, self.exp_avg_input)
         update_clipping = C.default(update_clipping, utils.trust_region_clip_)
-        inverse_free = C.default(inverse_free, self.quad)
-        if inverse_free:
-            raise ValueError(
-                "inverse_free (i.e., PSGD-QUAD) is not supported at the moment. Consider using https://github.com/evanatyourservice/quad_torch"
-            )
 
         params, defaults = C._build_defaults(locals())
 
@@ -1087,7 +1066,6 @@ def __init__(
         split: bool = False,
         multi_tensor: bool = True,
         q_dtype="float32",
-        stochastic_schedule: bool = False,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -1116,7 +1094,6 @@ def __init__(
 
         params, defaults = C._build_defaults(locals())
         defaults["store_triu_as_line"] = False
-        defaults["inverse_free"] = False
 
         self.precond_schedule = C.default(
             defaults.pop("preconditioner_update_probability"), utils.precond_update_prob_schedule()
@@ -1162,7 +1139,6 @@ def __init__(
         warmup_steps: int = 0,
         multi_tensor: bool = True,  # True: global LRA across all params. False: independent per-param LRA.
         q_dtype="float32",
-        stochastic_schedule: bool = False,
         storage_dtype: str = "float32",
         mars: bool = False,
         caution: bool = False,
@@ -1171,8 +1147,8 @@ def __init__(
         exp_avg_input: Optional[bool] = C.use_default,
         gradient_clipping: C.str_or_fn = C.use_default,
         update_clipping: C.str_or_fn = C.use_default,
-        eps: float = 1e-8,  #
-        precond_grad_accum: bool = False,  # expert parameters
+        eps: float = 1e-8,
+        precond_grad_accum: bool = False,
         precond_init_scale=None,
         precond_init_scale_scale: float = 1,
         precond_init_scale_power: Optional[float] = None,
diff --git a/heavyball/chainable.py b/heavyball/chainable.py
index bdad159..d9cd125 100644
--- a/heavyball/chainable.py
+++ b/heavyball/chainable.py
@@ -2,7 +2,6 @@
 import copy
 import functools
 import math
-import random
 from collections.abc import Iterable as _Iterable
 from typing import Iterable, List, Literal, Optional, Union
 
@@ -25,12 +24,6 @@ def _key_in_state(state, key):
     return True
 
 
-def _inplace_guard_(state, key, template_fn):
-    key_not_in_state = not _key_in_state(state, key)
-    if key_not_in_state:
-        template_fn()
-    return key_not_in_state
-
 
 def _guard_in_state(state, key, template_fn):
     if not _key_in_state(state, key):
@@ -45,7 +38,6 @@ def __init__(self, fn, names: list[str] | None = None):
         self.fn = fn
         self.fn_name = self.get_fn().__name__
         self.transform_idx = None
-        self.is_initialized = False
         self.names = names
 
     def _init(self, state: dict, group: dict, update: Tensor, grad: Tensor, param: Tensor, *args, **kwargs):
@@ -55,7 +47,7 @@ def _call(self, state, group, update, grad, param, vars, *args, **kwargs):
         raise NotImplementedError
 
     def __call__(self, state, group, update, grad, param, *args, **kwargs):
-        states = [state(p) for p in param]
+        states = state if isinstance(state, list) else [state(p) for p in param]
         skip_update = False
         for st, a in zip(states, zip(update, grad, param, *args)):
             if self.transform_idx not in st.get("is_initialized", set()):
@@ -77,9 +69,11 @@ def get_fn(self):
             return self.fn.get_fn()
         return self.fn
 
+    def _build_val_names(self):
+        self._val_names = {name: f"{self.fn_name}_{name}_{self.transform_idx}" for name in self.names}
+
     def val_name(self, name):
-        assert self.transform_idx is not None
-        return f"{self.fn_name}_{name}_{self.transform_idx}"
+        return self._val_names[name]
 
     def __repr__(self):
         return f"{self.__class__.__name__}({self.fn}, transform_idx={self.transform_idx})"
@@ -155,7 +149,7 @@ def _sel(lst, idx):
                 continue
             group["caution"] = caution
             if fns is not None:
-                u, skip = _inner_chain(state, group, _sel(update, idx), _sel(grad, idx), _sel(param, idx), *fns)
+                u, skip = _inner_chain(_sel(state, idx), group, _sel(update, idx), _sel(grad, idx), _sel(param, idx), *fns)
             else:
                 u, skip = _sel(update, idx), False
             results.append((u, skip, idx))
@@ -271,12 +265,11 @@ def _call(self, state, group, update, grad, param, vars, *args, **kwargs):
         if ecc is None:
             return self.fn(state, group, update, grad, param, *args, *vars, **kwargs)
 
-        states = [state(p) for p in param]
         names = [self.val_name(n) for n in self.names]
-        primary_vars = [[st[vn] for st in states] for vn in names]
+        primary_vars = [[st[vn] for st in state] for vn in names]
         with contextlib.ExitStack() as stack:
             for vn, plist in zip(names, primary_vars):
-                corrs = [st[vn + "::ecc"] for st in states]
+                corrs = [st[vn + "::ecc"] for st in state]
                 stack.enter_context(ecc.attached(plist, corrs))
             return self.fn(state, group, update, grad, param, *args, *primary_vars, **kwargs)
 
@@ -346,17 +339,6 @@ def __init__(self, fn, names, init_fn, skip_first: bool = True):
         super().__init__(fn, names)
         self.init_fn = init_fn
         self.skip_first = skip_first
-        self.named_to_anonymous = None
-        self.anonymous_to_named = None
-
-    def _map(self, state_fn, param, mapping):
-        for p in param:
-            state = state_fn(p)
-            for name, mapped in mapping.items():
-                if mapped in state:
-                    raise ValueError(f"Name {name} already mapped to {mapped}")
-                if name in state:
-                    state[mapped] = state.pop(name)
 
     def _init(self, state: dict, group: dict, update: Tensor, grad: Tensor, param: Tensor, *args, **kwargs):
         self.init_fn(state, group, update, grad, param, **kwargs)
@@ -370,12 +352,19 @@ def _call(self, state, group, update, grad, param, vars, *args, **kwargs):
 
 
 class NoState(FunctionTransform):
+    needs_init = False
+
     def __call__(self, state, group, update, grad, param, *args, **kwargs):
         return self.fn(group, update, grad, param, *args, **kwargs)
 
 
 class NoStateNoMultiTensor(FunctionTransform):
     def __call__(self, state, group, update, grad, param, *args, **kwargs):
+        states = state if isinstance(state, list) else [state(p) for p in param]
+        for st in states:
+            if "is_initialized" not in st:
+                st["is_initialized"] = set()
+            st["is_initialized"].add(self.transform_idx)
         updates = []
         skip_update = False
         for a in zip(update, grad, param, *args):
@@ -398,6 +387,8 @@ def _view_preserve_ecc(src, target):
 
 
 class SqueezeGrad(FunctionTransform):
+    needs_init = False
+
     def __call__(self, state, group, update, grad, param, *args, **kwargs):
         original_shapes = [u.shape for u in update]
         update = [u.squeeze() if u.numel() > 1 else u.view(-1) for u in update]
@@ -427,6 +418,32 @@ def _call(self, state, group, update, grad, param, vars, *args, **kwargs):
         return self.fn(state, group, update, grad, param, *args, **kwargs)
 
 
+class WarmupGuard(FunctionTransform):
+    def __init__(self, fn, warmup_fns):
+        super().__init__(fn, names=[])
+        self.warmup_fns = warmup_fns
+        self.warmup_key = None
+
+    def _build_val_names(self):
+        super()._build_val_names()
+        self.warmup_key = f"_warmup_{self.transform_idx}"
+
+    def __call__(self, state, group, update, grad, param, *args, **kwargs):
+        states = state if isinstance(state, list) else [state(p) for p in param]
+        warmup_step = min(st.get(self.warmup_key, 0) for st in states)
+        if warmup_step < len(self.warmup_fns):
+            fn = self.warmup_fns[warmup_step]
+            for st, a in zip(states, zip(update, grad, param, *args)):
+                fn(st, group, *a, **kwargs)
+                st[self.warmup_key] = st.get(self.warmup_key, 0) + 1
+            raise SkipUpdate from None
+        for st in states:
+            if "is_initialized" not in st:
+                st["is_initialized"] = set()
+            st["is_initialized"].add(self.transform_idx)
+        return self.fn(state, group, update, grad, param, *args, **kwargs)
+
+
 needs_full_param = functools.partial(TagGuard, needs_full_param=True)
 
 
@@ -442,6 +459,10 @@ def general_guard(*names, init_fn, skip_first: bool = True):
     return functools.partial(GeneralGuard, names=names, init_fn=init_fn, skip_first=skip_first)
 
 
+def warmup_guard(*warmup_fns):
+    return functools.partial(WarmupGuard, warmup_fns=list(warmup_fns))
+
+
 def no_state(fn):
     return NoState(fn)
 
@@ -700,7 +721,7 @@ def orthogonalize_grad_to_param(group, update, grad, param):
 @no_state
 def update_by_schedule_free(group, update, grad, param, z):
     # Compute weight_sum once per step, not per param in no-multi_tensor mode.
-    if group.get("_sf_step") != group["step"]:
+    if group.get("_sf_step") is not group["step"]:
         weight = abs(group["lr"]) ** group["weight_lr_power"] * max(group["step"], 1) ** group["r"]
         group["weight_sum"] = group.get("weight_sum", 0) + weight
         group["_sf_step"] = group["step"]
@@ -738,28 +759,21 @@ def update_by_msam(group, update, grad, param, z, exp_avg):
     raise SkipUpdate from None
 
 
+def _adopt_warmup_1(state, group, update, grad, param, exp_avg, exp_avg_sq):
+    utils.scale_by_exp_avg_sq_([exp_avg_sq], [update], 0, group["eps"])
+
+
+def _adopt_warmup_2(state, group, update, grad, param, exp_avg, exp_avg_sq):
+    u = utils.promote(update)
+    easq = utils.promote(exp_avg_sq)
+    utils.copy_stochastic_(exp_avg, u / easq.sqrt().clamp_(min=group["eps"]))
+    utils.scale_by_exp_avg_sq_([exp_avg_sq], [update], utils.beta_debias(utils.get_beta2(group), group["step"]), group["eps"])
+
+
 @zero_guard("exp_avg", "exp_avg_sq")
+@warmup_guard(_adopt_warmup_1, _adopt_warmup_2)
 @no_state
 def update_by_adopt(group, update, grad, param, exp_avg, exp_avg_sq):
-    if group["step"] == 1:
-        utils.scale_by_exp_avg_sq_(exp_avg_sq, update, 0, group["eps"])
-        raise SkipUpdate from None
-
-    if group["step"] == 2:
-        update = utils.promote(update)
-        easq = utils.promote(exp_avg_sq)
-        [
-            utils.copy_stochastic_(ea, u / easq_.sqrt().clamp_(min=group["eps"]))
-            for ea, u, easq_ in zip(exp_avg, update, easq)
-        ]
-        utils.scale_by_exp_avg_sq_(
-            exp_avg_sq,
-            update,
-            utils.beta_debias(utils.get_beta2(group), group["step"]),
-            group["eps"],
-        )
-        raise SkipUpdate from None
-
     utils.fused_adopt_(
         param,
         update,
@@ -777,14 +791,15 @@ def update_by_adopt(group, update, grad, param, exp_avg, exp_avg_sq):
     raise SkipUpdate from None
 
 
+def _suds_warmup_1(state, group, update, grad, param, exp_avg, exp_avg_sq, fisher_approx):
+    utils.copy_stochastic_(fisher_approx, update / update.norm().clamp(min=1e-8))
+
+
 @needs_full_param
 @zero_guard("exp_avg", "exp_avg_sq", "fisher_approx")
+@warmup_guard(_suds_warmup_1)
 @no_state_no_multi_tensor
 def scale_by_suds(group, update, grad, param, exp_avg, exp_avg_sq, fisher_approx):
-    if group["step"] == 1:
-        utils.copy_stochastic_(fisher_approx, update / update.norm().clamp(min=1e-8))
-        raise SkipUpdate from None
-
     precond_update, w = utils.eigvecs_product_rank1(update.flatten(), fisher_approx.flatten().to(update.dtype))
     precond_update = utils.adam_(
         exp_avg,
@@ -817,27 +832,9 @@ def scale_by_unscaled_adam(group, update, grad, param, exp_avg, exp_avg_sq):
 
 
 @zero_guard("exp_avg", "exp_avg_sq")
+@warmup_guard(_adopt_warmup_1, _adopt_warmup_2)
 @no_state
 def scale_by_adopt(group, update, grad, param, exp_avg, exp_avg_sq):
-    if group["step"] == 1:
-        utils.scale_by_exp_avg_sq_(exp_avg_sq, update, 0, group["eps"])
-        raise SkipUpdate from None
-
-    if group["step"] == 2:
-        update = utils.promote(update)
-        easq = utils.promote(exp_avg_sq)
-        [
-            utils.copy_stochastic_(ea, u / easq_.sqrt().clamp_(min=group["eps"]))
-            for ea, u, easq_ in zip(exp_avg, update, easq)
-        ]
-        utils.scale_by_exp_avg_sq_(
-            exp_avg_sq,
-            update,
-            utils.beta_debias(utils.get_beta2(group), group["step"]),
-            group["eps"],
-        )
-        raise SkipUpdate from None
-
     return utils.adopt(
         update,
         exp_avg_sq,
@@ -863,9 +860,7 @@ def _init_psgd_kron(state, group, update, grad, param, cached: bool = False, pro
     )
     state["Q"] = utils.triu_to_line(Q) if group["store_triu_as_line"] else Q
     state["running_lower_bound"] = [torch.zeros((1,), device=q.device, dtype=torch.float64) for q in Q]
-    state["step"] = torch.zeros((), device=param.device, dtype=torch.float64)  # torch casts int to float in ckpt load
-    if group["adaptive"]:
-        state["velocity"] = [torch.zeros((), device=q.device, dtype=q.dtype) for q in Q]
+    state["step"] = torch.zeros((), device=param.device, dtype=torch.float64)
     if not cached:
         return
 
@@ -907,21 +902,6 @@ def _init_psgd_lra(state, group, update, grad, param, cached: bool = False, prob
     )
 
 
-def precond_schedule(group, prob: Union[callable, float, None] = None, name: str = "cumulative_prob"):
-    step = group["step"]
-    if "precondition_frequency" in group:
-        return step > 0 and step % group["precondition_frequency"] == 0
-    if isinstance(step, torch.Tensor):
-        utils.warn_once("Preconditioner schedule is not supported with torch.Tensor step.")
-        rng = random.Random(0x172381)
-    else:
-        rng = random.Random(0x172381 ^ step)
-    if "precond_scheduler" in group:
-        return utils.precond_schedule(step, group["precond_scheduler"], rng)
-    if prob is not None:
-        return utils.psgd_should_update(group, prob, rng, name=name)
-    raise ValueError("No preconditioner update schedule specified.")
-
 
 @needs_full_param
 @no_state_no_multi_tensor
@@ -948,7 +928,7 @@ def nesterov_ema(group, updates, grads, params, momentum):  # equivalent to Grok
 
 
 def _store_init_norm(state, group, update, grad, param):
-    state["init_norm"] = param.float().norm()
+    state["init_norm"] = param.to(_storage_dtype(group)).norm()
 
 
 @needs_full_param
@@ -960,7 +940,7 @@ def update_by_hyperball(group, update, grad, param, init_norm):
 
 
 def _store_std(state, group, update, grad, param):
-    state["init_std"] = torch.std(param)
+    state["init_std"] = torch.std(param.to(_storage_dtype(group)))
 
 
 @needs_full_param
@@ -1145,7 +1125,6 @@ def _update_psgd_precond(
     param,
     grad,
     Q,
-    velocity,
     running_lower_bound,
     step,
     prob: Optional[callable] = None,
@@ -1160,8 +1139,6 @@ def _update_psgd_precond(
         vector, hessian_vector = param.vector, param.hessian_vector
         del param.vector
         del param.hessian_vector
-    elif group["inverse_free"]:
-        vector, hessian_vector = None, grad
     else:
         vector, hessian_vector = utils.dampen_grad(grad, group["dampening"])
 
@@ -1170,7 +1147,6 @@ def _update_psgd_precond(
         group["precond_lr"],
         Q,
         group["store_triu_as_line"],
-        velocity,
         utils.get_beta2(group),
         group["ortho_method"],
         vector,
@@ -1189,9 +1165,9 @@ def _update_psgd_precond(
     if precond is not None:
         return precond
     if not should_use_cache or not cached:
-        return None  # caching adds extra ops and is not worth the overhead when we precondition at every step
+        return None
 
-    Q_resolved = utils.line_to_triu(Q, group["inverse_free"]) if group["store_triu_as_line"] else Q
+    Q_resolved = utils.line_to_triu(Q) if group["store_triu_as_line"] else Q
     for i, (c_, q_) in enumerate(zip(Q_cache, Q_resolved)):
         if c_ is None:
             c_ = (
@@ -1263,7 +1239,7 @@ def _cached_psgd_precond_grad(group, update, Q, Q_cache, grad):
         out = utils.precond_grad_cached_(cached_q=Q_cache, **kwargs)
     else:
         out = utils.psgd_precond_grad(
-            preconds=Q, store_triu_as_line=group["store_triu_as_line"], symmetric_output=group["inverse_free"], **kwargs
+            preconds=Q, store_triu_as_line=group["store_triu_as_line"], **kwargs
         )
     group["caution"] = False  # we already cautioned here - shouldn't do it again
     return out
@@ -1282,7 +1258,7 @@ def _fused_cached_psgd_precond_grad(group, grad, param, update, Q, Q_cache):
         utils.fused_precond_grad_cached_(cached_q=Q_cache, **kwargs)
     else:
         utils.fused_psgd_precond_grad(
-            preconds=Q, store_triu_as_line=group["store_triu_as_line"], symmetric_output=group["inverse_free"], **kwargs
+            preconds=Q, store_triu_as_line=group["store_triu_as_line"], **kwargs
         )
 
 
@@ -1351,7 +1327,7 @@ def update_by_delayed_psgd_lra(group, update, grad, param, update_to_precond, U,
 @needs_full_param
 @SqueezeGrad
 @PrecondGradAccumGuard
-@general_guard("Q", "Q_cache", "velocity", "running_lower_bound", "step", init_fn=_init_psgd_kron, skip_first=False)
+@general_guard("Q", "Q_cache", "running_lower_bound", "step", init_fn=_init_psgd_kron, skip_first=False)
 @no_state_no_multi_tensor
 def scale_by_psgd(
     group,
@@ -1361,20 +1337,19 @@ def scale_by_psgd(
     update_to_precond,
     Q,
     Q_cache,
-    velocity: Optional[List[Tensor]],
     running_lower_bound: List[Tensor],
     step: Tensor,
     cached: bool = False,
     prob: Optional[callable] = None,
 ):
-    _update_psgd_precond(cached, Q_cache, group, param, update_to_precond, Q, velocity, running_lower_bound, step, prob)
+    _update_psgd_precond(cached, Q_cache, group, param, update_to_precond, Q, running_lower_bound, step, prob)
     return _cached_psgd_precond_grad(group, update, Q, Q_cache, grad)
 
 
 @needs_full_param
 @SqueezeGrad
 @PrecondGradAccumGuard
-@general_guard("Q", "Q_cache", "velocity", "running_lower_bound", "step", init_fn=_init_psgd_kron, skip_first=False)
+@general_guard("Q", "Q_cache", "running_lower_bound", "step", init_fn=_init_psgd_kron, skip_first=False)
 @no_state_no_multi_tensor
 def scale_by_delayed_psgd(
     group,
@@ -1384,26 +1359,22 @@ def scale_by_delayed_psgd(
     update_to_precond,
     Q,
     Q_cache,
-    velocity: Optional[List[Tensor]],
     running_lower_bound: List[Tensor],
     step: Tensor,
     cached: bool = False,
     prob: Optional[callable] = None,
 ):
-    if group.get("inverse_free", False):
-        precond = None
-    else:
-        precond = _cached_psgd_precond_grad(group, update, Q, Q_cache, grad)
-    new = _update_psgd_precond(
-        cached, Q_cache, group, param, update_to_precond, Q, velocity, running_lower_bound, step, prob
+    precond = _cached_psgd_precond_grad(group, update, Q, Q_cache, grad)
+    _update_psgd_precond(
+        cached, Q_cache, group, param, update_to_precond, Q, running_lower_bound, step, prob
     )
-    return new if precond is None else precond
+    return precond
 
 
 @needs_full_param
 @SqueezeGrad
 @PrecondGradAccumGuard
-@general_guard("Q", "Q_cache", "velocity", "running_lower_bound", "step", init_fn=_init_psgd_kron, skip_first=False)
+@general_guard("Q", "Q_cache", "running_lower_bound", "step", init_fn=_init_psgd_kron, skip_first=False)
 @no_state_no_multi_tensor
 def update_by_psgd(
     group,
@@ -1413,13 +1384,12 @@ def update_by_psgd(
     update_to_precond,
     Q,
     Q_cache,
-    velocity: Optional[List[Tensor]],
     running_lower_bound: List[Tensor],
     step: Tensor,
     cached: bool = False,
     prob: Optional[callable] = None,
 ):
-    _update_psgd_precond(cached, Q_cache, group, param, update_to_precond, Q, velocity, running_lower_bound, step, prob)
+    _update_psgd_precond(cached, Q_cache, group, param, update_to_precond, Q, running_lower_bound, step, prob)
     _fused_cached_psgd_precond_grad(group, update, param, update, Q, Q_cache)
     raise SkipUpdate from None
 
@@ -1439,7 +1409,7 @@ def global_clip(group, update, grad, param, clip_fn: Optional[callable] = None):
 @needs_full_param
 @SqueezeGrad
 @PrecondGradAccumGuard
-@general_guard("Q", "Q_cache", "velocity", "running_lower_bound", "step", init_fn=_init_psgd_kron, skip_first=False)
+@general_guard("Q", "Q_cache", "running_lower_bound", "step", init_fn=_init_psgd_kron, skip_first=False)
 @no_state_no_multi_tensor
 def update_by_delayed_psgd(
     group,
@@ -1449,14 +1419,13 @@ def update_by_delayed_psgd(
     update_to_precond,
     Q,
     Q_cache,
-    velocity: Optional[List[Tensor]],
     running_lower_bound: List[Tensor],
     step: Tensor,
     cached: bool = False,
     prob: Optional[callable] = None,
 ):
     _fused_cached_psgd_precond_grad(group, update, param, update, Q, Q_cache)
-    _update_psgd_precond(cached, Q_cache, group, param, update_to_precond, Q, velocity, running_lower_bound, step, prob)
+    _update_psgd_precond(cached, Q_cache, group, param, update_to_precond, Q, running_lower_bound, step, prob)
     raise SkipUpdate from None
 
 
@@ -1680,7 +1649,7 @@ def _inner_chain(state, group, update, grad, param, *fns):
     return update, skip_update
 
 
-def chain(state: Union[callable, dict], group, grad, param, *fns):
+def chain(state: list, group, grad, param, *fns):
     update = [torch.clone(g, memory_format=torch.preserve_format) for g in grad]
 
     ecc = ECCConfig.from_group(group, key="param_ecc")
@@ -1691,8 +1660,7 @@ def chain(state: Union[callable, dict], group, grad, param, *fns):
         utils.update_param_(param, update, group["lr"], group["weight_decay"], caution=group["caution"], grad=grad)
         return
 
-    states = [state(p) for p in param]
-    corrs = [st["param::ecc"] for st in states]
+    corrs = [st["param::ecc"] for st in state]
     with ecc.attached(param, corrs):
         update, skip_update = _inner_chain(state, group, update, grad, param, *fns)
         if not skip_update and update is not None:
@@ -1731,6 +1699,7 @@ def set_indices(fns: Iterable[callable], retain: bool = True, offset: int = 0):
     for ft in _walk_fns(new_fns):
         if not retain or ft.transform_idx is None:
             ft.transform_idx, offset = offset, offset + 1
+        ft._build_val_names()
 
     return new_fns
 
@@ -1754,8 +1723,9 @@ def __init__(self, params, defaults, multi_tensor: bool, *fns):
         base.update({k: v for k, v in defaults.items() if v is not use_default})
         super().__init__(params, base, multi_tensor)
         self.fns = fns
+        self._eager_chain = self._run_chain
         if self.compile_step:
-            self._chain = torch.compile(self._chain, fullgraph=True)
+            self._run_chain = torch.compile(self._run_chain, fullgraph=True)
         self.register_load_state_dict_post_hook(ChainOpt._restore_ecc_dtypes)
         self._init_param_ecc()
 
@@ -1846,10 +1816,20 @@ def fns(self, value):
         self._fns = value
         self._set_indices(retain=True)
         self._needs_gather = any(getattr(ft, "needs_full_param", False) for ft in _walk_fns(self._fns))
+        self._transform_ids = frozenset(
+            ft.transform_idx for ft in _walk_fns(self._fns)
+            if ft.transform_idx is not None and getattr(ft, "needs_init", True)
+        )
 
     def _set_indices(self, retain=True):
         self._fns = set_indices(self.fns, retain)
 
+    def _find_val_name(self, name):
+        for ft in _walk_fns(self._fns):
+            if name in ft._val_names:
+                return ft._val_names[name]
+        raise KeyError(f"No transform stores '{name}'")
+
     def _step(self, group):
         if "base_lr" not in group:
             group["base_lr"] = group["lr"]
@@ -1881,65 +1861,51 @@ def _step_inner(self, group):
 
         for param in p:
             state = self.state_(param)
-            if "step" in state:
-                step = state["step"]
-            elif self.compile_step:
-                step = utils.scalar_guard(0, param)
-            else:
-                step = 0
+            step = state.get("step", 0)
+            if not isinstance(step, torch.Tensor):
+                step = torch.tensor(step, dtype=torch.int64, device=param.device)
+                state["step"] = step
             break
 
         group["step"] = state["step"] = step = step + 1
         group["prev_lr"] = group["lr"] = group["base_lr"] * step / max(step, group["warmup_steps"] + 1)
 
-        if isinstance(step, torch.Tensor):
-            _orig_floats = {}
-            for k, v in group.items():
-                if isinstance(v, float):
-                    _orig_floats[k] = v
-                    group[k] = torch.tensor(v, dtype=torch.float64, device=step.device)
-                elif isinstance(v, tuple) and any(isinstance(x, float) for x in v):
-                    _orig_floats[k] = v
-                    group[k] = tuple(
-                        torch.tensor(x, dtype=torch.float64, device=step.device) if isinstance(x, float) else x
-                        for x in v
-                    )
-
         if not group["multi_tensor"] or len(p) == 1:
             for param, grad in zip(p, g):
                 self._chain(group, [grad], [param], caution)
         else:
             self._chain(group, g, p, caution)
 
-        if isinstance(step, torch.Tensor):
-            group.update(_orig_floats)
-
         group["caution"] = caution
         group["lr"] = group["prev_lr"]
         group["step"] = None
 
-    def _chain(self, group, g, p, caution):
-        chain(self.state_, group, g, p, *self.fns)
+    def _run_chain(self, state, group, g, p, caution):
+        chain(state, group, g, p, *self.fns)
         group["caution"] = caution
 
+    def _needs_init(self, state):
+        ids = self._transform_ids
+        return ids and any(not ids.issubset(st.get("is_initialized", set())) for st in state)
+
+    def _needs_eager(self, group, state):
+        if self._needs_init(state):
+            return True
+        if group.get("is_preconditioning", False):
+            return True
+        if group.get("ecc") or group.get("param_ecc"):
+            return True
+        return False
 
-str_or_fn = Union[str, callable, None, Literal[use_default]]
+    def _chain(self, group, g, p, caution):
+        state = [self.state_(pi) for pi in p]
+        fn = self._run_chain
+        if self.compile_step and self._needs_eager(group, state):
+            fn = self._eager_chain
+        fn(state, group, g, p, caution)
 
 
-def _get_clip_fn(name: str_or_fn, default_val: str_or_fn):
-    name = default(name, default_val)
-    if callable(name):
-        return name
-    elif name not in (
-        "l2_clip_",
-        "rmsnorm_clip_",
-        "trust_region_clip_",
-        "a_law_compress",
-        "mu_law_compress",
-        "softsign_compress",
-    ):
-        raise ValueError(f"Clipping function {name} not found")
-    return getattr(utils, name)
+str_or_fn = Union[str, callable, None, Literal[use_default]]
 
 
 def default(a, b):
@@ -1978,23 +1944,17 @@ class BaseOpt(ChainOpt):
     Base Optimizer
 
     compile_step: bool = False
-    Whether to change some internals to try to make the optimizer compilable
-    This does not compile the step by itself and breaks some optimizers loudly (e.g. SOAP)
+    Whether to torch.compile the optimizer step (fullgraph=True).
+    Initialization runs eagerly on the first step; subsequent steps are compiled.
 
     promote: bool = False
-    Whether to promote the gradients to fp32 before applying the optimizer
-    Improves update quality for low-precision parameters, but increases costs
-    Compiling the optimizer step would reduce memory and compute. Alternatively, `multi_tensor=False` decreases memory at the cost of runtime
+    Whether to promote the gradients to fp32 before applying the optimizer.
 
     gradient_clipping: str_or_fn = None
-    The function to use for clipping the incoming gradients, before any other transformations.
-    This is syntactic sugar, equivalent to manually passing the function as the first element of the optimizer chain.
+    Clipping function applied to incoming gradients before any other transforms.
 
     update_clipping: str_or_fn = None
-    The function to use for clipping the outgoing updates before applying them, after all other transformations.
-    This will turn off fused updates.
-    This is syntactic sugar, equivalent to manually passing the function as the last element of the optimizer chain.
-
+    Clipping function applied to outgoing updates. Disables fused updates.
     """
 
     gradient_clipping: str_or_fn = None
@@ -2059,28 +2019,29 @@ def __init__(
 
 class ScheduleFree(BaseOpt):
     def eval(self):
+        z_key = self._find_val_name("z")
         for group in self.param_groups:
-            group["train_mode"] = train_mode = not group.get("train_mode")
+            group["train_mode"] = train_mode = not group.get("train_mode", True)
             beta1 = utils.get_beta1(group)
             if beta1 > 0 and not train_mode:
                 for p in group["params"]:
                     state = self.state_(p)
-                    if "z" in state:
-                        # Set p.data to x
-                        z = utils.promote(state["z"])
+                    if z_key in state:
+                        z = utils.promote(state[z_key])
                         p32 = utils.promote(p.data)
                         p32.lerp_(end=z, weight=1 - 1 / beta1)
                         utils.copy_stochastic_(p.data, p32)
 
     def train(self):
+        z_key = self._find_val_name("z")
         for group in self.param_groups:
-            group["train_mode"] = train_mode = not group.get("train_mode")
+            group["train_mode"] = train_mode = not group.get("train_mode", False)
             beta1 = utils.get_beta1(group)
             if beta1 > 0 and train_mode:
                 for p in group["params"]:
                     state = self.state_(p)
-                    if "z" in state:
-                        z = utils.promote(state["z"])
+                    if z_key in state:
+                        z = utils.promote(state[z_key])
                         p32 = utils.promote(p.data)
                         p32.lerp_(end=z, weight=1 - beta1)
                         utils.copy_stochastic_(p.data, p32)
@@ -2088,23 +2049,25 @@ def train(self):
 
 class MSAM(BaseOpt):
     def eval(self):
+        z_key = self._find_val_name("z")
         for group in self.param_groups:
-            group["train_mode"] = train_mode = not group.get("train_mode")
+            group["train_mode"] = train_mode = not group.get("train_mode", True)
             if not train_mode:
                 for p in group["params"]:
                     state = self.state_(p)
-                    if "z" in state:
+                    if z_key in state:
                         p_copy = p.data.clone()
-                        utils.copy_stochastic_(p.data, state["z"])
-                        utils.copy_stochastic_(state["z"], p_copy)
+                        utils.copy_stochastic_(p.data, state[z_key])
+                        utils.copy_stochastic_(state[z_key], p_copy)
 
     def train(self):
+        z_key = self._find_val_name("z")
         for group in self.param_groups:
-            group["train_mode"] = train_mode = not group.get("train_mode")
+            group["train_mode"] = train_mode = not group.get("train_mode", False)
             if train_mode:
                 for p in group["params"]:
                     state = self.state_(p)
-                    if "z" in state:
+                    if z_key in state:
                         p_copy = p.data.clone()
-                        utils.copy_stochastic_(p.data, state["z"])
-                        utils.copy_stochastic_(state["z"], p_copy)
+                        utils.copy_stochastic_(p.data, state[z_key])
+                        utils.copy_stochastic_(state[z_key], p_copy)
diff --git a/heavyball/utils.py b/heavyball/utils.py
index d0154b5..50642ca 100644
--- a/heavyball/utils.py
+++ b/heavyball/utils.py
@@ -1293,7 +1293,6 @@ class StatefulOptimizer(torch.optim.Optimizer):
     compile_step: bool = False
     hessian_approx: bool = False
     precond_schedule: Union[Callable, float, None] = None
-    stochastic_schedule: bool | Literal[use_default] = use_default
     finite_differences: bool = False
     fallback_to_finite_differences: bool = True
     _fallback_enabled: bool = False
@@ -1318,17 +1317,7 @@ def __init__(self, params, defaults, multi_tensor: bool = True, use_ema: bool =
         self.mapping = {}
         self.mapping_inverse = {}
 
-        if self.stochastic_schedule is use_default:
-            stochastic_schedule = None
-            for group in self.param_groups:
-                new = group.get("stochastic_schedule", stochastic_schedule)
-                if stochastic_schedule is not None and new != stochastic_schedule:
-                    raise ValueError("All parameter groups must have the same stochastic_schedule.")
-                stochastic_schedule = new
-            self.stochastic_schedule = stochastic_schedule
-
-        self.inner_group = {"stochastic_schedule": self.stochastic_schedule}
-        self.precond_rng = random.Random(0x12312)
+        self.inner_group = {}
         self._is_preconditioning = None
 
         if self.hessian_approx and self.compile_step:
@@ -1340,22 +1329,24 @@ def __init__(self, params, defaults, multi_tensor: bool = True, use_ema: bool =
     def _store_stats(self, state_dict: dict[str, any]):
         state_dict["heavyball"] = {
             "inner_group": self.inner_group,
-            "precond_rng": pickle.dumps(self.precond_rng),
             "use_ema": self.use_ema,
             "ema_decay": self.ema_decay,
             "compile_step": self.compile_step,
             "hessian_approx": self.hessian_approx,
             "precond_schedule": pickle.dumps(self.precond_schedule),
-            "stochastic_schedule": self.stochastic_schedule,
             "fallback_to_finite_differences": self.fallback_to_finite_differences,
             "_fallback_enabled": self._fallback_enabled,
             "hvp_interval": self.hvp_interval,
         }
 
+    _REMOVED_STATS = frozenset({"stochastic_schedule", "precond_rng"})
+
     def _load_stats(self, state_dict):
         sd = state_dict.pop("heavyball", {})
         for k, v in sd.items():
-            if k in ("precond_rng", "precond_schedule"):
+            if k in self._REMOVED_STATS:
+                continue
+            if k in ("precond_schedule",):
                 v = pickle.loads(v)
             setattr(self, k, v)
 
@@ -1603,7 +1594,7 @@ def step(self, closure: Optional[Callable] = None):
         if self.precond_schedule is None:
             self._is_preconditioning = False
         else:
-            self._is_preconditioning = psgd_should_update(self.inner_group, self.precond_schedule, self.precond_rng)
+            self._is_preconditioning = psgd_should_update(self.inner_group, self.precond_schedule)
         loss = self._handle_closure(closure)
 
         if self.use_ema:
@@ -2861,10 +2852,10 @@ def _approx():
 
 
 @decorator_knowngood
-def _balance_to_triu(Q: "TriuOrLine", symmetric_output: bool = False):
+def _balance_to_triu(Q: "TriuOrLine"):
     if isinstance(Q[0], tuple):
         psgd_balance_Q([o[1] for o in Q])
-        return line_to_triu(Q, symmetric_output)
+        return line_to_triu(Q)
     psgd_balance_Q(Q)
     return Q
 
@@ -2980,7 +2971,6 @@ def psgd_update_precond(
     precond_lr: float,
     oq: "TriuOrLine",
     store_triu_as_line: bool,
-    velocity: Optional[List[Tensor]],
     beta2: float,
     ortho_method: Optional[str],
     V: Tensor,
@@ -3176,64 +3166,9 @@ def _psgd_precond_update_(
 
 
 @decorator_knowngood
-def _psgd_quad_preconditioner_grad(GG: List[Tensor], Q: List[Tensor], numel: int):
-    """
-    I: Identity
-    U: Update / gg / target
-    Q: q, preconditioner
-    scale: scalar scale
-    ---
-    U = T * scale - I
-    F = I - U  # = 2I - U * scale
-    O = F @ Q @ F - Q
-    """
-    out = []
-    for gg, q in zip(GG, Q):
-        if gg.ndim < 2:
-            scale = max(1, gg.numel()) / numel
-            target = promote(gg)
-            update = target * scale - 1
-            out.append(q - (1 - update) * q * (1 - update))
-        else:
-            scale = gg.size(0) / numel
-            gg = 2 * torch.eye(gg.size(0), device=gg.device, dtype=gg.dtype) - gg * scale
-            update = q - casted_einsum("ab,cd,bc", gg, gg, q)
-            out.append(update + update.T)  # make matrix symmetric
-    return out
 
 
 @decorator
-def inverse_free_psgd_update_precond(
-    G: Tensor,
-    precond_lr: float,
-    oq: List[Tensor],
-    store_triu_as_line: bool,
-    velocity: Optional[List[Tensor]],
-    beta2: float,
-    ortho_method: Optional[str],
-    V: None,
-    running_lower_bound: List[Tensor],
-    lower_bount_beta: float,
-    power_iter: int,
-) -> Tensor:
-    """Update Kronecker product preconditioner Q with pair (V, G)."""
-    assert V is None
-    assert ortho_method is None
-    assert velocity is None
-    del V, ortho_method, velocity
-
-    Q = _balance_to_triu(oq, True)
-    precond_lr, beta2, lower_bount_beta = scalar_guard(precond_lr, beta2, lower_bount_beta, G)
-    exprGs = calcG_expr(ndim_tuple(Q), G.ndim)
-
-    G = psgd_precond_grad(G, Q)
-    terms = [compiled_einsum(exprG, G, G) for exprG in exprGs]
-    matmuled = _psgd_quad_preconditioner_grad(terms, Q, G.numel())
-    _psgd_precond_update_(
-        matmuled, oq, running_lower_bound, lower_bount_beta, precond_lr, store_triu_as_line, power_iter
-    )
-    return G
-
 
 @decorator_knowngood
 def _clip(x, norm, clip_at, eps=1e-8):
@@ -3495,15 +3430,13 @@ def triu_to_line(Q_list: List[Tensor]):
 
 
 @decorator_knowngood
-def line_to_triu(Q_list: List[Tuple[Optional[List[int]], Tensor]], symmetric_output: bool = False):
+def line_to_triu(Q_list: List[Tuple[Optional[List[int]], Tensor]]):
     new = []
     for shape, q in Q_list:
         if shape is not None:
             x, y = torch.triu_indices(*shape, device=q.device)
             q_mat = torch.zeros(shape, device=q.device, dtype=q.dtype)
             q_mat[x, y] = q
-            if symmetric_output:
-                q_mat[y, x] = q
             q = q_mat
         new.append(q)
     return new
@@ -3518,14 +3451,10 @@ def warn_once(msg):
         _warned.add(msg)
 
 
-def psgd_should_update(
-    group, prob: Union[float, callable], rng: Optional[random.Random] = None, name: str = "cumulative_prob"
-):
+def psgd_should_update(group, prob: Union[float, callable], name: str = "cumulative_prob"):
     group[f"{name}_prob_step"] = group.get(f"{name}_prob_step", 0) + 1
     if not isinstance(prob, float):
         prob = prob(group[f"{name}_prob_step"])
-    if group["stochastic_schedule"]:
-        return rng.random() < prob
     cumulative_prob = group.get(name, 0)
     group[name] = cumulative_prob + prob
     return int(group[name]) > int(cumulative_prob)
@@ -3587,12 +3516,11 @@ def psgd_precond_grad(
     caution: bool = False,
     grad: Optional[Tensor] = None,
     store_triu_as_line: bool = False,
-    symmetric_output: bool = False,
 ):
     if caution:
         ea = _compilable_cautioning(grad, ea)
     if store_triu_as_line:
-        preconds = line_to_triu(preconds, symmetric_output)
+        preconds = line_to_triu(preconds)
     args = [promote(q) for q in preconds]
     expr = precond_grad_expr(ndim_tuple(args), ea.ndim)
     return compiled_einsum(expr, *[a for a in args for _ in (0, 1)], promote(ea))
@@ -3608,7 +3536,6 @@ def _compilable_fused_psgd_precond_grad(
     caution,
     preconds: TriuOrLine,
     store_triu_as_line: bool = False,
-    symmetric_output: bool = False,
 ):
     precond = psgd_precond_grad(
         ea,
@@ -3616,7 +3543,6 @@ def _compilable_fused_psgd_precond_grad(
         caution=caution,
         grad=grad,
         store_triu_as_line=store_triu_as_line,
-        symmetric_output=symmetric_output,
     )
     update_param_(param, precond, lr, decay, caution=False, grad=grad)
 
@@ -3630,11 +3556,10 @@ def fused_psgd_precond_grad(
     caution,
     preconds: TriuOrLine,
     store_triu_as_line: bool = False,
-    symmetric_output: bool = False,
 ):
     lr, decay = scalar_guard(lr, decay, param[0])
     _compilable_fused_psgd_precond_grad(
-        ea, param, lr, grad, decay, caution, preconds, store_triu_as_line, symmetric_output
+        ea, param, lr, grad, decay, caution, preconds, store_triu_as_line
     )
 
 
diff --git a/scripts/migrate_optimizer_state.py b/scripts/migrate_optimizer_state.py
index 1eef0aa..8931cc7 100644
--- a/scripts/migrate_optimizer_state.py
+++ b/scripts/migrate_optimizer_state.py
@@ -104,7 +104,7 @@ def walk(queue: Iterable[Any]):
                 stack.append(current.fn)
             elif isinstance(current, functools.partial):  # type: ignore[name-defined]
                 stack.append(current.func)
-            elif isinstance(current, C.Branch):
+            elif isinstance(current, C.Parallel):
                 for branch in current.branches:
                     stack.extend(branch)
             elif isinstance(current, (list, tuple)):
diff --git a/test/test_chainable_cpu.py b/test/test_chainable_cpu.py
index 6612028..64e24c6 100644
--- a/test/test_chainable_cpu.py
+++ b/test/test_chainable_cpu.py
@@ -36,7 +36,7 @@ def negate(_, __, update, ___, ____):
     def merge_fn(outputs):
         return [sum(vals) / len(vals) for vals in zip(*outputs)]
 
-    branch = C.Branch([[double], [negate]], merge_fn)
+    branch = C.Parallel([[double], [negate]], merge_fn)
 
     update = [torch.ones(2)]
     grad = [torch.ones(2)]
diff --git a/test/test_compile_step.py b/test/test_compile_step.py
index 14b8f80..de210e7 100644
--- a/test/test_compile_step.py
+++ b/test/test_compile_step.py
@@ -80,4 +80,4 @@ def test_compile_step_matches_eager(opt_name, opt_cls):
 
     for p_ref, p_test in zip(model_ref.parameters(), model_test.parameters()):
         diff = (p_ref.data - p_test.data).abs().max().item()
-        assert diff < 1e-5, f"compile_step diverged: max_diff={diff}"
+        assert diff < 1e-4, f"compile_step diverged: max_diff={diff}"
diff --git a/test/test_ecc.py b/test/test_ecc.py
index 1dd7364..163d4f9 100644
--- a/test/test_ecc.py
+++ b/test/test_ecc.py
@@ -130,7 +130,7 @@ def test_param_ecc_convergence(combined):
     kw = {"param_ecc": "bf16+8"}
     if combined:
         kw["ecc"] = "bf16+8"
-    m1, o1 = _model_opt(heavyball.SFAdamW, 16, 8, 1e-2)
+    m1, o1 = _model_opt(heavyball.SFAdamW, 16, 8, 1e-2, **kw)
     losses_ecc = _train(m1, o1, data, target, 200)
     p = list(m1.parameters())[0]
     assert p.dtype == torch.bfloat16
@@ -302,7 +302,7 @@ def _measure_peak(cls, n, lr, ecc=None, param_ecc=None, steps=3):
         kw["ecc"] = ecc
     if param_ecc:
         kw["param_ecc"] = param_ecc
-    opt = cls([p], lr=lr)
+    opt = cls([p], lr=lr, **kw)
 
     for _ in range(steps):
         p.grad = torch.randn_like(p)
diff --git a/test/test_migrate_cli.py b/test/test_migrate_cli.py
index 7507289..253c6d8 100644
--- a/test/test_migrate_cli.py
+++ b/test/test_migrate_cli.py
@@ -169,7 +169,6 @@ def test_cli_migrates_legacy_checkpoint(runner, tmp_path):
             assert view_state["is_initialized"] == [0]
 
         assert "heavyball" in migrated_state
-        assert migrated_state["heavyball"]["inner_group"]["stochastic_schedule"] is None
         assert "Migrated checkpoint written to" in result.stdout
     finally:
         for name in list(sys.modules):
diff --git a/test/test_stochastic_updates.py b/test/test_stochastic_updates.py
deleted file mode 100644
index bd3f409..0000000
--- a/test/test_stochastic_updates.py
+++ /dev/null
@@ -1,58 +0,0 @@
-import pytest
-import torch
-from torch import nn
-from utils import REPRESENTATIVE_OPTS
-
-import heavyball
-from heavyball.utils import clean, set_torch
-
-_SAVED_COMPILE_MODE = heavyball.utils.compile_mode
-heavyball.utils.compile_mode = "default"
-
-
-@pytest.fixture(autouse=True)
-def _isolate_compile_mode():
-    heavyball.utils.compile_mode = "default"
-    yield
-    heavyball.utils.compile_mode = _SAVED_COMPILE_MODE
-
-
-PSGD_OPTS = [o for o in REPRESENTATIVE_OPTS if "PSGD" in o]
-
-
-@pytest.mark.parametrize("opt", PSGD_OPTS)
-def test_foreach(opt, size: int = 128, depth: int = 1, iterations: int = 512, outer_iterations: int = 2):
-    set_torch()
-
-    opt = getattr(heavyball, opt)
-
-    losses = []
-
-    for stochastic in [False, True]:
-        print("stochastic", stochastic)
-        torch.manual_seed(0x2131290)
-        losses.append([])
-
-        for i in range(outer_iterations):
-            model = nn.Sequential(*[nn.Linear(size, size, bias=False) for _ in range(depth)]).cuda()
-            o = opt(
-                model.parameters(),
-                lr=1e-3,
-                stochastic_schedule=stochastic,
-                preconditioner_update_probability=lambda step: 0.1,
-            )
-
-            for _ in range(iterations):
-                loss = model(torch.randn((128, size), device="cuda")).square().mean()
-                loss.backward()
-                o.step()
-                o.zero_grad()
-                losses[-1].append(loss.detach())
-
-            del model, o
-            clean()
-
-    stochastic = sum([l.item() for l in losses[1]])
-    deterministic = sum([l.item() for l in losses[0]])
-    print(f"{deterministic=}, {stochastic=}")
-    assert not torch.isclose(torch.tensor(deterministic), torch.tensor(stochastic), rtol=0.01)
diff --git a/test/test_stochastic_utils_cpu.py b/test/test_stochastic_utils_cpu.py
index 0b16f2d..693533d 100644
--- a/test/test_stochastic_utils_cpu.py
+++ b/test/test_stochastic_utils_cpu.py
@@ -1,8 +1,6 @@
-import os
-
-os.environ.setdefault("TORCH_COMPILE_DISABLE", "1")
-
+import pytest
 import torch
+from torch._dynamo import config
 
 import heavyball
 from heavyball.utils import (
@@ -13,7 +11,15 @@
     stochastic_divide_with_eps_,
 )
 
-heavyball.utils.atan2_scale = 1024.0
+config.cache_size_limit = 128
+
+
+@pytest.fixture(autouse=True)
+def _restore_atan2_scale():
+    orig = heavyball.utils.atan2_scale
+    heavyball.utils.atan2_scale = 1024.0
+    yield
+    heavyball.utils.atan2_scale = orig
 
 
 def _average_stochastic_round(source: torch.Tensor, trials: int = 512) -> torch.Tensor:
diff --git a/test/test_utils_cpu.py b/test/test_utils_cpu.py
index 54786a4..621056c 100644
--- a/test/test_utils_cpu.py
+++ b/test/test_utils_cpu.py
@@ -40,6 +40,9 @@
 
 # Ensure Torch dynamo stays disabled on CI runners without GPU support.
 os.environ.setdefault("TORCH_COMPILE_DISABLE", "1")
+from torch._dynamo import config
+
+config.cache_size_limit = 128
 _SAVED_COMPILE_MODE = heavyball.utils.compile_mode
 heavyball.utils.compile_mode = None
 
@@ -173,9 +176,9 @@ def test_triu_line_roundtrip_on_cpu():
         torch.arange(9, dtype=torch.float32).reshape(3, 3),
     ]
     packed = triu_to_line(tensors)
-    restored = line_to_triu(packed, symmetric_output=True)
+    restored = line_to_triu(packed)
     for original, rebuilt in zip(tensors, restored, strict=True):
-        assert torch.allclose(rebuilt, torch.triu(original) + torch.triu(original, diagonal=1).T)
+        assert torch.allclose(rebuilt, torch.triu(original))
 
 
 def test_warn_once_only_emits_single_warning(monkeypatch):
@@ -192,7 +195,7 @@ def test_warn_once_only_emits_single_warning(monkeypatch):
 
 
 def test_psgd_should_update_accumulates_probability():
-    group = {"stochastic_schedule": False}
+    group = {}
     outcomes = [psgd_should_update(group, 0.4) for _ in range(4)]
     assert outcomes[:2] == [False, False]
     assert outcomes[2] is True
@@ -200,15 +203,6 @@ def test_psgd_should_update_accumulates_probability():
     assert group["cumulative_prob_prob_step"] == 4
 
 
-def test_psgd_should_update_stochastic_schedule_uses_rng():
-    rng = random.Random(123)
-    group = {"stochastic_schedule": True}
-    calls = [psgd_should_update(group, 0.5, rng=rng) for _ in range(5)]
-    rng = random.Random(123)
-    expected = [rng.random() < 0.5 for _ in range(5)]
-    assert calls == expected
-
-
 def test_stochastic_math_helpers_match_expected_results(n=1024):
     torch.manual_seed(0x172893)
     a = torch.arange(n).float()
@@ -226,7 +220,8 @@ def test_stochastic_math_helpers_match_expected_results(n=1024):
     stochastic_add_divide_(c, b, alpha=1.0, divisor=2.0)
     assert torch.allclose(c.float(), (a + b * 1) / 2)
 
-    orig = heavyball.utils.default_division_backend
+    orig_backend = heavyball.utils.default_division_backend
+    orig_scale = heavyball.utils.atan2_scale
     try:
         heavyball.utils.atan2_scale = 1024
         for backend in heavyball.utils.DivisionBackend:
@@ -235,7 +230,8 @@ def test_stochastic_math_helpers_match_expected_results(n=1024):
             stochastic_divide_with_eps_(c, b)
             assert torch.allclose(c.float(), a / b), f"Backend {backend} failed"
     finally:
-        heavyball.utils.default_division_backend = orig
+        heavyball.utils.default_division_backend = orig_backend
+        heavyball.utils.atan2_scale = orig_scale
 
 
 def test_stochastic_math_accuracy():
diff --git a/test/test_utils_property.py b/test/test_utils_property.py
index d0c25cb..ec6c3e5 100644
--- a/test/test_utils_property.py
+++ b/test/test_utils_property.py
@@ -22,6 +22,9 @@
 
 # Ensure torch.compile stays disabled on CPU-only CI runners.
 os.environ.setdefault("TORCH_COMPILE_DISABLE", "1")
+from torch._dynamo import config
+
+config.cache_size_limit = 128
 
 
 heavyball.utils.compile_mode = None
diff --git a/test/utils.py b/test/utils.py
index 906526a..163445f 100644
--- a/test/utils.py
+++ b/test/utils.py
@@ -15,7 +15,6 @@
 _SKIP_GET_OPTIM = {
     "AdEMAMix",
     "SOAPAdEMAMix",
-    "SOAPAdEMAMix",
     "SplitOpt",
     "SAMWrapper",
 }

From bf882d81d9ee411a93a93720ecfa72bd810fdffd Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Sun, 29 Mar 2026 20:26:49 +0000
Subject: [PATCH 07/24] cleanup

---
 benchmarks/bench_singular_values.py |    2 +-
 docs/benchmark.md                   |    4 +-
 examples/autoencoder.py             |    1 -
 heavyball/__init__.py               |  230 ++--
 heavyball/chainable.py              |    7 +-
 heavyball/utils.py                  |    4 +-
 interactive/playground.py           | 1596 ---------------------------
 interactive/static/init-globals.js  |    2 -
 interactive/static/node-editor.js   |  570 ----------
 pyproject.toml                      |    2 +-
 scripts/migrate_optimizer_state.py  |  124 ++-
 test/test_compile_step.py           |   31 +
 test/test_ecc.py                    |    2 +-
 test/test_migrate_cli.py            |  797 ++++++++++---
 test/test_param_ecc_compile.py      |    2 +-
 test/test_toy_training.py           |    6 +-
 test/utils.py                       |    2 +-
 17 files changed, 908 insertions(+), 2474 deletions(-)
 delete mode 100644 interactive/playground.py
 delete mode 100644 interactive/static/init-globals.js
 delete mode 100644 interactive/static/node-editor.js

diff --git a/benchmarks/bench_singular_values.py b/benchmarks/bench_singular_values.py
index c324b64..f95f735 100644
--- a/benchmarks/bench_singular_values.py
+++ b/benchmarks/bench_singular_values.py
@@ -113,7 +113,7 @@ def key_fn(r):
                 f"{key[0]:<8} {key[1]:<5} {key[2]:>3}  {min(rerrs):>10.6f}  {max(rerrs):>10.6f}  {errs:>6}  {len(items):>5}"
             )
         else:
-            print(f"{key[0]:<8} {key[1]:<5} {key[2]:>3}  {'—':>10}  {'—':>10}  {errs:>6}  {len(items):>5}")
+            print(f"{key[0]:<8} {key[1]:<5} {key[2]:>3}  {'-':>10}  {'-':>10}  {errs:>6}  {len(items):>5}")
 
 
 def main():
diff --git a/docs/benchmark.md b/docs/benchmark.md
index 5fdb320..f6ff709 100644
--- a/docs/benchmark.md
+++ b/docs/benchmark.md
@@ -82,7 +82,7 @@ informed choice.
 ### Case Study: Escaping the Saddle Point
 
 An optimizer’s inability to navigate a saddle point is a classic example of a silent failure. A key test of an
-optimizer's robustness is its ability to navigate a saddle point—a region that is a minimum in one direction but a
+optimizer's robustness is its ability to navigate a saddle point - a region that is a minimum in one direction but a
 maximum in another. The gradient approaches zero at the center, trapping first-order methods that rely solely on the
 gradient.
 
@@ -95,7 +95,7 @@ optimizer may be unreliable in these settings.
 ## Conclusion
 
 The HeavyBall Benchmark represents a necessary shift in how we evaluate optimizers, moving from a culture of
-score-chasing to one of deep, diagnostic understanding. These hidden failures aren’t rare edge cases—they’re a routine
+score-chasing to one of deep, diagnostic understanding. These hidden failures aren’t rare edge cases - they’re a routine
 source of wasted compute and disappointing models. By making them explicit, the benchmark equips researchers and
 practitioners with a detailed map of an optimizer's capabilities. By clearly identifying hidden failure modes,
 practitioners can confidently choose, tune, or reconsider their optimization strategies, ultimately leading to more
diff --git a/examples/autoencoder.py b/examples/autoencoder.py
index 20350cb..615ddba 100644
--- a/examples/autoencoder.py
+++ b/examples/autoencoder.py
@@ -96,7 +96,6 @@ def main(epochs: int, batch: int, log_interval: int = 16):
         lr=1e-4,
         mars=True,
         lower_bound_beta=0.9,
-        inverse_free=True,
         precond_update_power_iterations=6,
         store_triu_as_line=False,
     )
diff --git a/heavyball/__init__.py b/heavyball/__init__.py
index d760970..a7a69ee 100644
--- a/heavyball/__init__.py
+++ b/heavyball/__init__.py
@@ -598,7 +598,30 @@ def __init__(
         )
 
 
-class SOAP(C.BaseOpt):
+class SOAPBase(C.BaseOpt):
+    use_precond_schedule: bool = False
+
+    def _build_soap_defaults(self, locals_dict, fns):
+        use_precond_schedule = C.default(locals_dict["use_precond_schedule"], self.use_precond_schedule)
+        params, defaults = C._build_defaults(locals_dict)
+        if use_precond_schedule:
+            del defaults["precondition_frequency"]
+            self.precond_schedule = utils.get_soap_precond_schedule(defaults.pop("precond_scheduler"))
+        else:
+            del defaults["precond_scheduler"]
+            self.precond_schedule = 1 / defaults.pop("precondition_frequency")
+        super().__init__(
+            params,
+            defaults,
+            locals_dict["multi_tensor"],
+            locals_dict["gradient_clipping"],
+            locals_dict["update_clipping"],
+            locals_dict.get("palm", False),
+            fns=fns,
+        )
+
+
+class SOAP(SOAPBase):
     """
     SOAP
 
@@ -610,8 +633,6 @@ class SOAP(C.BaseOpt):
             https://github.com/nikhilvyas/SOAP
     """
 
-    use_precond_schedule: bool = False
-
     def __init__(
         self,
         params,
@@ -644,30 +665,10 @@ def __init__(
         param_ecc: str | None = None,
         **kwargs,
     ):
-        use_precond_schedule = C.default(use_precond_schedule, self.use_precond_schedule)
+        self._build_soap_defaults(locals(), fns=(C.scale_by_soap,))
 
-        params, defaults = C._build_defaults(locals())
-
-        if use_precond_schedule:
-            del defaults["precondition_frequency"]
-            self.precond_schedule = utils.get_soap_precond_schedule(defaults.pop("precond_scheduler"))
-        else:
-            del defaults["precond_scheduler"]
-            self.precond_schedule = 1 / defaults.pop("precondition_frequency")
-        super().__init__(
-            params,
-            defaults,
-            multi_tensor,
-            gradient_clipping,
-            update_clipping,
-            palm,  #
-            fns=(C.scale_by_soap,),
-        )
-
-
-class SOAPNAdam(C.BaseOpt):
-    use_precond_schedule: bool = False
 
+class SOAPNAdam(SOAPBase):
     def __init__(
         self,
         params,
@@ -702,30 +703,10 @@ def __init__(
         param_ecc: str | None = None,
         **kwargs,
     ):
-        use_precond_schedule = C.default(use_precond_schedule, self.use_precond_schedule)
+        self._build_soap_defaults(locals(), fns=(C.scale_by_soap_nadam,))
 
-        params, defaults = C._build_defaults(locals())
-
-        if use_precond_schedule:
-            del defaults["precondition_frequency"]
-            self.precond_schedule = utils.get_soap_precond_schedule(defaults.pop("precond_scheduler"))
-        else:
-            del defaults["precond_scheduler"]
-            self.precond_schedule = 1 / defaults.pop("precondition_frequency")
-        super().__init__(
-            params,
-            defaults,
-            multi_tensor,
-            gradient_clipping,
-            update_clipping,
-            palm,
-            fns=(C.scale_by_soap_nadam,),
-        )
-
-
-class SOAPAdEMAMix(C.BaseOpt):
-    use_precond_schedule: bool = False
 
+class SOAPAdEMAMix(SOAPBase):
     def __init__(
         self,
         params,
@@ -761,25 +742,7 @@ def __init__(
         param_ecc: str | None = None,
         **kwargs,
     ):
-        use_precond_schedule = C.default(use_precond_schedule, self.use_precond_schedule)
-
-        params, defaults = C._build_defaults(locals())
-
-        if use_precond_schedule:
-            del defaults["precondition_frequency"]
-            self.precond_schedule = utils.get_soap_precond_schedule(defaults.pop("precond_scheduler"))
-        else:
-            del defaults["precond_scheduler"]
-            self.precond_schedule = 1 / defaults.pop("precondition_frequency")
-        super().__init__(
-            params,
-            defaults,
-            multi_tensor,
-            gradient_clipping,
-            update_clipping,
-            palm,
-            fns=(C.scale_by_soap_ademamix,),
-        )
+        self._build_soap_defaults(locals(), fns=(C.scale_by_soap_ademamix,))
 
 
 class SignLaProp(C.BaseOpt):
@@ -818,7 +781,7 @@ def __init__(
         )
 
 
-class SOLP(C.BaseOpt):
+class SOLP(SOAPBase):
     """
     SOLP
 
@@ -830,8 +793,6 @@ class SOLP(C.BaseOpt):
             https://github.com/nikhilvyas/SOAP
     """
 
-    use_precond_schedule: bool = False
-
     def __init__(
         self,
         params,
@@ -863,25 +824,7 @@ def __init__(
         param_ecc: str | None = None,
         **kwargs,
     ):
-        use_precond_schedule = C.default(use_precond_schedule, self.use_precond_schedule)
-
-        params, defaults = C._build_defaults(locals())
-
-        if use_precond_schedule:
-            del defaults["precondition_frequency"]
-            self.precond_schedule = utils.get_soap_precond_schedule(defaults.pop("precond_scheduler"))
-        else:
-            del defaults["precond_scheduler"]
-            self.precond_schedule = 1 / defaults.pop("precondition_frequency")
-        super().__init__(
-            params,
-            defaults,
-            multi_tensor,
-            gradient_clipping,
-            update_clipping,
-            palm,  #
-            fns=(C.scale_by_soap_laprop,),
-        )
+        self._build_soap_defaults(locals(), fns=(C.scale_by_soap_laprop,))
 
 
 class OrthoLaProp(C.BaseOpt):
@@ -956,7 +899,37 @@ def __init__(
         )
 
 
-class PSGDKron(C.BaseOpt):
+class PSGDBase(C.BaseOpt):
+    delayed: bool = False
+    cached: bool = False
+    exp_avg_input: bool = True
+
+    def _build_psgd_defaults(self, locals_dict, fns, *, default_update_clipping=utils.trust_region_clip_, extra_defaults=None):
+        exp_avg_input = C.default(locals_dict.get("exp_avg_input", C.use_default), self.exp_avg_input)
+        update_clipping = C.default(locals_dict["update_clipping"], default_update_clipping)
+
+        locals_dict = {**locals_dict, "exp_avg_input": exp_avg_input, "update_clipping": update_clipping}
+        params, defaults = C._build_defaults(locals_dict)
+
+        self.precond_schedule = C.default(
+            defaults.pop("preconditioner_update_probability"), utils.precond_update_prob_schedule()
+        )
+
+        if extra_defaults:
+            defaults.update(extra_defaults)
+
+        super().__init__(
+            params,
+            defaults,
+            locals_dict["multi_tensor"],
+            locals_dict["gradient_clipping"],
+            update_clipping,
+            False,
+            fns=(*(C.exp_avg,) * exp_avg_input, *fns),
+        )
+
+
+class PSGDKron(PSGDBase):
     """
     Originally from Evan Walters and Omead Pooladzandi, 2024
     Modified under Creative Commons Attribution 4.0 International
@@ -1016,30 +989,13 @@ def __init__(
     ):
         delayed = C.default(delayed, self.delayed)
         cached = C.default(cached, self.cached)
-        exp_avg_input = C.default(exp_avg_input, self.exp_avg_input)
-        update_clipping = C.default(update_clipping, utils.trust_region_clip_)
-
-        params, defaults = C._build_defaults(locals())
-
-        self.precond_schedule = C.default(
-            defaults.pop("preconditioner_update_probability"), utils.precond_update_prob_schedule()
-        )
-
-        super().__init__(
-            params,
-            defaults,
-            multi_tensor,
-            gradient_clipping,
-            update_clipping,
-            False,  #
-            fns=(
-                *(C.exp_avg,) * exp_avg_input,
-                functools.partial(C.scale_by_delayed_psgd if delayed else C.scale_by_psgd, cached=cached),
-            ),
+        self._build_psgd_defaults(
+            locals(),
+            fns=(functools.partial(C.scale_by_delayed_psgd if delayed else C.scale_by_psgd, cached=cached),),
         )
 
 
-class PSGDPRO(C.BaseOpt):
+class PSGDPRO(PSGDBase):
     """
     PSGD with Q0.5EQ1.5 (PRO/Procrustes) preconditioner update.
     Solve-free alternative to standard PSGD-Kron (EQ method).
@@ -1089,31 +1045,15 @@ def __init__(
         **kwargs,
     ):
         cached = C.default(cached, self.cached)
-        exp_avg_input = C.default(exp_avg_input, self.exp_avg_input)
-        update_clipping = C.default(update_clipping, None)
-
-        params, defaults = C._build_defaults(locals())
-        defaults["store_triu_as_line"] = False
-
-        self.precond_schedule = C.default(
-            defaults.pop("preconditioner_update_probability"), utils.precond_update_prob_schedule()
-        )
-
-        super().__init__(
-            params,
-            defaults,
-            multi_tensor,
-            gradient_clipping,
-            update_clipping,
-            False,
-            fns=(
-                *(C.exp_avg,) * exp_avg_input,
-                functools.partial(C.scale_by_psgd_pro, cached=cached),
-            ),
+        self._build_psgd_defaults(
+            locals(),
+            fns=(functools.partial(C.scale_by_psgd_pro, cached=cached),),
+            default_update_clipping=None,
+            extra_defaults={"store_triu_as_line": False},
         )
 
 
-class PSGDLRA(C.BaseOpt):
+class PSGDLRA(PSGDBase):
     """
     Originally from Evan Walters and Omead Pooladzandi, 2024
     Modified under Creative Commons Attribution 4.0 International
@@ -1164,31 +1104,18 @@ def __init__(
         **kwargs,
     ):
         delayed = C.default(delayed, self.delayed)
-        exp_avg_input = C.default(exp_avg_input, self.exp_avg_input)
-        update_clipping = C.default(update_clipping, utils.trust_region_clip_)
-
-        params, defaults = C._build_defaults(locals())
-
-        self.precond_schedule = C.default(
-            defaults.pop("preconditioner_update_probability"), utils.precond_update_prob_schedule()
-        )
 
         if rank is None:
             utils.warn_once(
                 f"{rank=}. It will be set to log2(param_count). This requires `params` to be of type list. Currently, {type(params)=}"
             )
             params = list(params)
-            defaults["rank"] = max(1, round(math.log2(sum(p.numel() for p in params))))
-            utils.warn_once(f"rank was set to {defaults['rank']}")
+            rank = max(1, round(math.log2(sum(p.numel() for p in params))))
+            utils.warn_once(f"rank was set to {rank}")
 
-        super().__init__(
-            params,
-            defaults,
-            multi_tensor,
-            gradient_clipping,
-            update_clipping,
-            False,  #
-            fns=(*(C.exp_avg,) * exp_avg_input, C.scale_by_delayed_psgd_lra if delayed else C.scale_by_psgd_lra),
+        self._build_psgd_defaults(
+            locals(),
+            fns=(C.scale_by_delayed_psgd_lra if delayed else C.scale_by_psgd_lra,),
         )
 
 
@@ -1288,4 +1215,5 @@ def zero_grad(self, set_to_none: bool = True):
 
 
 capture_param_shapes = utils.capture_param_shapes
-__all__ = [k for k, v in globals().items() if isinstance(v, type) and issubclass(v, torch.optim.Optimizer)]
+_BASE_CLASSES = {SOAPBase, PSGDBase}
+__all__ = [k for k, v in globals().items() if isinstance(v, type) and issubclass(v, torch.optim.Optimizer) and v not in _BASE_CLASSES]
diff --git a/heavyball/chainable.py b/heavyball/chainable.py
index d9cd125..b37e43d 100644
--- a/heavyball/chainable.py
+++ b/heavyball/chainable.py
@@ -1886,7 +1886,12 @@ def _run_chain(self, state, group, g, p, caution):
 
     def _needs_init(self, state):
         ids = self._transform_ids
-        return ids and any(not ids.issubset(st.get("is_initialized", set())) for st in state)
+        if not ids:
+            return False
+        all_initialized = set()
+        for st in state:
+            all_initialized.update(st.get("is_initialized", ()))
+        return not ids.issubset(all_initialized)
 
     def _needs_eager(self, group, state):
         if self._needs_init(state):
diff --git a/heavyball/utils.py b/heavyball/utils.py
index 50642ca..44b4b28 100644
--- a/heavyball/utils.py
+++ b/heavyball/utils.py
@@ -3102,8 +3102,8 @@ def eigvecs_product_rank1(
     using the Householder reflector with first column v. Never materializes V.
 
     Args:
-        G: shape (..., d) — gradient row(s) you want to rotate into eigenbasis.
-        v: shape (d,)      — current unit direction (top eigenvector of P).
+        G: shape (..., d) - gradient row(s) you want to rotate into eigenbasis.
+        v: shape (d,)     - current unit direction (top eigenvector of P).
         w: optional Householder vector w; pass to reuse across calls.
 
     Returns:
diff --git a/interactive/playground.py b/interactive/playground.py
deleted file mode 100644
index bc80f62..0000000
--- a/interactive/playground.py
+++ /dev/null
@@ -1,1596 +0,0 @@
-import functools
-from abc import ABC, abstractmethod
-from typing import Any, Dict, List, Optional, Tuple
-
-import gradio as gr
-import numpy as np
-import plotly.graph_objects as go
-import torch
-import torch.nn as nn
-from plotly.subplots import make_subplots
-from sklearn.decomposition import PCA
-
-import heavyball
-import heavyball.chainable as C
-
-# TensorFlow Playground inspired colors
-COLORS = {
-    "bg": "#ffffff",
-    "surface": "#f7f7f7",
-    "primary": "#ff6f00",  # Orange
-    "secondary": "#0d47a1",  # Blue
-    "positive": "#4caf50",  # Green
-    "negative": "#f44336",  # Red
-    "text": "#212121",
-    "text_light": "#757575",
-    "border": "#e0e0e0",  # Component categories
-    "gradient": "#9c27b0",  # Purple - Gradient input
-    "momentum": "#2196f3",  # Blue - Momentum transforms
-    "scaling": "#ff5722",  # Deep Orange - Scaling transforms
-    "regularization": "#009688",  # Teal - Regularization
-    "normalization": "#795548",  # Brown - Normalization
-    "update": "#4caf50",  # Green - Update rules
-}
-
-
-# Problem base class
-class Problem(ABC):
-    """Base class for optimization problems"""
-
-    @property
-    @abstractmethod
-    def dim(self) -> int:
-        """Dimension of the parameter space"""
-        pass
-
-    @abstractmethod
-    def init(self) -> np.ndarray:
-        """Initial parameters"""
-        pass
-
-    @abstractmethod
-    def loss(self, x: torch.Tensor) -> torch.Tensor:
-        """Compute loss given parameters"""
-        pass
-
-    def bounds(self) -> Optional[List[Tuple[float, float]]]:
-        """Parameter bounds for visualization (None if unbounded)"""
-        return None
-
-    def optimum(self) -> Optional[np.ndarray]:
-        """Known optimal point if available"""
-        return None
-
-
-class Function2D(Problem):
-    """Wrapper for 2D test functions"""
-
-    def __init__(self, func, bounds, init, optimal=None):
-        self.func = func
-        self._bounds = bounds
-        self._init = init
-        self._optimal = optimal
-
-    @property
-    def dim(self) -> int:
-        return 2
-
-    def init(self) -> np.ndarray:
-        return np.array(self._init)
-
-    def loss(self, x: torch.Tensor) -> torch.Tensor:
-        if x.dim() == 1:
-            return self.func(x)
-        else:
-            # Handle batch of parameters
-            return self.func(x[0])
-
-    def bounds(self):
-        return self._bounds
-
-    def optimum(self):
-        return np.array(self._optimal) if self._optimal else None
-
-
-class MLPProblem(Problem):
-    """Train a small MLP to predict |x|"""
-
-    def _data(self, n_samples: int = 128, seed: int = 42) -> Tuple[torch.Tensor, torch.Tensor]:
-        raise NotImplementedError
-
-    def __init__(self, hidden_size=4, n_samples=128):
-        self.model = nn.Sequential(
-            nn.Linear(1, hidden_size),
-            nn.ReLU(),
-            nn.Linear(hidden_size, hidden_size),
-            nn.ReLU(),
-            nn.Linear(hidden_size, 1),
-        )
-        self.x_data, self.y_data = self._data(n_samples)
-        self._dim = sum(p.numel() for p in self.model.parameters())
-
-    @property
-    def dim(self) -> int:
-        return self._dim
-
-    def init(self) -> np.ndarray:
-        # Initialize model and return flattened parameters
-        torch.manual_seed(42)
-        for p in self.model.parameters():
-            if len(p.shape) >= 2:
-                nn.init.xavier_uniform_(p)
-            else:
-                nn.init.zeros_(p)
-        return self._flatten_params()
-
-    def loss(self, x: torch.Tensor) -> torch.Tensor:
-        # Instead of modifying model parameters, we'll use functional approach
-        # Split x into weight and bias tensors
-        idx = 0
-        params = []
-        for p in self.model.parameters():
-            numel = p.numel()
-            param = x[idx : idx + numel].view(p.shape)
-            params.append(param)
-            idx += numel
-
-        # Manually compute forward pass using the parameters from x
-        # For a 2-layer MLP: Linear -> ReLU -> Linear
-        w1, b1, w2, b2, w3, b3 = params
-
-        h = torch.nn.functional.linear(self.x_data, w1, b1)
-        h = torch.nn.functional.relu(h)
-        pred = torch.nn.functional.linear(h, w2, b2)
-        h = torch.nn.functional.relu(h)
-        pred = torch.nn.functional.linear(h, w3, b3)
-
-        return nn.functional.mse_loss(pred, self.y_data)
-
-    def _flatten_params(self) -> np.ndarray:
-        """Flatten model parameters to vector"""
-        return torch.cat([p.data.view(-1) for p in self.model.parameters()]).numpy()
-
-    def _unflatten_params(self, x: torch.Tensor):
-        """Set model parameters from flat vector (used for evaluation, not training)"""
-        idx = 0
-        for p in self.model.parameters():
-            numel = p.numel()
-            p.data.copy_(x[idx : idx + numel].view(p.shape))
-            idx += numel
-
-
-class AbsMLP(MLPProblem):
-    def _data(self, n_samples: int = 128, seed: int = 42):
-        x = torch.rand((n_samples, 1)) * 4 - 2
-        return x, x.abs()
-
-
-class SineMLP(MLPProblem):
-    def _data(self, n_samples: int = 128, seed: int = 42):
-        x = torch.rand((n_samples, 1)) * 4 - 2
-        return x, x.sin()
-
-
-class ExpMLP(MLPProblem):
-    def _data(self, n_samples: int = 128, seed: int = 42):
-        x = torch.rand((n_samples, 1)) * 4 - 2
-        return x, x.exp()
-
-
-class QuadraticBowl(Problem):
-    """N-dimensional quadratic bowl"""
-
-    def __init__(self, dim=10):
-        self._dim = dim
-        self.center = np.random.randn(dim) * 2
-
-    @property
-    def dim(self) -> int:
-        return self._dim
-
-    def init(self) -> np.ndarray:
-        return np.random.randn(self._dim) * 3
-
-    def loss(self, x: torch.Tensor) -> torch.Tensor:
-        center = torch.tensor(self.center, dtype=x.dtype, device=x.device)
-        return torch.sum((x - center) ** 2)
-
-    def optimum(self):
-        return self.center
-
-
-class StyblinskiTang(Problem):
-    """Styblinski-Tang function (separable, multimodal)"""
-
-    def __init__(self, dim=4):
-        self._dim = dim
-
-    @property
-    def dim(self) -> int:
-        return self._dim
-
-    def init(self) -> np.ndarray:
-        return np.random.uniform(-5, 5, self._dim)
-
-    def loss(self, x: torch.Tensor) -> torch.Tensor:
-        return 0.5 * torch.sum(x**4 - 16 * x**2 + 5 * x)
-
-    def bounds(self):
-        return [(-5, 5)] * self._dim
-
-    def optimum(self):
-        # Global minimum at x_i = -2.903534 for all i
-        return np.full(self._dim, -2.903534)
-
-
-# Test functions
-PROBLEMS = {  # 2D Problems
-    "Simple Bowl (2D)": Function2D(
-        func=lambda x: (x[0] - 1) ** 2 + (x[1] - 2) ** 2,
-        bounds=[(-3, 5), (-2, 6)],
-        init=[-1.0, 0.0],
-        optimal=[1.0, 2.0],
-    ),
-    "Ravine (2D)": Function2D(
-        func=lambda x: (x[0] - 1) ** 2 + (x[1] - 2) ** 100,
-        bounds=[(-3, 5), (-2, 6)],
-        init=[-1.0, 1.0],
-        optimal=[1.0, 2.0],
-    ),
-    "Rosenbrock (2D)": Function2D(
-        func=lambda x: (1 - x[0]) ** 2 + 100 * (x[1] - x[0] ** 2) ** 2,
-        bounds=[(-2, 2), (-1, 3)],
-        init=[-1.0, 1.0],
-        optimal=[1.0, 1.0],
-    ),
-    "Himmelblau (2D)": Function2D(
-        func=lambda x: (x[0] ** 2 + x[1] - 11) ** 2 + (x[0] + x[1] ** 2 - 7) ** 2,
-        bounds=[(-5, 5), (-5, 5)],
-        init=[0.0, 0.0],
-        optimal=[3.0, 2.0],
-    ),
-    "Beale (2D)": Function2D(
-        func=lambda x: (
-            (1.5 - x[0] + x[0] * x[1]) ** 2
-            + (2.25 - x[0] + x[0] * x[1] ** 2) ** 2
-            + (2.625 - x[0] + x[0] * x[1] ** 3) ** 2
-        ),
-        bounds=[(-4.5, 4.5), (-4.5, 4.5)],
-        init=[1.0, 1.0],
-        optimal=[3.0, 0.5],
-    ),  # High-dimensional Problems
-    "MLP abs(x) (13D)": AbsMLP(hidden_size=4, n_samples=128),
-    "MLP sin(x) (13D)": SineMLP(hidden_size=4, n_samples=128),
-    "MLP exp(x) (13D)": ExpMLP(hidden_size=4, n_samples=128),
-    "Quadratic Bowl (10D)": QuadraticBowl(dim=10),
-    "Styblinski-Tang (4D)": StyblinskiTang(dim=4),
-    "Styblinski-Tang (8D)": StyblinskiTang(dim=8),
-}
-
-# Chainable optimizer components
-OPTIMIZER_BLOCKS = {
-    "gradient": {
-        "name": "🎯 Gradient Input",
-        "color": COLORS["gradient"],
-        "components": [
-            {
-                "id": "gradient_input",
-                "name": "Raw Gradient",
-                "icon": "∇",
-                "description": "Start of the pipeline - raw gradients from backprop",
-                "func": None,  # This is just a placeholder
-                "params": {},
-            }
-        ],
-    },
-    "momentum": {
-        "name": "⚡ Momentum",
-        "color": COLORS["momentum"],
-        "components": [
-            {
-                "id": "heavyball",
-                "name": "Heavy Ball",
-                "icon": "🏐",
-                "description": "Classic momentum: v = βv - g",
-                "func": C.heavyball_momentum,
-                "params": {"beta": 0.9},
-            },
-            {
-                "id": "nesterov",
-                "name": "Nesterov",
-                "icon": "🚀",
-                "description": "Look-ahead momentum",
-                "func": C.nesterov_momentum,
-                "params": {"beta": 0.9},
-            },
-            {
-                "id": "nesterov_ema",
-                "name": "Nesterov EMA",
-                "icon": "📈",
-                "description": "Exponential moving average variant",
-                "func": C.nesterov_ema,
-                "params": {"beta": 0.9},
-            },
-            {
-                "id": "basic_ema",
-                "name": "Basic EMA",
-                "icon": "📉",
-                "description": "Simple exponential moving average",
-                "func": C.exp_avg,
-                "params": {"betas": (0.9, 0.999)},
-            },
-        ],
-    },
-    "scaling": {
-        "name": "📊 Adaptive Scaling",
-        "color": COLORS["scaling"],
-        "components": [
-            {
-                "id": "adam_scale",
-                "name": "Adam Scaling",
-                "icon": "👑",
-                "description": "Adaptive per-parameter learning rates",
-                "func": C.scale_by_adam,
-                "params": {"betas": (0.9, 0.999), "eps": 1e-8},
-            },
-            {
-                "id": "rmsprop_scale",
-                "name": "RMSprop Scaling",
-                "icon": "📉",
-                "description": "Root mean square normalization",
-                "func": C.scale_by_exp_avg_sq,
-                "params": {"beta2": 0.999, "eps": 1e-8},
-            },
-            {
-                "id": "adagrad_scale",
-                "name": "AdaGrad Scaling",
-                "icon": "📐",
-                "description": "Accumulate all past gradients",
-                "func": C.scale_by_exp_avg_sq,
-                "params": {"beta2": 1.0, "eps": 1e-8},
-            },
-        ],
-    },
-    "regularization": {
-        "name": "⚖️ Regularization",
-        "color": COLORS["regularization"],
-        "components": [
-            {
-                "id": "weight_decay",
-                "name": "Weight Decay",
-                "icon": "🪶",
-                "description": "L2 regularization (AdamW style)",
-                "func": C.weight_decay_to_ema,
-                "params": {"weight_decay_to_ema": 0.01, "ema_beta": 0.999},
-            },
-            {
-                "id": "weight_decay_init",
-                "name": "Decay to Init",
-                "icon": "🎯",
-                "description": "Pull weights toward initialization",
-                "func": C.weight_decay_to_init,
-                "params": {"weight_decay_to_init": 0.01},
-            },
-            {
-                "id": "l1_weight_decay",
-                "name": "L1 Weight Decay",
-                "icon": "⚡",
-                "description": "L1 regularization to EMA",
-                "func": C.l1_weight_decay_to_ema,
-                "params": {"weight_decay_to_ema": 0.01, "ema_beta": 0.999},
-            },
-        ],
-    },
-    "normalization": {
-        "name": "🔧 Gradient Processing",
-        "color": COLORS["normalization"],
-        "components": [
-            {
-                "id": "grad_clip",
-                "name": "Gradient Clipping",
-                "icon": "✂️",
-                "description": "Clip gradient norm",
-                "func": functools.partial(C.global_clip, clip_fn=heavyball.utils.l2_clip_),
-                "params": {"max_norm": 1.0},
-            },
-            {
-                "id": "sign",
-                "name": "Sign SGD",
-                "icon": "±",
-                "description": "Use only gradient signs",
-                "func": C.sign,
-                "params": {"graft": True},
-            },
-            {
-                "id": "orthogonalize",
-                "name": "Orthogonalize",
-                "icon": "⊥",
-                "description": "Orthogonalize gradient to parameter",
-                "func": C.orthogonalize_grad_to_param,
-                "params": {"eps": 1e-8},
-            },
-            {
-                "id": "orthogonalize_update",
-                "name": "Orthogonalize Update",
-                "icon": "⊗",
-                "description": "Orthogonalize the update itself",
-                "func": C.orthogonalize_update,
-                "params": {},
-            },
-        ],
-    },
-    "advanced_scaling": {
-        "name": "🚀 Advanced Optimizers",
-        "color": COLORS["scaling"],
-        "components": [
-            {
-                "id": "laprop",
-                "name": "Laprop",
-                "icon": "🌊",
-                "description": "Layerwise adaptive propagation",
-                "func": C.scale_by_laprop,
-                "params": {"betas": (0.9, 0.999), "eps": 1e-8},
-            },
-            {
-                "id": "adopt",
-                "name": "ADOPT",
-                "icon": "🎯",
-                "description": "Adaptive gradient methods",
-                "func": C.scale_by_adopt,
-                "params": {"betas": (0.9, 0.9999), "eps": 1e-12},
-            },
-        ],
-    },
-    "preconditioning": {
-        "name": "🔮 Preconditioning",
-        "color": COLORS["gradient"],
-        "components": [
-            {
-                "id": "soap",
-                "name": "SOAP",
-                "icon": "🧼",
-                "description": "Shampoo-based preconditioning",
-                "func": C.scale_by_soap,
-                "params": {
-                    "shampoo_beta": 0.99,
-                    "max_precond_dim": 10000,
-                    "precondition_1d": False,
-                    "is_preconditioning": True,
-                    "betas": (0.9, 0.999),
-                    "eps": 1e-8,
-                },
-            },
-            {
-                "id": "psgd",
-                "name": "PSGD",
-                "icon": "🎲",
-                "description": "Preconditioned SGD",
-                "func": functools.partial(C.scale_by_psgd, cached=False),
-                "params": {
-                    "precond_lr": 0.1,
-                    "max_size_triangular": 1024,
-                    "precondition_frequency": 10,
-                    "adaptive": False,
-                    "store_triu_as_line": True,
-                    "q_dtype": "float32",
-                    "inverse_free": False,
-                    "precond_init_scale": 1.0,
-                    "precond_init_scale_scale": 0.0,
-                    "precond_init_scale_power": 1.0,
-                    "min_ndim_triangular": 2,
-                    "memory_save_mode": None,
-                    "dampening": 1.0,
-                    "is_preconditioning": True,
-                    "betas": (0.9, 0.999),
-                    "eps": 1e-8,
-                    "ortho_method": "qr",
-                    "lower_bound_beta": 0.999,
-                    "precond_update_power_iterations": 1,
-                },
-            },
-            {
-                "id": "psgd_lra",
-                "name": "PSGD LRA",
-                "icon": "📐",
-                "description": "Low-rank approximation PSGD",
-                "func": C.scale_by_psgd_lra,
-                "params": {
-                    "precond_lr": 0.1,
-                    "rank": 4,
-                    "param_count": 10000,
-                    "precondition_frequency": 10,
-                    "precond_init_scale": 1.0,
-                    "precond_init_scale_scale": 0.0,
-                    "precond_init_scale_power": 1.0,
-                    "q_dtype": "float32",
-                    "is_preconditioning": True,
-                    "eps": 1e-8,
-                    "betas": (0.9, 0.999),
-                },
-            },
-            {
-                "id": "delayed_psgd",
-                "name": "Delayed PSGD",
-                "icon": "⏱️",
-                "description": "PSGD with delayed preconditioner updates",
-                "func": functools.partial(C.scale_by_delayed_psgd, cached=False),
-                "params": {
-                    "precond_lr": 0.1,
-                    "max_size_triangular": 1024,
-                    "precondition_frequency": 10,
-                    "adaptive": False,
-                    "store_triu_as_line": True,
-                    "q_dtype": "float32",
-                    "inverse_free": False,
-                    "precond_init_scale": 1.0,
-                    "precond_init_scale_scale": 0.0,
-                    "precond_init_scale_power": 1.0,
-                    "min_ndim_triangular": 2,
-                    "memory_save_mode": None,
-                    "dampening": 1.0,
-                    "is_preconditioning": True,
-                    "betas": (0.9, 0.999),
-                    "eps": 1e-8,
-                    "ortho_method": "qr",
-                    "lower_bound_beta": 0.999,
-                    "precond_update_power_iterations": 1,
-                },
-            },
-            {
-                "id": "delayed_psgd_lra",
-                "name": "Delayed PSGD LRA",
-                "icon": "⏰",
-                "description": "Delayed low-rank PSGD",
-                "func": C.scale_by_delayed_psgd_lra,
-                "params": {
-                    "precond_lr": 0.1,
-                    "rank": 4,
-                    "param_count": 10000,
-                    "precondition_frequency": 10,
-                    "precond_init_scale": 1.0,
-                    "precond_init_scale_scale": 0.0,
-                    "precond_init_scale_power": 1.0,
-                    "q_dtype": "float32",
-                    "is_preconditioning": True,
-                    "eps": 1e-8,
-                    "betas": (0.9, 0.999),
-                },
-            },
-        ],
-    },
-    "adaptive_lr": {
-        "name": "🎛️ Adaptive Learning Rate",
-        "color": COLORS["regularization"],
-        "components": [
-            {
-                "id": "d_adapt",
-                "name": "D-Adaptation",
-                "icon": "📈",
-                "description": "Automatic learning rate adaptation",
-                "func": C.scale_by_d_adaptation,
-                "params": {"initial_d": 1.0},
-            },
-            {
-                "id": "lr_adapt",
-                "name": "LR Adaptation",
-                "icon": "🔄",
-                "description": "Learning rate adaptation",
-                "func": C.scale_by_lr_adaptation,
-                "params": {"initial_d": 1.0, "lr_lr": 0.1},
-            },
-            {
-                "id": "pointwise_lr_adapt",
-                "name": "Pointwise LR",
-                "icon": "🎚️",
-                "description": "Per-parameter learning rate",
-                "func": C.scale_by_pointwise_lr_adaptation,
-                "params": {"initial_d": 1.0, "lr_lr": 0.1},
-            },
-        ],
-    },
-    "special": {
-        "name": "✨ Special Methods",
-        "color": COLORS["update"],
-        "components": [
-            {
-                "id": "schedule_free",
-                "name": "Schedule-Free",
-                "icon": "🗓️",
-                "description": "No learning rate schedule needed",
-                "func": C.update_by_schedule_free,
-                "params": {"r": 0.0, "weight_lr_power": 2.0},
-            },
-            {
-                "id": "msam",
-                "name": "MSAM",
-                "icon": "🏔️",
-                "description": "Momentum SAM optimizer",
-                "func": C.update_by_msam,
-                "params": {"sam_step_size": 0.05},
-            },
-            {
-                "id": "mup",
-                "name": "μP Approx",
-                "icon": "📏",
-                "description": "Maximal update parametrization",
-                "func": C.mup_approx,
-                "params": {},
-            },
-            {
-                "id": "palm_beta2",
-                "name": "PALM β₂",
-                "icon": "🌴",
-                "description": "Dynamic β₂ scheduling for PALM",
-                "func": C.palm_beta2,
-                "params": {"beta2_scale": 0.8},
-            },
-            {
-                "id": "identity",
-                "name": "Identity",
-                "icon": "🔄",
-                "description": "Pass-through (no operation)",
-                "func": C.identity,
-                "params": {},
-            },
-        ],
-    },
-}
-
-# Pre-built optimizer recipes
-RECIPES = {
-    "SGD": ["gradient_input"],
-    "SGD + Momentum": ["gradient_input", "heavyball"],
-    "Adam": ["gradient_input", "adam_scale"],
-    "AdamW": ["gradient_input", "adam_scale", "weight_decay"],
-    "RMSprop": ["gradient_input", "rmsprop_scale"],
-    "Nesterov SGD": ["gradient_input", "nesterov"],
-    "SOAP": ["gradient_input", "soap"],
-    "Laprop": ["gradient_input", "laprop"],
-    "ADOPT": ["gradient_input", "adopt"],
-    "Sign SGD": ["gradient_input", "sign"],
-    "AdamW + Clipping": ["gradient_input", "grad_clip", "adam_scale", "weight_decay"],
-    "D-Adapted Adam": ["gradient_input", "adam_scale", "d_adapt"],
-    "PSGD": ["gradient_input", "psgd"],
-    "Schedule-Free AdamW": ["gradient_input", "adam_scale", "weight_decay", "schedule_free"],
-    "EMA SGD": ["gradient_input", "basic_ema"],
-    "Orthogonal Adam": ["gradient_input", "orthogonalize_update", "adam_scale"],
-    "PALM": ["gradient_input", "palm_beta2", "adam_scale"],
-    "Delayed PSGD": ["gradient_input", "delayed_psgd"],
-    "μP Adam": ["gradient_input", "mup", "adam_scale"],
-}
-
-
-def get_component_info(comp_id):
-    """Get component info by ID"""
-    for category in OPTIMIZER_BLOCKS.values():
-        for comp in category["components"]:
-            if comp["id"] == comp_id:
-                return comp, category["color"]
-    return None, "#757575"
-
-
-def create_pipeline_display(pipeline):
-    """Create HTML display for the current pipeline"""
-    if not pipeline or pipeline == ["gradient_input"]:
-        return """
-        <div style="min-height: 120px; background: linear-gradient(135deg, #f5f5f5 25%, transparent 25%), linear-gradient(225deg, #f5f5f5 25%, transparent 25%), linear-gradient(45deg, #f5f5f5 25%, transparent 25%), linear-gradient(315deg, #f5f5f5 25%, #fafafa 25%); background-size: 20px 20px; background-position: 0 0, 10px 0, 10px -10px, 0px 10px; border: 2px dashed #bdbdbd; border-radius: 12px; padding: 20px; display: flex; align-items: center; justify-content: center; color: #9e9e9e; font-style: italic;">
-            Drop components here to build your optimizer pipeline
-        </div>
-        """
-
-    blocks_html = ""
-    for i, comp_id in enumerate(pipeline):
-        comp_info, color = get_component_info(comp_id)
-        if comp_info:
-            show_arrow = i < len(pipeline) - 1
-            blocks_html += f"""
-            <div style="display: inline-block; position: relative; margin: 0 10px;">
-                <div style="background: white; border: 3px solid {color}; border-radius: 8px; padding: 16px; min-width: 100px; text-align: center; box-shadow: 0 2px 8px rgba(0,0,0,0.1); position: relative;">
-                    <div style="font-size: 32px; margin-bottom: 8px;">{comp_info["icon"]}</div>
-                    <div style="font-weight: 600; font-size: 13px;">{comp_info["name"]}</div>
-                    <button onclick="window.removePipelineBlock({i})" style="position: absolute; top: 4px; right: 4px; width: 24px; height: 24px; border-radius: 50%; background: #f44336; color: white; border: none; cursor: pointer; opacity: 0.7; font-size: 16px; line-height: 1; padding: 0;">×</button>
-                </div>
-                {'<div style="position: absolute; right: -30px; top: 50%; transform: translateY(-50%); font-size: 24px; color: #ff6f00;">→</div>' if show_arrow else ""}
-            </div>
-            """
-
-    return f"""
-    <div style="min-height: 120px; background: white; border: 2px solid #e0e0e0; border-radius: 12px; padding: 20px; display: flex; align-items: center; overflow-x: auto; gap: 10px;">
-        {blocks_html}
-    </div>
-    """
-
-
-def build_optimizer_from_pipeline(pipeline: List[str], params, kwargs):
-    """Build optimizer from pipeline of component IDs"""
-    fns = []
-    opt_params = {
-        "lr": 0.001,
-        "step": 1,  # Required for many functions
-        "caution": False,
-        "weight_decay": 0.0,
-        **kwargs,
-    }
-
-    for comp_id in pipeline:
-        if comp_id == "gradient_input":
-            continue  # Skip the input block
-
-        # Find component
-        comp_info, _ = get_component_info(comp_id)
-        if comp_info and comp_info["func"] is not None:
-            fns.append(comp_info["func"])
-            # Update parameters, handling special cases
-            params_to_add = comp_info["params"].copy()
-
-            # Handle special parameter mappings
-            if "beta" in params_to_add and "betas" not in params_to_add:
-                # Convert single beta to betas tuple for functions expecting it
-                beta = params_to_add.pop("beta")
-                if "betas" in opt_params:
-                    opt_params["betas"] = (beta, opt_params["betas"][1])
-                else:
-                    opt_params["betas"] = (beta, 0.999)
-
-            # First add component defaults, then override with user-provided kwargs
-            for key, value in params_to_add.items():
-                if key not in kwargs:  # Only use default if not provided by user
-                    opt_params[key] = value
-
-    if not fns:
-        # Default to simple gradient descent
-        return C.BaseOpt(params, opt_params, fns=[C.identity])
-
-    return C.BaseOpt(params, opt_params, fns=fns)
-
-
-def run_optimization(problem_name: str, pipeline: List[str], steps: int, **kwargs) -> Tuple[Any, Dict]:
-    """Run optimization with the custom pipeline"""
-    problem = PROBLEMS[problem_name]
-    kwargs["lr"] = 10 ** kwargs.get("lr", -2)
-
-    # Initialize parameters
-    init = problem.init()
-    x = torch.nn.Parameter(torch.tensor(init, dtype=torch.float32))
-    params = [x]
-
-    # Build optimizer from pipeline
-    optimizer = build_optimizer_from_pipeline(pipeline, params, kwargs)
-
-    # Run optimization
-    trajectory = []
-    losses = []
-    gradients = []
-
-    for i in range(steps):
-        trajectory.append(x.detach().numpy().copy())
-
-        def closure():
-            optimizer.zero_grad()
-            loss = problem.loss(x)
-            loss.backward()
-            if x.grad is not None:
-                gradients.append(x.grad.detach().numpy().copy())
-            return loss
-
-        loss = optimizer.step(closure)
-        optimizer.zero_grad()
-        losses.append(loss.item())
-
-    trajectory = np.array(trajectory)
-
-    # Create visualization
-    fig = create_visualization(problem_name, trajectory, losses, gradients, pipeline)
-
-    return fig, {
-        "trajectory": trajectory.tolist(),
-        "losses": losses,
-        "final_loss": losses[-1],
-        "steps_to_converge": find_convergence(losses),
-    }
-
-
-def find_convergence(losses, threshold=1e-6):
-    """Find when optimization converged"""
-    if len(losses) < 10:
-        return len(losses)
-
-    for i in range(10, len(losses)):
-        if abs(losses[i] - losses[i - 5]) < threshold:
-            return i
-    return len(losses)
-
-
-def create_visualization(problem_name, trajectory, losses, gradients, pipeline):
-    """Create integrated visualization"""
-    problem = PROBLEMS[problem_name]
-
-    if problem.dim == 2:
-        return create_2d_visualization(problem_name, trajectory, losses, gradients, pipeline)
-    return create_highdim_visualization(problem_name, trajectory, losses, gradients, pipeline)
-
-
-def create_2d_visualization(problem_name, trajectory, losses, gradients, pipeline):
-    """Create visualization for 2D problems"""
-    problem = PROBLEMS[problem_name]
-    bounds = problem.bounds()
-
-    # Create subplots
-    fig = make_subplots(
-        rows=2,
-        cols=2,
-        subplot_titles=("Optimization Landscape", "Pipeline Architecture", "Loss Curve", "Learning Dynamics"),
-        column_widths=[0.6, 0.4],
-        row_heights=[0.6, 0.4],
-        specs=[[{"type": "contour"}, {"type": "scatter"}], [{"type": "scatter"}, {"type": "scatter"}]],
-    )
-
-    # 1. Optimization landscape
-    x = np.linspace(bounds[0][0], bounds[0][1], 100)
-    y = np.linspace(bounds[1][0], bounds[1][1], 100)
-    X, Y = np.meshgrid(x, y)
-    Z = np.zeros_like(X)
-
-    for i in range(X.shape[0]):
-        for j in range(X.shape[1]):
-            point = torch.tensor([X[i, j], Y[i, j]], dtype=torch.float32)
-            Z[i, j] = problem.loss(point).item()
-
-    # Contour plot
-    fig.add_trace(
-        go.Contour(
-            x=x,
-            y=y,
-            z=Z,
-            colorscale=[[0, "#e3f2fd"], [0.5, "#2196f3"], [1, "#0d47a1"]],
-            showscale=False,
-            contours=dict(
-                start=0,
-                end=Z.max(),
-                size=Z.max() / 15,
-            ),
-        ),
-        row=1,
-        col=1,
-    )
-
-    # Add optimization path
-    if len(trajectory) > 0:
-        colors = np.linspace(0, 1, len(trajectory))
-
-        for i in range(1, len(trajectory)):
-            fig.add_trace(
-                go.Scatter(
-                    x=[trajectory[i - 1, 0], trajectory[i, 0]],
-                    y=[trajectory[i - 1, 1], trajectory[i, 1]],
-                    mode="lines",
-                    line=dict(color=f"rgba(255, {int(111 * (1 - colors[i]))}, 0, {0.3 + 0.7 * colors[i]})", width=3),
-                    showlegend=False,
-                    hoverinfo="skip",
-                ),
-                row=1,
-                col=1,
-            )
-
-        # Start and end points
-        fig.add_trace(
-            go.Scatter(
-                x=[trajectory[0, 0]],
-                y=[trajectory[0, 1]],
-                mode="markers+text",
-                marker=dict(size=12, color="#4caf50", line=dict(color="white", width=2)),
-                text=["Start"],
-                textposition="top center",
-                showlegend=False,
-            ),
-            row=1,
-            col=1,
-        )
-
-        fig.add_trace(
-            go.Scatter(
-                x=[trajectory[-1, 0]],
-                y=[trajectory[-1, 1]],
-                mode="markers+text",
-                marker=dict(size=12, color="#ff6f00", line=dict(color="white", width=2)),
-                text=["End"],
-                textposition="top center",
-                showlegend=False,
-            ),
-            row=1,
-            col=1,
-        )
-
-    # 2. Pipeline visualization
-    block_x = []
-    block_y = []
-    block_text = []
-    block_colors = []
-
-    for i, comp_id in enumerate(pipeline):
-        block_x.append(i / (len(pipeline) - 1) if len(pipeline) > 1 else 0.5)
-        block_y.append(0.5)
-
-        comp_info, comp_color = get_component_info(comp_id)
-        block_text.append(comp_info["icon"] if comp_info else "?")
-        block_colors.append(comp_color)
-
-    fig.add_trace(
-        go.Scatter(
-            x=block_x,
-            y=block_y,
-            mode="markers+text",
-            marker=dict(size=40, color=block_colors, line=dict(color="white", width=2)),
-            text=block_text,
-            textposition="middle center",
-            showlegend=False,
-            hoverinfo="skip",
-        ),
-        row=1,
-        col=2,
-    )
-
-    # Add arrows between blocks
-    for i in range(len(pipeline) - 1):
-        fig.add_annotation(
-            x=block_x[i + 1],
-            y=0.5,
-            ax=block_x[i],
-            ay=0.5,
-            xref="x2",
-            yref="y2",
-            axref="x2",
-            ayref="y2",
-            showarrow=True,
-            arrowhead=2,
-            arrowsize=1,
-            arrowwidth=2,
-            arrowcolor="#ff6f00",
-            row=1,
-            col=2,
-        )
-
-    # 3. Loss curve
-    fig.add_trace(
-        go.Scatter(
-            x=list(range(len(losses))),
-            y=losses,
-            mode="lines",
-            line=dict(color="#ff6f00", width=3),
-            fill="tozeroy",
-            fillcolor="rgba(255, 111, 0, 0.1)",
-            showlegend=False,
-        ),
-        row=2,
-        col=1,
-    )
-
-    # 4. Learning dynamics (gradient norm)
-    if gradients:
-        grad_norms = [np.linalg.norm(g) for g in gradients]
-        fig.add_trace(
-            go.Scatter(
-                x=list(range(len(grad_norms))),
-                y=grad_norms,
-                mode="lines",
-                line=dict(color="#2196f3", width=2),
-                fill="tozeroy",
-                fillcolor="rgba(33, 150, 243, 0.1)",
-                showlegend=False,
-            ),
-            row=2,
-            col=2,
-        )
-
-    # Update layout
-    fig.update_layout(
-        height=700,
-        showlegend=False,
-        paper_bgcolor="white",
-        plot_bgcolor="white",
-        margin=dict(l=40, r=40, t=60, b=40),
-    )
-
-    # Update axes
-    fig.update_xaxes(showgrid=True, gridcolor="#f0f0f0")
-    fig.update_yaxes(showgrid=True, gridcolor="#f0f0f0")
-
-    # Pipeline plot
-    fig.update_xaxes(showticklabels=False, showgrid=False, row=1, col=2)
-    fig.update_yaxes(showticklabels=False, showgrid=False, range=[0, 1], row=1, col=2)
-
-    # Loss plot
-    fig.update_xaxes(title_text="Iteration", row=2, col=1)
-    fig.update_yaxes(title_text="Loss", type="log", row=2, col=1)
-
-    # Gradient plot
-    fig.update_xaxes(title_text="Iteration", row=2, col=2)
-    fig.update_yaxes(title_text="Gradient Norm", row=2, col=2)
-
-    return fig
-
-
-def create_highdim_visualization(problem_name, trajectory, losses, gradients, pipeline):
-    """Create visualization for high-dimensional problems using PCA"""
-    problem = PROBLEMS[problem_name]
-
-    # Create subplots
-    fig = make_subplots(
-        rows=2,
-        cols=2,
-        subplot_titles=("PCA Trajectory Projection", "Pipeline Architecture", "Loss Curve", "Learning Dynamics"),
-        column_widths=[0.6, 0.4],
-        row_heights=[0.6, 0.4],
-        specs=[[{"type": "contour"}, {"type": "scatter"}], [{"type": "scatter"}, {"type": "scatter"}]],
-    )
-
-    # 1. PCA projection of trajectory
-    if len(trajectory) > 2:
-        # Fit PCA on trajectory
-        trajectory_array = np.array(trajectory)
-        pca = PCA(n_components=min(2, trajectory_array.shape[1]))
-        trajectory_2d = pca.fit_transform(trajectory_array)
-
-        # Create loss landscape in PCA space
-        # Determine bounds based on trajectory
-        margin = 0.2
-        x_min, x_max = trajectory_2d[:, 0].min(), trajectory_2d[:, 0].max()
-        x_range = x_max - x_min
-        x_min -= margin * x_range
-        x_max += margin * x_range
-
-        if trajectory_2d.shape[1] > 1:
-            y_min, y_max = trajectory_2d[:, 1].min(), trajectory_2d[:, 1].max()
-            y_range = y_max - y_min
-            y_min -= margin * y_range
-            y_max += margin * y_range
-        else:
-            y_min, y_max = -1, 1
-
-        # Create grid in PCA space
-        n_points = 50
-        x_grid = np.linspace(x_min, x_max, n_points)
-        y_grid = np.linspace(y_min, y_max, n_points)
-        X_grid, Y_grid = np.meshgrid(x_grid, y_grid)
-
-        # Compute losses on grid
-        Z_grid = np.zeros_like(X_grid)
-        mean_trajectory = pca.mean_
-
-        for i in range(n_points):
-            for j in range(n_points):
-                # Map 2D point back to high-dimensional space
-                pca_coords = np.array([X_grid[i, j], Y_grid[i, j]])
-                if trajectory_2d.shape[1] == 1:
-                    pca_coords = pca_coords[:1]  # Use only first coordinate
-
-                # Reconstruct high-dimensional point
-                high_dim_point = mean_trajectory + pca_coords @ pca.components_[: len(pca_coords)]
-
-                # Evaluate loss
-                x_tensor = torch.tensor(high_dim_point, dtype=torch.float32)
-                Z_grid[i, j] = problem.loss(x_tensor).item()
-
-        # Add contour plot
-        fig.add_trace(
-            go.Contour(
-                x=x_grid,
-                y=y_grid,
-                z=Z_grid,
-                colorscale=[[0, "#e3f2fd"], [0.5, "#2196f3"], [1, "#0d47a1"]],
-                showscale=False,
-                contours=dict(
-                    start=Z_grid.min(),
-                    end=Z_grid.max(),
-                    size=(Z_grid.max() - Z_grid.min()) / 15,
-                ),
-            ),
-            row=1,
-            col=1,
-        )
-
-        # Add trajectory on top of contour
-        colors = np.linspace(0, 1, len(trajectory_2d))
-
-        for i in range(1, len(trajectory_2d)):
-            fig.add_trace(
-                go.Scatter(
-                    x=[trajectory_2d[i - 1, 0], trajectory_2d[i, 0]],
-                    y=[trajectory_2d[i - 1, 1] if trajectory_2d.shape[1] > 1 else [0, 0]],
-                    mode="lines",
-                    line=dict(color=f"rgba(255, {int(111 * (1 - colors[i]))}, 0, {0.3 + 0.7 * colors[i]})", width=3),
-                    showlegend=False,
-                    hoverinfo="skip",
-                ),
-                row=1,
-                col=1,
-            )
-
-        # Start and end points
-        fig.add_trace(
-            go.Scatter(
-                x=[trajectory_2d[0, 0]],
-                y=[trajectory_2d[0, 1] if trajectory_2d.shape[1] > 1 else 0],
-                mode="markers+text",
-                marker=dict(size=12, color="#4caf50", line=dict(color="white", width=2)),
-                text=["Start"],
-                textposition="top center",
-                showlegend=False,
-            ),
-            row=1,
-            col=1,
-        )
-
-        fig.add_trace(
-            go.Scatter(
-                x=[trajectory_2d[-1, 0]],
-                y=[trajectory_2d[-1, 1] if trajectory_2d.shape[1] > 1 else 0],
-                mode="markers+text",
-                marker=dict(size=12, color="#ff6f00", line=dict(color="white", width=2)),
-                text=["End"],
-                textposition="top center",
-                showlegend=False,
-            ),
-            row=1,
-            col=1,
-        )
-
-        # Add explained variance text
-        if trajectory_2d.shape[1] > 1:
-            explained_var = pca.explained_variance_ratio_
-            fig.add_annotation(
-                x=0.5,
-                y=1.1,
-                xref="x domain",
-                yref="y domain",
-                text=f"Explained variance: PC1={explained_var[0]:.1%}, PC2={explained_var[1]:.1%}",
-                showarrow=False,
-                row=1,
-                col=1,
-            )
-
-    # 2. Pipeline visualization (same as 2D)
-    block_x = []
-    block_y = []
-    block_text = []
-    block_colors = []
-
-    for i, comp_id in enumerate(pipeline):
-        block_x.append(i / (len(pipeline) - 1) if len(pipeline) > 1 else 0.5)
-        block_y.append(0.5)
-
-        comp_info, comp_color = get_component_info(comp_id)
-        block_text.append(comp_info["icon"] if comp_info else "?")
-        block_colors.append(comp_color)
-
-    fig.add_trace(
-        go.Scatter(
-            x=block_x,
-            y=block_y,
-            mode="markers+text",
-            marker=dict(size=40, color=block_colors, line=dict(color="white", width=2)),
-            text=block_text,
-            textposition="middle center",
-            showlegend=False,
-            hoverinfo="skip",
-        ),
-        row=1,
-        col=2,
-    )
-
-    # Add arrows between blocks
-    for i in range(len(pipeline) - 1):
-        fig.add_annotation(
-            x=block_x[i + 1],
-            y=0.5,
-            ax=block_x[i],
-            ay=0.5,
-            xref="x2",
-            yref="y2",
-            axref="x2",
-            ayref="y2",
-            showarrow=True,
-            arrowhead=2,
-            arrowsize=1,
-            arrowwidth=2,
-            arrowcolor="#ff6f00",
-            row=1,
-            col=2,
-        )
-
-    # 3. Loss curve
-    fig.add_trace(
-        go.Scatter(
-            x=list(range(len(losses))),
-            y=losses,
-            mode="lines",
-            line=dict(color="#ff6f00", width=3),
-            fill="tozeroy",
-            fillcolor="rgba(255, 111, 0, 0.1)",
-            showlegend=False,
-        ),
-        row=2,
-        col=1,
-    )
-
-    # 4. Learning dynamics (gradient norm)
-    if gradients:
-        grad_norms = [np.linalg.norm(g) for g in gradients]
-        fig.add_trace(
-            go.Scatter(
-                x=list(range(len(grad_norms))),
-                y=grad_norms,
-                mode="lines",
-                line=dict(color="#2196f3", width=2),
-                fill="tozeroy",
-                fillcolor="rgba(33, 150, 243, 0.1)",
-                showlegend=False,
-            ),
-            row=2,
-            col=2,
-        )
-
-    # Update layout
-    fig.update_layout(
-        height=700,
-        showlegend=False,
-        paper_bgcolor="white",
-        plot_bgcolor="white",
-        margin=dict(l=40, r=40, t=60, b=40),
-    )
-
-    # Update axes
-    fig.update_xaxes(showgrid=True, gridcolor="#f0f0f0")
-    fig.update_yaxes(showgrid=True, gridcolor="#f0f0f0")
-
-    # PCA plot
-    fig.update_xaxes(title_text="First Principal Component", row=1, col=1)
-    fig.update_yaxes(title_text="Second Principal Component", row=1, col=1)
-
-    # Pipeline plot
-    fig.update_xaxes(showticklabels=False, showgrid=False, row=1, col=2)
-    fig.update_yaxes(showticklabels=False, showgrid=False, range=[0, 1], row=1, col=2)
-
-    # Loss plot
-    fig.update_xaxes(title_text="Iteration", row=2, col=1)
-    fig.update_yaxes(title_text="Loss", type="log", row=2, col=1)
-
-    # Gradient plot
-    fig.update_xaxes(title_text="Iteration", row=2, col=2)
-    fig.update_yaxes(title_text="Gradient Norm", row=2, col=2)
-
-    return fig
-
-
-def create_app():
-    with gr.Blocks(theme=gr.themes.Base()) as app:
-        # Custom CSS
-        gr.HTML("""
-        <style>
-        .component-block {
-            background: white;
-            border: 2px solid #e0e0e0;
-            border-radius: 8px;
-            padding: 12px;
-            margin: 8px 4px;
-            cursor: pointer;
-            transition: all 0.2s;
-            text-align: center;
-            display: inline-block;
-        }
-        .component-block:hover {
-            transform: translateY(-2px);
-            box-shadow: 0 4px 12px rgba(0,0,0,0.15);
-            border-color: #ff6f00;
-        }
-        .category-header {
-            background: #f5f5f5;
-            padding: 8px 16px;
-            margin: 16px 0 8px 0;
-            border-radius: 8px;
-            font-weight: 600;
-            font-size: 14px;
-            color: #616161;
-        }
-        </style>
-        """)
-
-        # Header
-        gr.Markdown("""
-        # 🧩 HeavyBall Chainable Optimizer Playground
-
-        ### Build custom optimizers by combining components like LEGO blocks!
-
-        Click components to add them to your pipeline. Each component transforms the gradient in a specific way - stack them to create powerful optimization algorithms!
-        """)
-
-        # Hidden state for pipeline
-        pipeline_state = gr.State(["gradient_input"])
-
-        with gr.Row():
-            # Left column - Component palette
-            with gr.Column(scale=1):
-                gr.Markdown("### 🎨 Component Palette")
-                gr.Markdown("*Click blocks to add to pipeline*")
-
-                # Component buttons organized by category
-                for cat_id, category in OPTIMIZER_BLOCKS.items():
-                    if cat_id == "gradient":  # Skip gradient input in palette
-                        continue
-
-                    gr.HTML(f'<div class="category-header">{category["name"]}</div>')
-
-                    with gr.Row():
-                        for comp in category["components"]:
-                            btn = gr.Button(
-                                value=f"{comp['icon']} {comp['name']}", elem_id=f"btn_{comp['id']}", size="sm"
-                            )
-                            # Store component ID in button for click handler
-                            btn.click(
-                                fn=lambda p, cid=comp["id"]: p + [cid],
-                                inputs=[pipeline_state],
-                                outputs=[pipeline_state],
-                            )
-
-                # Recipe selector
-                gr.Markdown("### 📚 Preset Recipes")
-                recipe_dropdown = gr.Dropdown(choices=list(RECIPES.keys()), value=None, label="Load a preset optimizer")
-                load_recipe_btn = gr.Button("Load Recipe", size="sm")
-
-            # Center column - Main visualization
-            with gr.Column(scale=2):
-                # Pipeline builder
-                gr.Markdown("### 🔧 Pipeline Builder")
-                pipeline_display = gr.HTML()
-
-                with gr.Row():
-                    clear_pipeline_btn = gr.Button("🗑️ Clear Pipeline", size="sm", variant="secondary")
-                    refresh_btn = gr.Button("🔄 Refresh Display", size="sm")
-
-                # Visualization
-                viz_plot = gr.Plot(label="")
-
-                # Run button
-                run_btn = gr.Button("🚀 Run Optimization", variant="primary", size="lg")
-
-            # Right column - Parameters and metrics
-            with gr.Column(scale=1):
-                gr.Markdown("### ⚙️ Parameters")
-
-                problem_select = gr.Dropdown(choices=list(PROBLEMS.keys()), value="Rosenbrock (2D)", label="Problem")
-
-                lr_slider = gr.Slider(minimum=-4, maximum=-1, value=-2, step=0.1, label="Learning Rate (10^x)")
-
-                steps_slider = gr.Slider(minimum=10, maximum=500, value=200, step=10, label="Steps")
-
-                # Component-specific parameters
-                with gr.Accordion("Advanced Parameters", open=False):
-                    beta_slider = gr.Slider(minimum=0.0, maximum=0.999, value=0.9, step=0.001, label="Momentum β")
-                    beta2_slider = gr.Slider(minimum=0.0, maximum=0.999, value=0.999, step=0.001, label="Adam β₂")
-                    eps_slider = gr.Slider(minimum=1e-8, maximum=1e-4, value=1e-8, step=1e-8, label="Epsilon")
-
-                    # Weight decay parameters
-                    weight_decay_slider = gr.Slider(
-                        minimum=0.0, maximum=0.1, value=0.01, step=0.001, label="Weight Decay"
-                    )
-                    ema_beta_slider = gr.Slider(
-                        minimum=0.9, maximum=0.999, value=0.999, step=0.001, label="EMA β (for weight decay)"
-                    )
-
-                    # Gradient clipping
-                    max_norm_slider = gr.Slider(
-                        minimum=0.1, maximum=10.0, value=1.0, step=0.1, label="Gradient Clip Norm"
-                    )
-
-                    # Preconditioning parameters
-                    shampoo_beta_slider = gr.Slider(
-                        minimum=0.9, maximum=0.999, value=0.99, step=0.001, label="Shampoo β"
-                    )
-                    precond_lr_slider = gr.Slider(
-                        minimum=0.01, maximum=1.0, value=0.1, step=0.01, label="Preconditioner LR"
-                    )
-                    precondition_frequency_slider = gr.Slider(
-                        minimum=1, maximum=100, value=10, step=1, label="Precondition Frequency"
-                    )
-                    rank_slider = gr.Slider(minimum=1, maximum=32, value=4, step=1, label="Low-rank Approximation Rank")
-                    param_count_slider = gr.Slider(
-                        minimum=1000, maximum=100000, value=10000, step=1000, label="Param Count (PSGD LRA)"
-                    )
-
-                    # Adaptive LR parameters
-                    initial_d_slider = gr.Slider(
-                        minimum=0.1, maximum=10.0, value=1.0, step=0.1, label="Initial D (D-adaptation)"
-                    )
-                    lr_lr_slider = gr.Slider(minimum=0.01, maximum=1.0, value=0.1, step=0.01, label="Learning Rate LR")
-
-                    # Special method parameters
-                    r_slider = gr.Slider(minimum=0.0, maximum=1.0, value=0.0, step=0.1, label="Schedule-Free r")
-                    weight_lr_power_slider = gr.Slider(
-                        minimum=0.0, maximum=4.0, value=2.0, step=0.1, label="Weight LR Power"
-                    )
-                    sam_step_size_slider = gr.Slider(
-                        minimum=0.01, maximum=0.5, value=0.05, step=0.01, label="SAM Step Size"
-                    )
-                    beta2_scale_slider = gr.Slider(
-                        minimum=0.5, maximum=1.0, value=0.8, step=0.01, label="PALM β₂ Scale"
-                    )
-
-                    # Sign SGD parameters
-                    graft_checkbox = gr.Checkbox(value=True, label="Graft (Sign SGD)")
-
-                gr.Markdown("### 📊 Metrics")
-
-                final_loss_display = gr.Textbox(label="Final Loss", value="-")
-                convergence_display = gr.Textbox(label="Steps to Converge", value="-")
-
-        # Footer
-        gr.Markdown("""
-        ---
-        ### 💡 How it works:
-
-        1. **Start with Gradient** - Every pipeline begins with raw gradients
-        2. **Add Transforms** - Click components to add them to your pipeline
-        3. **Order Matters** - Components are applied in sequence
-        4. **Run & Compare** - See how different combinations perform!
-
-        **Example combinations:**
-        - Adam = Gradient → Adam Scaling
-        - AdamW = Gradient → Adam Scaling → Weight Decay
-        - Momentum SGD = Gradient → Heavy Ball
-        """)
-
-        # Event handlers
-        def update_display(pipeline):
-            return create_pipeline_display(pipeline)
-
-        def load_recipe(recipe_name):
-            if recipe_name in RECIPES:
-                return RECIPES[recipe_name].copy()
-            return ["gradient_input"]
-
-        def clear_pipeline():
-            return ["gradient_input"]
-
-        def remove_block(pipeline, index):
-            """Remove a block from the pipeline"""
-            if 0 <= index < len(pipeline) and pipeline[index] != "gradient_input":
-                new_pipeline = pipeline.copy()
-                new_pipeline.pop(index)
-                return new_pipeline
-            return pipeline
-
-        def run_optimization_handler(
-            problem,
-            pipeline,
-            steps,
-            lr,
-            beta,
-            beta2,
-            eps,
-            weight_decay,
-            ema_beta,
-            max_norm,
-            shampoo_beta,
-            precond_lr,
-            precondition_frequency,
-            rank,
-            param_count,
-            initial_d,
-            lr_lr,
-            r,
-            weight_lr_power,
-            sam_step_size,
-            beta2_scale,
-            graft,
-        ):
-            """Run optimization with current pipeline"""
-            if not pipeline or len(pipeline) == 1:
-                pipeline = ["gradient_input"]
-
-            # Run optimization with all parameters
-            fig, metrics = run_optimization(
-                problem,
-                pipeline,
-                steps,
-                lr=lr,
-                beta=beta,
-                betas=(beta, beta2),
-                beta2=beta2,
-                eps=eps,
-                weight_decay_to_ema=weight_decay,
-                weight_decay_to_init=weight_decay,
-                ema_beta=ema_beta,
-                max_norm=max_norm,
-                shampoo_beta=shampoo_beta,
-                precond_lr=precond_lr,
-                precondition_frequency=precondition_frequency,
-                rank=rank,
-                param_count=param_count,
-                initial_d=initial_d,
-                lr_lr=lr_lr,
-                r=r,
-                weight_lr_power=weight_lr_power,
-                sam_step_size=sam_step_size,
-                beta2_scale=beta2_scale,
-                graft=graft,
-            )
-
-            return fig, f"{metrics['final_loss']:.2e}", str(metrics["steps_to_converge"])
-
-        # Connect events
-        # Update display when pipeline changes
-        pipeline_state.change(fn=update_display, inputs=[pipeline_state], outputs=[pipeline_display])
-
-        # Recipe loading
-        load_recipe_btn.click(fn=load_recipe, inputs=[recipe_dropdown], outputs=[pipeline_state])
-
-        # Clear pipeline
-        clear_pipeline_btn.click(fn=clear_pipeline, outputs=[pipeline_state])
-
-        # Refresh display
-        refresh_btn.click(fn=update_display, inputs=[pipeline_state], outputs=[pipeline_display])
-
-        # Run optimization
-        run_btn.click(
-            fn=run_optimization_handler,
-            inputs=[
-                problem_select,
-                pipeline_state,
-                steps_slider,
-                lr_slider,
-                beta_slider,
-                beta2_slider,
-                eps_slider,
-                weight_decay_slider,
-                ema_beta_slider,
-                max_norm_slider,
-                shampoo_beta_slider,
-                precond_lr_slider,
-                precondition_frequency_slider,
-                rank_slider,
-                param_count_slider,
-                initial_d_slider,
-                lr_lr_slider,
-                r_slider,
-                weight_lr_power_slider,
-                sam_step_size_slider,
-                beta2_scale_slider,
-                graft_checkbox,
-            ],
-            outputs=[viz_plot, final_loss_display, convergence_display],
-        )
-
-        # Add JavaScript for removing blocks
-        app.load(
-            None,
-            None,
-            None,
-            js="""
-            function() {
-                // Function to remove pipeline blocks
-                window.removePipelineBlock = function(index) {
-                    // This would need to trigger a Gradio event
-                    console.log('Remove block at index:', index);
-                    // In a real implementation, this would update the pipeline state
-                };
-
-                console.log('Playground initialized');
-            }
-            """,
-        )
-
-        # Initialize display
-        app.load(
-            fn=lambda: (
-                create_pipeline_display(["gradient_input"]),
-                run_optimization("Rosenbrock (2D)", ["gradient_input", "adam_scale"], 200, lr=-2)[0],
-            ),
-            outputs=[pipeline_display, viz_plot],
-        )
-
-    return app
-
-
-if __name__ == "__main__":
-    app = create_app()
-    app.launch(share=False)
diff --git a/interactive/static/init-globals.js b/interactive/static/init-globals.js
deleted file mode 100644
index b820bc9..0000000
--- a/interactive/static/init-globals.js
+++ /dev/null
@@ -1,2 +0,0 @@
-// This file initializes global variables for the node editor
-// It will be populated by Python when the page loads
diff --git a/interactive/static/node-editor.js b/interactive/static/node-editor.js
deleted file mode 100644
index 525597f..0000000
--- a/interactive/static/node-editor.js
+++ /dev/null
@@ -1,570 +0,0 @@
-console.log('Node editor script starting execution...');
-
-class NodeEditor {
-    constructor(containerId) {
-        this.container = document.getElementById(containerId);
-        this.canvas = document.getElementById('canvas');
-        this.palette = document.getElementById('palette');
-        this.inspector = document.getElementById('inspector');
-        this.nodes = [];
-        this.connections = [];
-        this.selectedNode = null;
-        this.draggingNode = null;
-        this.connecting = null;
-        this.nodeIdCounter = 0;
-        this.offset = { x: 0, y: 0 };
-
-        this.init();
-    }
-
-    init() {
-        // Set up SVG for connections
-        this.svg = document.createElementNS('http://www.w3.org/2000/svg', 'svg');
-        this.svg.style.position = 'absolute';
-        this.svg.style.width = '100%';
-        this.svg.style.height = '100%';
-        this.svg.style.pointerEvents = 'none';
-        this.svg.style.zIndex = '1';
-        this.svg.style.top = '0';
-        this.svg.style.left = '0';
-        this.canvas.appendChild(this.svg);
-
-        // Set up event listeners
-        this.setupPalette();
-        this.setupCanvas();
-
-        // Add gradient input node by default
-        this.addNode('gradient_input', 100, 300);
-    }
-
-    setupPalette() {
-        // Make palette items draggable
-        const items = this.palette.querySelectorAll('.palette-item');
-        items.forEach(item => {
-            item.draggable = true;
-            item.addEventListener('dragstart', (e) => this.onPaletteDragStart(e));
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-
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-        this.canvas.addEventListener('mouseup', (e) => this.onCanvasMouseUp(e));
-    }
-
-    onPaletteDragStart(e) {
-        e.target.classList.add('dragging');
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-        e.dataTransfer.setData('nodeType', e.target.dataset.type);
-    }
-
-    onPaletteDragEnd(e) {
-        e.target.classList.remove('dragging');
-    }
-
-    onCanvasDrop(e) {
-        e.preventDefault();
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-            const rect = this.canvas.getBoundingClientRect();
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-            this.updateCodePreview();
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-        console.log(`Adding node: type=${type}, x=${x}, y=${y}`);
-        const nodeId = `node-${this.nodeIdCounter++}`;
-        const nodeData = window.CHAINABLE_FUNCTIONS[type] || {
-            description: type === 'gradient_input' ? 'Gradient Input' : 'Unknown',
-            color: '#666',
-            inputs: type === 'gradient_input' ? [] : ['grad'],
-            outputs: type === 'gradient_input' ? ['grad'] : []
-        };
-
-        const node = document.createElement('div');
-        node.className = 'node';
-        node.id = nodeId;
-        node.style.left = x + 'px';
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-        node.style.setProperty('--node-color', nodeData.color);
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-        node.style.borderLeftWidth = '4px';
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-
-        console.log('Canvas element:', this.canvas);
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-
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-        node.addEventListener('mousedown', (e) => this.onNodeMouseDown(e, nodeId));
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-        });
-
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-
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-            portType: portType,
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-            startY: rect.top + rect.height / 2 - canvasRect.top
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-
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-        this.svg.appendChild(line);
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-    onCanvasMouseMove(e) {
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-            this.updateConnections();
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-
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-
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-        if (this.connecting) {
-            const preview = document.getElementById('preview-connection');
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-
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-            if (target && target.classList.contains('node-port')) {
-                const targetNode = target.closest('.node');
-                const targetNodeId = targetNode.id;
-                const targetPortType = target.classList.contains('node-port-input') ? 'input' : 'output';
-
-                // Validate connection
-                if (this.canConnect(this.connecting.nodeId, this.connecting.portType, targetNodeId, targetPortType)) {
-                    this.addConnection(this.connecting.nodeId, this.connecting.portType, targetNodeId, targetPortType);
-                    this.updateCodePreview();
-                }
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-
-            this.connecting = null;
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-
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-        // Can't connect to same node
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-
-        // Must connect output to input
-        if (fromPortType === toPortType) return false;
-
-        // Check if connection already exists
-        const exists = this.connections.some(c =>
-            (c.from.nodeId === fromNodeId && c.to.nodeId === toNodeId) ||
-            (c.from.nodeId === toNodeId && c.to.nodeId === fromNodeId)
-        );
-
-        return !exists;
-    }
-
-    addConnection(fromNodeId, fromPortType, toNodeId, toPortType) {
-        // Ensure output connects to input
-        if (fromPortType === 'input') {
-            [fromNodeId, toNodeId] = [toNodeId, fromNodeId];
-            [fromPortType, toPortType] = [toPortType, fromPortType];
-        }
-
-        const connection = {
-            from: { nodeId: fromNodeId, portType: fromPortType },
-            to: { nodeId: toNodeId, portType: toPortType },
-            element: null
-        };
-
-        const line = document.createElementNS('http://www.w3.org/2000/svg', 'path');
-        line.classList.add('connection');
-        line.classList.add('animated');
-        this.svg.appendChild(line);
-
-        connection.element = line;
-        this.connections.push(connection);
-
-        this.updateConnections();
-    }
-
-    updateConnections() {
-        this.connections.forEach(conn => {
-            const fromNode = this.nodes.find(n => n.id === conn.from.nodeId);
-            const toNode = this.nodes.find(n => n.id === conn.to.nodeId);
-
-            if (fromNode && toNode) {
-                const fromPort = fromNode.element.querySelector('.node-port-output');
-                const toPort = toNode.element.querySelector('.node-port-input');
-
-                if (fromPort && toPort) {
-                    const fromRect = fromPort.getBoundingClientRect();
-                    const toRect = toPort.getBoundingClientRect();
-                    const canvasRect = this.canvas.getBoundingClientRect();
-
-                    const x1 = fromRect.left + fromRect.width / 2 - canvasRect.left;
-                    const y1 = fromRect.top + fromRect.height / 2 - canvasRect.top;
-                    const x2 = toRect.left + toRect.width / 2 - canvasRect.left;
-                    const y2 = toRect.top + toRect.height / 2 - canvasRect.top;
-
-                    const path = this.createConnectionPath(x1, y1, x2, y2);
-                    conn.element.setAttribute('d', path);
-
-                    // Store path coordinates for particle animation
-                    conn.pathCoords = { x1, y1, x2, y2 };
-                }
-            }
-        });
-    }
-
-    // Animate gradient flow particles
-    startGradientFlow() {
-        if (this.flowInterval) return;
-
-        this.flowInterval = setInterval(() => {
-            this.connections.forEach(conn => {
-                if (conn.pathCoords) {
-                    this.createFlowParticle(conn.pathCoords);
-                }
-            });
-        }, 500);
-    }
-
-    stopGradientFlow() {
-        if (this.flowInterval) {
-            clearInterval(this.flowInterval);
-            this.flowInterval = null;
-        }
-
-        // Remove all particles
-        const particles = this.canvas.querySelectorAll('.flow-particle');
-        particles.forEach(p => p.remove());
-    }
-
-    createFlowParticle(coords) {
-        const particle = document.createElement('div');
-        particle.className = 'flow-particle';
-        particle.style.left = coords.x1 + 'px';
-        particle.style.top = coords.y1 + 'px';
-        this.canvas.appendChild(particle);
-
-        // Animate along bezier curve
-        const duration = 2000;
-        const startTime = Date.now();
-
-        const animate = () => {
-            const elapsed = Date.now() - startTime;
-            const t = Math.min(elapsed / duration, 1);
-
-            if (t >= 1) {
-                particle.remove();
-                return;
-            }
-
-            // Calculate position on bezier curve
-            const dx = Math.abs(coords.x2 - coords.x1);
-            const cp1x = coords.x1 + dx * 0.5;
-            const cp2x = coords.x2 - dx * 0.5;
-
-            // Bezier curve formula
-            const x = Math.pow(1-t, 3) * coords.x1 +
-                     3 * Math.pow(1-t, 2) * t * cp1x +
-                     3 * (1-t) * Math.pow(t, 2) * cp2x +
-                     Math.pow(t, 3) * coords.x2;
-
-            const y = Math.pow(1-t, 3) * coords.y1 +
-                     3 * Math.pow(1-t, 2) * t * coords.y1 +
-                     3 * (1-t) * Math.pow(t, 2) * coords.y2 +
-                     Math.pow(t, 3) * coords.y2;
-
-            particle.style.left = x + 'px';
-            particle.style.top = y + 'px';
-            particle.style.opacity = Math.sin(t * Math.PI);
-
-            requestAnimationFrame(animate);
-        };
-
-        requestAnimationFrame(animate);
-    }
-
-    createConnectionPath(x1, y1, x2, y2) {
-        const dx = Math.abs(x2 - x1);
-        const cp1x = x1 + dx * 0.5;
-        const cp2x = x2 - dx * 0.5;
-        return `M ${x1} ${y1} C ${cp1x} ${y1}, ${cp2x} ${y2}, ${x2} ${y2}`;
-    }
-
-    selectNode(nodeId) {
-        // Deselect previous
-        if (this.selectedNode) {
-            this.selectedNode.element.classList.remove('selected');
-        }
-
-        // Select new
-        const node = this.nodes.find(n => n.id === nodeId);
-        if (node) {
-            node.element.classList.add('selected');
-            this.selectedNode = node;
-            this.showInspector(node);
-        }
-    }
-
-    showInspector(node) {
-        this.inspector.classList.add('active');
-
-        const nodeData = window.CHAINABLE_FUNCTIONS[node.type];
-        if (!nodeData || !nodeData.params) return;
-
-        // Build inspector content
-        let html = `<h3>${node.type.replace(/_/g, ' ')}</h3>`;
-
-        Object.entries(nodeData.params).forEach(([key, defaultValue]) => {
-            const value = node.params[key] || defaultValue;
-            html += `
-                <div class="inspector-field">
-                    <div class="inspector-label">${key}</div>
-                    <input class="inspector-input"
-                           type="${typeof defaultValue === 'number' ? 'number' : 'text'}"
-                           data-param="${key}"
-                           value="${value}"
-                           step="${typeof defaultValue === 'number' ? '0.001' : ''}"
-                    />
-                </div>
-            `;
-        });
-
-        this.inspector.innerHTML = html;
-
-        // Set up parameter change listeners
-        this.inspector.querySelectorAll('.inspector-input').forEach(input => {
-            input.addEventListener('change', (e) => {
-                const param = e.target.dataset.param;
-                let value = e.target.value;
-
-                // Convert to appropriate type
-                if (e.target.type === 'number') {
-                    value = parseFloat(value);
-                }
-
-                node.params[param] = value;
-                this.updateCodePreview();
-            });
-        });
-    }
-
-    updateCodePreview() {
-        const codePreview = document.getElementById('code-output');
-        if (!codePreview) return;
-
-        // Generate Python code from pipeline
-        const pipelineData = this.exportPipeline();
-        const nodes = pipelineData.nodes.filter(n => n.type !== 'gradient_input');
-
-        if (nodes.length === 0) {
-            codePreview.textContent = '# Add optimizer components to build your pipeline';
-            return;
-        }
-
-        let code = 'optimizer = BaseOpt(\n';
-        code += '    model.parameters(),\n';
-        code += '    lr=0.001,\n';
-
-        // Add relevant parameters
-        const params = {};
-        nodes.forEach(node => {
-            Object.assign(params, node.params);
-        });
-
-        Object.entries(params).forEach(([key, value]) => {
-            if (typeof value === 'string') {
-                code += `    ${key}="${value}",\n`;
-            } else {
-                code += `    ${key}=${value},\n`;
-            }
-        });
-
-        code += '    fns=[\n';
-        nodes.forEach(node => {
-            code += `        ${node.type},\n`;
-        });
-        code += '    ]\n';
-        code += ')';
-
-        codePreview.textContent = code;
-
-        // Update hidden pipeline data
-        const pipelineInput = document.getElementById('pipeline-data');
-        if (pipelineInput) {
-            pipelineInput.value = JSON.stringify(pipelineData);
-        }
-    }
-
-    exportPipeline() {
-        return {
-            nodes: this.nodes.map(n => ({
-                id: n.id,
-                type: n.type,
-                x: n.x,
-                y: n.y,
-                params: n.params
-            })),
-            connections: this.connections.map(c => ({
-                from: c.from,
-                to: c.to
-            }))
-        };
-    }
-
-    loadRecipe(recipe) {
-        // Clear existing nodes except gradient input
-        this.nodes = this.nodes.filter(n => n.type === 'gradient_input');
-        this.connections = [];
-        this.selectedNode = null;
-
-        // Clear canvas except gradient input
-        const nodesToRemove = this.canvas.querySelectorAll('.node:not([id="node-0"])');
-        nodesToRemove.forEach(n => n.remove());
-
-        // Clear connections
-        this.svg.innerHTML = '';
-
-        // Add nodes from recipe
-        let lastNodeId = 'node-0'; // gradient input
-        let x = 300;
-        const y = 300;
-
-        recipe.forEach((item, index) => {
-            const nodeId = this.addNode(item.name, x, y);
-            const node = this.nodes.find(n => n.id === nodeId);
-
-            // Set parameters
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-                node.params = item.params;
-            }
-
-            // Connect to previous node
-            this.addConnection(lastNodeId, 'output', nodeId, 'input');
-
-            lastNodeId = nodeId;
-            x += 200;
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-
-        this.updateCodePreview();
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-}
-
-// Initialize when DOM is ready
-function initializeNodeEditor() {
-    try {
-        console.log('Attempting to initialize NodeEditor...');
-        const editorElement = document.getElementById('node-editor');
-        if (!editorElement) {
-            console.error('node-editor element not found! Retrying in 100ms...');
-            setTimeout(initializeNodeEditor, 100);
-            return;
-        }
-        console.log('Found node-editor element:', editorElement);
-        console.log('Editor dimensions:', editorElement.offsetWidth, 'x', editorElement.offsetHeight);
-
-        if (window.nodeEditor) {
-            console.log('NodeEditor already initialized');
-            return;
-        }
-
-        window.nodeEditor = new NodeEditor('node-editor');
-        console.log('NodeEditor initialized successfully');
-    } catch (error) {
-        console.error('Error initializing NodeEditor:', error);
-    }
-}
-
-// Try multiple initialization methods
-document.addEventListener('DOMContentLoaded', initializeNodeEditor);
-// Also try after a delay in case content loads after DOMContentLoaded
-setTimeout(initializeNodeEditor, 100);
-setTimeout(initializeNodeEditor, 500);
-setTimeout(initializeNodeEditor, 1000);
diff --git a/pyproject.toml b/pyproject.toml
index 36916e8..54c4d55 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -4,7 +4,7 @@ build-backend = "setuptools.build_meta"
 
 [project]
 name = "heavyball"
-description = "Compile-first PyTorch optimizer library — AdamW, Muon, SOAP/Shampoo, PSGD, Schedule-Free, and 30+ more with torch.compile fusion and composable features"
+description = "Compile-first PyTorch optimizer library - AdamW, Muon, SOAP/Shampoo, PSGD, Schedule-Free, and 30+ more with torch.compile fusion and composable features"
 version = "2.3.2"
 authors = [{ name = "HeavyBall Authors", email = "github.heavyball@nestler.sh" }]
 classifiers = ["Intended Audience :: Developers",
diff --git a/scripts/migrate_optimizer_state.py b/scripts/migrate_optimizer_state.py
index 8931cc7..0c0e3e0 100644
--- a/scripts/migrate_optimizer_state.py
+++ b/scripts/migrate_optimizer_state.py
@@ -1,18 +1,21 @@
 #!/usr/bin/env python3
 """
-Utility to migrate HeavyBall 1.x optimizer state dicts to the 2.0.0 layout.
+Utility to migrate HeavyBall optimizer state dicts to the current (3.x) layout.
 
-The script rewrites per-parameter state keys to the new transform-indexed names,
-reshapes state storage so each parameter-view owns its own dictionary, and
-injects the HeavyBall-specific metadata block expected by 2.0.0 optimizers.
+Supports two migration paths:
+- 1.x → 3.x: rewrites per-parameter state keys, reshapes storage, fixes param groups and metadata
+- 2.x → 3.x: renames foreach→multi_tensor in param groups, strips stale metadata
+
+Version auto-detection:
+- 1.x: flat per-parameter state (not nested by view index)
+- 2.x: nested state with 'foreach' in param groups
+- 3.x: nested state with 'multi_tensor' in param groups (already current)
 """
 
 from __future__ import annotations
 
 import functools
 import importlib
-import pickle
-import random
 from dataclasses import dataclass
 from pathlib import Path
 from typing import Any, Dict, Iterable, List, Optional, Sequence, Tuple
@@ -20,6 +23,42 @@
 import torch
 import typer
 
+_CLASS_RENAMES = {
+    "ForeachAdamW": "AdamW",
+    "ForeachNAdam": "NAdam",
+    "ForeachAdEMAMix": "AdEMAMix",
+    "ForeachAdamC": "AdamC",
+    "ForeachRMSprop": "RMSprop",
+    "ForeachSFAdamW": "SFAdamW",
+    "ForeachADOPT": "ADOPT",
+    "ForeachMuon": "Muon",
+    "ForeachLaProp": "LaProp",
+    "ForeachSOAP": "SOAP",
+    "ForeachSOAPNAdam": "SOAPNAdam",
+    "ForeachSOAPAdEMAMix": "SOAPAdEMAMix",
+    "ForeachSignLaProp": "SignLaProp",
+    "ForeachSOLP": "SOLP",
+    "ForeachPSGDKron": "PSGDKron",
+    "ForeachPSGDLRA": "PSGDLRA",
+    # Deleted subclasses → parent (all were __init__-only default overrides)
+    "PaLMForeachSFAdamW": "SFAdamW",
+    "PaLMForeachSOAP": "SOAP",
+    "PrecondScheduleForeachSOAP": "SOAP",
+    "PrecondSchedulePaLMForeachSOAP": "SOAP",
+    "ForeachPurePSGD": "PSGDKron",
+    "ForeachCachedPSGDKron": "PSGDKron",
+    "ForeachCachedDelayedPSGDKron": "PSGDKron",
+    "ForeachDelayedPSGD": "PSGDKron",
+    "ForeachCachedNewtonPSGD": "PSGDKron",
+    "NewtonHybrid2PSGDKron": "PSGDKron",
+    "ForeachDelayedPSGDLRA": "PSGDLRA",
+    "ForeachNewtonPSGDLRA": "PSGDLRA",
+    "NewtonHybrid2PSGDLRA": "PSGDLRA",
+}
+
+_REMOVED_GROUP_KEYS = frozenset({"stochastic_schedule"})
+_REMOVED_META_KEYS = frozenset({"stochastic_schedule", "precond_rng"})
+
 
 @dataclass
 class TransformMapping:
@@ -28,16 +67,37 @@ class TransformMapping:
     transform_idx: int
 
 
+def _resolve_class_name(class_name: str) -> str:
+    return _CLASS_RENAMES.get(class_name, class_name)
+
+
 def _load_optimizer_class(qualified_name: str):
     if "." in qualified_name:
         module_name, class_name = qualified_name.rsplit(".", 1)
     else:
         module_name, class_name = "heavyball", qualified_name
+    class_name = _resolve_class_name(class_name)
     module = importlib.import_module(module_name)
     try:
         return getattr(module, class_name)
     except AttributeError as exc:
-        raise ValueError(f"Optimizer class '{qualified_name}' not found") from exc
+        raise ValueError(f"Optimizer class '{module_name}.{class_name}' not found") from exc
+
+
+def _detect_version(state_dict: Dict[str, Any]) -> int:
+    nested = False
+    for entry in state_dict.get("state", {}).values():
+        if isinstance(entry, dict):
+            nested = any(isinstance(v, dict) for v in entry.values())
+            if not nested:
+                return 1
+            break
+
+    groups = state_dict.get("param_groups", [])
+    has_multi_tensor = any(isinstance(g, dict) and "multi_tensor" in g for g in groups)
+    if nested:
+        return 3 if has_multi_tensor else 2
+    return 3 if has_multi_tensor else 1
 
 
 def _guess_tensor_meta(state_entry: Dict[str, Any]) -> Tuple[Tuple[int, ...], torch.dtype]:
@@ -69,8 +129,9 @@ def _build_dummy_parameters(state: Dict[int, Dict[str, Any]], param_groups: Sequ
 def _normalise_group_options(group: Dict[str, Any]) -> Dict[str, Any]:
     options: Dict[str, Any] = {}
     for key, value in group.items():
-        if key == "params":
+        if key == "params" or key in _REMOVED_GROUP_KEYS:
             continue
+        key = "multi_tensor" if key == "foreach" else key
         if isinstance(value, list) and key in {"betas", "weight_decay_steps"}:
             options[key] = tuple(value)
         else:
@@ -107,6 +168,12 @@ def walk(queue: Iterable[Any]):
             elif isinstance(current, C.Parallel):
                 for branch in current.branches:
                     stack.extend(branch)
+            elif isinstance(current, C.Route):
+                for _, fns in current.routes:
+                    if fns:
+                        stack.extend(fns)
+                if current.default:
+                    stack.extend(current.default)
             elif isinstance(current, (list, tuple)):
                 stack.extend(current)
 
@@ -180,7 +247,24 @@ def _migrate_single_state(entry: Dict[str, Any], mappings: List[TransformMapping
     return migrated
 
 
-def migrate_state_dict(old_state: Dict[str, Any], optimizer_class: str) -> Dict[str, Any]:
+def _migrate_v2_to_v3(state_dict: Dict[str, Any]) -> None:
+    for group in state_dict.get("param_groups", []):
+        if not isinstance(group, dict):
+            continue
+        if "foreach" in group:
+            group["multi_tensor"] = group.pop("foreach")
+        for key in _REMOVED_GROUP_KEYS:
+            group.pop(key, None)
+
+    hb = state_dict.get("heavyball", {})
+    for key in _REMOVED_META_KEYS:
+        hb.pop(key, None)
+    inner = hb.get("inner_group", {})
+    for key in _REMOVED_META_KEYS:
+        inner.pop(key, None)
+
+
+def _migrate_v1_state(old_state: Dict[str, Any], optimizer_class: str) -> Dict[str, Any]:
     opt_cls = _load_optimizer_class(optimizer_class)
     optimizer, _ = _instantiate_optimizer(opt_cls, old_state)
     template = optimizer.state_dict()
@@ -199,11 +283,19 @@ def migrate_state_dict(old_state: Dict[str, Any], optimizer_class: str) -> Dict[
 
     heavyball_meta = migrated.setdefault("heavyball", template.get("heavyball", {}))
     if "inner_group" not in heavyball_meta:
-        heavyball_meta["inner_group"] = {"stochastic_schedule": None}
-    if "stochastic_schedule" not in heavyball_meta:
-        heavyball_meta["stochastic_schedule"] = None
-    if "precond_rng" not in heavyball_meta:
-        heavyball_meta["precond_rng"] = pickle.dumps(random.Random(0x12312))
+        heavyball_meta["inner_group"] = {}
+    return migrated
+
+
+def migrate_state_dict(old_state: Dict[str, Any], optimizer_class: str) -> Dict[str, Any]:
+    version = _detect_version(old_state)
+    if version == 1:
+        migrated = _migrate_v1_state(old_state, optimizer_class)
+    elif version == 2:
+        migrated = dict(old_state)
+    else:
+        return dict(old_state)
+    _migrate_v2_to_v3(migrated)
     return migrated
 
 
@@ -221,7 +313,7 @@ def _resolve_state_container(root: Dict[str, Any], key_path: Sequence[str]) -> D
 app = typer.Typer(help="Utilities for migrating HeavyBall optimizer checkpoints.")
 
 
-@app.command(help="Migrate a HeavyBall optimizer state dict to the 2.0.0 layout.")
+@app.command(help="Migrate a HeavyBall optimizer state dict to the current (3.x) layout.")
 def migrate(
     checkpoint: Path = typer.Argument(
         ...,
@@ -234,7 +326,7 @@ def migrate(
     ),
     optimizer_class: str = typer.Argument(
         ...,
-        help="Optimizer class to instantiate (e.g., heavyball.AdamW)",
+        help="Optimizer class name (e.g., heavyball.AdamW). Old names like ForeachAdamW are resolved automatically.",
     ),
     state_key: str = typer.Option(
         "optimizer",
diff --git a/test/test_compile_step.py b/test/test_compile_step.py
index de210e7..eb7bbaf 100644
--- a/test/test_compile_step.py
+++ b/test/test_compile_step.py
@@ -4,6 +4,7 @@
 import torch
 
 import heavyball
+from heavyball.chainable import ChainOpt, WarmupGuard, _walk_fns
 
 DEVICE = torch.device("cuda" if torch.cuda.is_available() else "cpu")
 
@@ -81,3 +82,33 @@ def test_compile_step_matches_eager(opt_name, opt_cls):
     for p_ref, p_test in zip(model_ref.parameters(), model_test.parameters()):
         diff = (p_ref.data - p_test.data).abs().max().item()
         assert diff < 1e-4, f"compile_step diverged: max_diff={diff}"
+
+
+def _max_warmup(opt):
+    return max((len(ft.warmup_fns) for ft in _walk_fns(opt.fns) if isinstance(ft, WarmupGuard)), default=0)
+
+
+@pytest.mark.parametrize("opt_name,opt_cls", _optimizer_params())
+def test_needs_init_clears(opt_name, opt_cls):
+    """_needs_init must become False after max_warmup + 1 steps for all ChainOpt optimizers.
+
+    Catches bugs where Route-based or warmup_guard-based optimizers permanently
+    force eager mode because different params accumulate different is_initialized
+    sets that never individually cover _transform_ids.
+    """
+    if not issubclass(opt_cls, ChainOpt):
+        pytest.skip("not a ChainOpt")
+
+    kwargs = dict(EXTRA_KWARGS.get(opt_name, {}))
+    model = _make_model()
+    opt = opt_cls(model.parameters(), **kwargs)
+    n = _max_warmup(opt) + 1
+
+    _run_steps(model, opt, n=n)
+
+    for group in opt.param_groups:
+        state = [opt.state_(p) for p in group["params"]]
+        assert not opt._needs_init(state), (
+            f"{opt_name}: _needs_init stuck True after {n} steps | "
+            f"compile_step will never engage"
+        )
diff --git a/test/test_ecc.py b/test/test_ecc.py
index 163d4f9..45c4758 100644
--- a/test/test_ecc.py
+++ b/test/test_ecc.py
@@ -362,7 +362,7 @@ def test_ecc_live_path_nonzero_correction():
     p = list(m.parameters())[0]
     st, ecc_keys = _ecc_keys(o, p)
     for ek in ecc_keys:
-        assert st[ek].any(), f"ECC correction '{ek}' is all zeros — stochastic_round_ likely mutating source"
+        assert st[ek].any(), f"ECC correction '{ek}' is all zeros - stochastic_round_ likely mutating source"
     del m, o
     clean()
 
diff --git a/test/test_migrate_cli.py b/test/test_migrate_cli.py
index 253c6d8..d3f3de7 100644
--- a/test/test_migrate_cli.py
+++ b/test/test_migrate_cli.py
@@ -1,5 +1,7 @@
 import importlib.util
 import pathlib
+import pickle
+import random
 import sys
 
 import pytest
@@ -14,164 +16,711 @@
 sys.modules[MODULE_NAME] = migrate_script
 SPEC.loader.exec_module(migrate_script)  # type: ignore[arg-type]
 
+# ---------------------------------------------------------------------------
+# Rename tables (exhaustive, mirrors _CLASS_RENAMES in the script)
+# ---------------------------------------------------------------------------
+
+_DIRECT_RENAMES = [
+    ("ForeachAdamW", "AdamW"),
+    ("ForeachNAdam", "NAdam"),
+    ("ForeachAdEMAMix", "AdEMAMix"),
+    ("ForeachAdamC", "AdamC"),
+    ("ForeachRMSprop", "RMSprop"),
+    ("ForeachSFAdamW", "SFAdamW"),
+    ("ForeachADOPT", "ADOPT"),
+    ("ForeachMuon", "Muon"),
+    ("ForeachLaProp", "LaProp"),
+    ("ForeachSOAP", "SOAP"),
+    ("ForeachSOAPNAdam", "SOAPNAdam"),
+    ("ForeachSOAPAdEMAMix", "SOAPAdEMAMix"),
+    ("ForeachSignLaProp", "SignLaProp"),
+    ("ForeachSOLP", "SOLP"),
+    ("ForeachPSGDKron", "PSGDKron"),
+    ("ForeachPSGDLRA", "PSGDLRA"),
+]
+
+_DELETED_RENAMES = [
+    ("PaLMForeachSFAdamW", "SFAdamW"),
+    ("PaLMForeachSOAP", "SOAP"),
+    ("PrecondScheduleForeachSOAP", "SOAP"),
+    ("PrecondSchedulePaLMForeachSOAP", "SOAP"),
+    ("ForeachPurePSGD", "PSGDKron"),
+    ("ForeachCachedPSGDKron", "PSGDKron"),
+    ("ForeachCachedDelayedPSGDKron", "PSGDKron"),
+    ("ForeachDelayedPSGD", "PSGDKron"),
+    ("ForeachCachedNewtonPSGD", "PSGDKron"),
+    ("NewtonHybrid2PSGDKron", "PSGDKron"),
+    ("ForeachDelayedPSGDLRA", "PSGDLRA"),
+    ("ForeachNewtonPSGDLRA", "PSGDLRA"),
+    ("NewtonHybrid2PSGDLRA", "PSGDLRA"),
+]
+
+_ALL_RENAMES = _DIRECT_RENAMES + _DELETED_RENAMES
+
+# PSGDLRA uses a different constructor signature (beta not betas, rank param, etc.)
+# so e2e tests using AdamW-style param_groups must exclude it
+_LRA_TARGETS = {"PSGDLRA"}
+_DIRECT_RENAMES_NO_LRA = [(o, n) for o, n in _DIRECT_RENAMES if n not in _LRA_TARGETS]
+_DELETED_RENAMES_NO_LRA = [(o, n) for o, n in _DELETED_RENAMES if n not in _LRA_TARGETS]
+_DIRECT_RENAMES_LRA = [(o, n) for o, n in _DIRECT_RENAMES if n in _LRA_TARGETS]
+_DELETED_RENAMES_LRA = [(o, n) for o, n in _DELETED_RENAMES if n in _LRA_TARGETS]
+
+_PASSTHROUGH = ["AdamW", "NAdam", "PSGDKron", "SGD", "SOAP", "Muon", "ADOPT", "LaProp", "PSGDLRA", "SFAdamW"]
+
+# ---------------------------------------------------------------------------
+# Helpers
+# ---------------------------------------------------------------------------
+
+
+def _flat_state(*shapes):
+    return {
+        i: {
+            "update_by_adam_exp_avg": torch.ones(s),
+            "update_by_adam_exp_avg_sq": torch.full(s, 2.0),
+            "is_initialized": [0],
+        }
+        for i, s in enumerate(shapes)
+    }
+
+
+def _nested_state(*shapes):
+    return {i: {0: {"key_0": torch.zeros(s), "is_initialized": [0]}} for i, s in enumerate(shapes)}
+
+
+def _v1_group(pids):
+    return {
+        "params": pids,
+        "lr": 0.0025,
+        "betas": [0.9, 0.99],
+        "eps": 1e-8,
+        "weight_decay": 0.0,
+        "warmup_steps": 0,
+        "foreach": True,
+        "stochastic_schedule": False,
+        "storage_dtype": "float32",
+        "mars": False,
+        "caution": False,
+        "mars_gamma": 0.0025,
+        "gradient_clipping": "use_default",
+        "update_clipping": "use_default",
+        "palm": "use_default",
+        "beta2_scale": 0.8,
+    }
+
+
+def _v2_group(pids):
+    return {**_v1_group(pids), "__class__": "heavyball.ForeachAdamW"}
+
+
+def _v3_group(pids):
+    g = _v1_group(pids)
+    g.pop("foreach")
+    g.pop("stochastic_schedule")
+    g["multi_tensor"] = True
+    return g
+
+
+def _v2_meta():
+    return {
+        "inner_group": {"stochastic_schedule": None},
+        "stochastic_schedule": None,
+        "precond_rng": pickle.dumps(random.Random(0x12312)),
+        "use_ema": False,
+    }
+
+
+def _v3_meta():
+    return {"inner_group": {}, "use_ema": False}
+
+
+def _load_heavyball_fresh():
+    package_root = pathlib.Path(__file__).resolve().parents[1]
+    heavyball_pkg = package_root / "heavyball"
+    saved = {n: sys.modules[n] for n in list(sys.modules) if n == "heavyball" or n.startswith("heavyball.")}
+    for n in list(sys.modules):
+        if n == "heavyball" or n.startswith("heavyball."):
+            sys.modules.pop(n)
+    spec = importlib.util.spec_from_file_location(
+        "heavyball", heavyball_pkg / "__init__.py", submodule_search_locations=[str(heavyball_pkg)]
+    )
+    mod = importlib.util.module_from_spec(spec)
+    sys.modules["heavyball"] = mod
+    spec.loader.exec_module(mod)
+    return saved
+
+
+def _restore_heavyball(saved):
+    for n in list(sys.modules):
+        if n == "heavyball" or n.startswith("heavyball."):
+            sys.modules.pop(n)
+    sys.modules.update(saved)
+
 
 @pytest.fixture()
 def runner():
     return CliRunner()
 
 
-def test_cli_dry_run_updates_state(monkeypatch, runner, tmp_path):
-    checkpoint_path = tmp_path / "ckpt.pt"
-    checkpoint_path.touch()
+# ====================================================================
+# _resolve_class_name
+# ====================================================================
 
-    state_container = {"state": {"initial": True}, "param_groups": ["group"]}
-    checkpoint = {"optimizer": state_container}
 
-    def fake_load(path, map_location=None):
-        return checkpoint
+@pytest.mark.parametrize("old,new", _ALL_RENAMES)
+def test_resolve_class_name_renames(old, new):
+    assert migrate_script._resolve_class_name(old) == new
 
-    def fake_migrate(state, _):
-        return {"state": {"migrated": True}, "param_groups": []}
 
-    def fail_save(*args, **kwargs):
-        pytest.fail("torch.save should not run during dry-run")
+@pytest.mark.parametrize("name", _PASSTHROUGH)
+def test_resolve_class_name_passthrough(name):
+    assert migrate_script._resolve_class_name(name) == name
 
-    monkeypatch.setattr(migrate_script.torch, "load", fake_load)
-    monkeypatch.setattr(migrate_script, "migrate_state_dict", fake_migrate)
-    monkeypatch.setattr(migrate_script.torch, "save", fail_save)
 
-    result = runner.invoke(
-        migrate_script.app,
-        [str(checkpoint_path), "heavyball.Mock", "--state-key", "optimizer", "--dry-run"],
-    )
+# ====================================================================
+# _load_optimizer_class
+# ====================================================================
+
+
+@pytest.mark.parametrize("old,new", _ALL_RENAMES)
+def test_load_optimizer_class_old_names(old, new):
+    import heavyball
+
+    assert migrate_script._load_optimizer_class(f"heavyball.{old}") is getattr(heavyball, new)
+
+
+@pytest.mark.parametrize("name", _PASSTHROUGH)
+def test_load_optimizer_class_current_names(name):
+    import heavyball
+
+    assert migrate_script._load_optimizer_class(name) is getattr(heavyball, name)
+
+
+def test_load_optimizer_class_bare_name():
+    import heavyball
+
+    assert migrate_script._load_optimizer_class("AdamW") is heavyball.AdamW
+
+
+def test_load_optimizer_class_invalid_raises():
+    with pytest.raises(ValueError, match="not found"):
+        migrate_script._load_optimizer_class("heavyball.TotallyFakeOptimizer")
+
+
+# ====================================================================
+# _detect_version
+# ====================================================================
+
+_DETECT_CASES = [
+    ("flat_foreach", {"state": _flat_state((2,)), "param_groups": [{"foreach": True}]}, 1),
+    ("flat_multi_tensor", {"state": _flat_state((2,)), "param_groups": [{"multi_tensor": True}]}, 1),
+    ("flat_neither", {"state": _flat_state((2,)), "param_groups": [{}]}, 1),
+    ("flat_multi_group", {"state": _flat_state((2,), (3,)), "param_groups": [{"foreach": True}, {}]}, 1),
+    ("nested_foreach", {"state": _nested_state((2,)), "param_groups": [{"foreach": True}]}, 2),
+    ("nested_foreach_multi_group", {"state": _nested_state((2,), (3,)), "param_groups": [{"foreach": True}, {"foreach": True}]}, 2),
+    ("nested_multi_tensor", {"state": _nested_state((2,)), "param_groups": [{"multi_tensor": True}]}, 3),
+    ("nested_multi_tensor_multi_group", {"state": _nested_state((2,), (3,)), "param_groups": [{"multi_tensor": True}, {}]}, 3),
+    ("empty_state_multi_tensor", {"state": {}, "param_groups": [{"multi_tensor": True}]}, 3),
+    ("empty_state_foreach", {"state": {}, "param_groups": [{"foreach": True}]}, 1),
+    ("empty_state_bare", {"state": {}, "param_groups": [{}]}, 1),
+    ("empty_state_empty_groups", {"state": {}, "param_groups": []}, 1),
+]
+
+
+@pytest.mark.parametrize("name,sd,expected", _DETECT_CASES, ids=[c[0] for c in _DETECT_CASES])
+def test_detect_version(name, sd, expected):
+    assert migrate_script._detect_version(sd) == expected
+
+
+# ====================================================================
+# _normalise_group_options
+# ====================================================================
+
+_NORM_CASES = [
+    ("foreach_renamed", {"foreach": True, "lr": 0.01}, {"multi_tensor": True, "lr": 0.01}),
+    ("foreach_false", {"foreach": False, "lr": 0.01}, {"multi_tensor": False, "lr": 0.01}),
+    ("multi_tensor_passthrough", {"multi_tensor": False, "lr": 0.01}, {"multi_tensor": False, "lr": 0.01}),
+    ("stochastic_stripped", {"foreach": True, "stochastic_schedule": False}, {"multi_tensor": True}),
+    ("betas_tuple", {"betas": [0.9, 0.999]}, {"betas": (0.9, 0.999)}),
+    ("weight_decay_steps_tuple", {"weight_decay_steps": [100, 200]}, {"weight_decay_steps": (100, 200)}),
+    ("params_stripped", {"params": [0, 1], "lr": 0.01}, {"lr": 0.01}),
+    ("empty_group", {}, {}),
+    ("params_only", {"params": [0]}, {}),
+    ("all_removed", {"params": [0], "stochastic_schedule": None}, {}),
+    ("kitchen_sink", {"params": [0, 1], "foreach": True, "stochastic_schedule": True, "lr": 0.01, "betas": [0.9, 0.99]}, {"multi_tensor": True, "lr": 0.01, "betas": (0.9, 0.99)}),
+]
+
+
+@pytest.mark.parametrize("name,group,expected", _NORM_CASES, ids=[c[0] for c in _NORM_CASES])
+def test_normalise_group_options(name, group, expected):
+    assert migrate_script._normalise_group_options(group) == expected
+
+
+# ====================================================================
+# _ensure_set
+# ====================================================================
+
+
+@pytest.mark.parametrize(
+    "inp,expected",
+    [
+        ({1, 2}, {1, 2}),
+        ([3, 4], {3, 4}),
+        ((5,), {5}),
+        (None, set()),
+        (7, {7}),
+        ([], set()),
+    ],
+    ids=["set", "list", "tuple", "none", "scalar", "empty_list"],
+)
+def test_ensure_set(inp, expected):
+    assert migrate_script._ensure_set(inp) == expected
+
+
+# ====================================================================
+# _guess_tensor_meta
+# ====================================================================
+
+
+@pytest.mark.parametrize(
+    "entry,shape,dtype",
+    [
+        ({"a": torch.zeros(3, 4, dtype=torch.float16)}, (3, 4), torch.float16),
+        ({"a": [torch.zeros(2, dtype=torch.bfloat16)]}, (2,), torch.bfloat16),
+        ({"a": "not_a_tensor", "b": torch.ones(5)}, (5,), torch.float32),
+        ({}, (1,), torch.float32),
+        ({"a": 42}, (1,), torch.float32),
+    ],
+    ids=["tensor", "tensor_list", "mixed_finds_tensor", "empty", "no_tensors"],
+)
+def test_guess_tensor_meta(entry, shape, dtype):
+    s, d = migrate_script._guess_tensor_meta(entry)
+    assert s == shape
+    assert d == dtype
+
+
+# ====================================================================
+# _resolve_state_container
+# ====================================================================
+
+
+def test_resolve_state_container_single_key():
+    root = {"optimizer": {"state": {}, "param_groups": []}}
+    assert migrate_script._resolve_state_container(root, ["optimizer"]) is root["optimizer"]
+
+
+def test_resolve_state_container_nested_key():
+    inner = {"state": {}, "param_groups": []}
+    root = {"model": {"training": {"opt": inner}}}
+    assert migrate_script._resolve_state_container(root, ["model", "training", "opt"]) is inner
+
+
+def test_resolve_state_container_missing_key():
+    with pytest.raises(KeyError, match="not found"):
+        migrate_script._resolve_state_container({"a": {}}, ["a", "b"])
+
+
+def test_resolve_state_container_not_optimizer():
+    with pytest.raises(ValueError, match="not an optimizer state dict"):
+        migrate_script._resolve_state_container({"opt": {"just_data": 1}}, ["opt"])
+
+
+# ====================================================================
+# _migrate_v2_to_v3
+# ====================================================================
+
+
+@pytest.mark.parametrize(
+    "meta_keys",
+    [
+        {"stochastic_schedule": None, "precond_rng": pickle.dumps(random.Random(0))},
+        {"stochastic_schedule": None},
+        {"precond_rng": b"rng"},
+        {},
+    ],
+    ids=["both", "stochastic_only", "precond_rng_only", "clean"],
+)
+def test_migrate_v2_to_v3_strips_stale_meta(meta_keys):
+    sd = {
+        "state": _nested_state((3,)),
+        "param_groups": [{"params": [0], "foreach": True, "stochastic_schedule": False}],
+        "heavyball": {"inner_group": {"stochastic_schedule": None}, "use_ema": False, **meta_keys},
+    }
+    migrate_script._migrate_v2_to_v3(sd)
+    group = sd["param_groups"][0]
+    assert group["multi_tensor"] is True
+    assert "foreach" not in group
+    assert "stochastic_schedule" not in group
+    hb = sd["heavyball"]
+    for key in ("stochastic_schedule", "precond_rng"):
+        assert key not in hb
+        assert key not in hb["inner_group"]
+    assert hb["use_ema"] is False
+
+
+def test_migrate_v2_to_v3_multi_group():
+    sd = {
+        "state": _nested_state((2,), (3,)),
+        "param_groups": [
+            {"params": [0], "foreach": True, "stochastic_schedule": False},
+            {"params": [1], "foreach": False, "stochastic_schedule": True, "lr": 0.1},
+        ],
+        "heavyball": _v2_meta(),
+    }
+    migrate_script._migrate_v2_to_v3(sd)
+    assert sd["param_groups"][0]["multi_tensor"] is True
+    assert sd["param_groups"][1]["multi_tensor"] is False
+    assert sd["param_groups"][1]["lr"] == 0.1
+    for g in sd["param_groups"]:
+        assert "foreach" not in g
+        assert "stochastic_schedule" not in g
+
+
+def test_migrate_v2_to_v3_preserves_non_stale_meta():
+    sd = {
+        "state": _nested_state((2,)),
+        "param_groups": [{"params": [0], "foreach": True}],
+        "heavyball": {**_v2_meta(), "use_ema": True, "ema_decay": 0.005, "compile_step": True},
+    }
+    migrate_script._migrate_v2_to_v3(sd)
+    assert sd["heavyball"]["use_ema"] is True
+    assert sd["heavyball"]["ema_decay"] == 0.005
+    assert sd["heavyball"]["compile_step"] is True
+
+
+def test_migrate_v2_to_v3_no_heavyball_key():
+    sd = {
+        "state": _nested_state((2,)),
+        "param_groups": [{"params": [0], "foreach": True}],
+    }
+    migrate_script._migrate_v2_to_v3(sd)
+    assert sd["param_groups"][0]["multi_tensor"] is True
+
+
+# ====================================================================
+# _migrate_single_state
+# ====================================================================
+
+
+@pytest.mark.parametrize("n_views", [1, 2, 5])
+def test_migrate_single_state_rewrites_keys(n_views):
+    mappings = [
+        migrate_script.TransformMapping("exp_avg", "exp_avg_0", 0),
+        migrate_script.TransformMapping("exp_avg_sq", "exp_avg_sq_0", 0),
+    ]
+    entry = {
+        "exp_avg": [torch.ones(2)] * n_views if n_views > 1 else torch.ones(2),
+        "exp_avg_sq": [torch.full((2,), 2.0)] * n_views if n_views > 1 else torch.full((2,), 2.0),
+        "is_initialized": [0],
+    }
+    migrated = migrate_script._migrate_single_state(entry, mappings)
+    for view_idx in range(n_views):
+        bucket = migrated[view_idx]
+        assert "exp_avg_0" in bucket
+        assert "exp_avg_sq_0" in bucket
+        assert "exp_avg" not in bucket
+        assert "exp_avg_sq" not in bucket
+        assert 0 in bucket["is_initialized"]
+
+
+def test_migrate_single_state_empty_mappings():
+    entry = {"some_key": torch.ones(3), "is_initialized": {0, 1}}
+    migrated = migrate_script._migrate_single_state(entry, [])
+    assert "some_key" in migrated[0]
+    assert set(migrated[0]["is_initialized"]) == {0, 1}
+
+
+def test_migrate_single_state_multiple_transforms():
+    mappings = [
+        migrate_script.TransformMapping("exp_avg", "update_by_adam_exp_avg_0", 0),
+        migrate_script.TransformMapping("exp_avg_sq", "update_by_adam_exp_avg_sq_0", 0),
+        migrate_script.TransformMapping("momentum", "heavyball_momentum_momentum_1", 1),
+    ]
+    entry = {
+        "exp_avg": torch.ones(4),
+        "exp_avg_sq": torch.full((4,), 2.0),
+        "momentum": torch.full((4,), 0.5),
+        "is_initialized": [0, 1],
+    }
+    migrated = migrate_script._migrate_single_state(entry, mappings)
+    bucket = migrated[0]
+    assert "update_by_adam_exp_avg_0" in bucket
+    assert "update_by_adam_exp_avg_sq_0" in bucket
+    assert "heavyball_momentum_momentum_1" in bucket
+    assert set(bucket["is_initialized"]) == {0, 1}
+
+
+def test_migrate_single_state_preserves_values():
+    t = torch.arange(6, dtype=torch.float32)
+    mappings = [migrate_script.TransformMapping("old", "new_0", 0)]
+    migrated = migrate_script._migrate_single_state({"old": t, "is_initialized": [0]}, mappings)
+    assert torch.equal(migrated[0]["new_0"], t)
+
+
+# ====================================================================
+# Full migrate_state_dict
+# ====================================================================
+
+
+def test_migrate_v2_state_dict():
+    sd = {
+        "state": _nested_state((4,)),
+        "param_groups": [_v2_group([0])],
+        "heavyball": _v2_meta(),
+    }
+    migrated = migrate_script.migrate_state_dict(sd, "heavyball.ForeachAdamW")
+    group = migrated["param_groups"][0]
+    assert group["multi_tensor"] is True
+    assert "foreach" not in group
+    assert "stochastic_schedule" not in group
+    hb = migrated.get("heavyball", {})
+    assert "stochastic_schedule" not in hb
+    assert "precond_rng" not in hb
+
+
+def test_migrate_v3_is_noop():
+    sd = {
+        "state": _nested_state((4,)),
+        "param_groups": [_v3_group([0])],
+        "heavyball": _v3_meta(),
+    }
+    original_key0 = sd["state"][0][0]["key_0"].clone()
+    migrated = migrate_script.migrate_state_dict(sd, "heavyball.AdamW")
+    assert migrated is not sd
+    assert torch.equal(migrated["state"][0][0]["key_0"], original_key0)
+    assert migrated["param_groups"][0]["multi_tensor"] is True
+
+
+def test_migrate_v2_with_old_class_name():
+    sd = {
+        "state": _nested_state((4,)),
+        "param_groups": [_v2_group([0])],
+        "heavyball": _v2_meta(),
+    }
+    migrated = migrate_script.migrate_state_dict(sd, "ForeachAdamW")
+    assert migrated["param_groups"][0]["multi_tensor"] is True
+
+
+def test_migrate_v2_multi_param():
+    sd = {
+        "state": _nested_state((4, 4), (8,), (2, 2, 2)),
+        "param_groups": [_v2_group([0, 1, 2])],
+        "heavyball": _v2_meta(),
+    }
+    migrated = migrate_script.migrate_state_dict(sd, "AdamW")
+    for pid in (0, 1, 2):
+        assert pid in migrated["state"]
+        assert 0 in migrated["state"][pid]
+
+
+# ====================================================================
+# CLI (typer) | mocked
+# ====================================================================
+
 
+def test_cli_dry_run(monkeypatch, runner, tmp_path):
+    ckpt = tmp_path / "ckpt.pt"
+    ckpt.touch()
+    container = {"state": {}, "param_groups": []}
+    checkpoint = {"optimizer": container}
+
+    monkeypatch.setattr(migrate_script.torch, "load", lambda *a, **kw: checkpoint)
+    monkeypatch.setattr(migrate_script, "migrate_state_dict", lambda s, _: {"state": {"ok": True}, "param_groups": []})
+    monkeypatch.setattr(migrate_script.torch, "save", lambda *a, **kw: pytest.fail("save during dry-run"))
+
+    result = runner.invoke(migrate_script.app, [str(ckpt), "heavyball.Mock", "--dry-run"])
     assert result.exit_code == 0
     assert "Dry run" in result.stdout
-    assert state_container == {"state": {"migrated": True}, "param_groups": []}
+    assert container["state"] == {"ok": True}
 
 
 def test_cli_writes_output(monkeypatch, runner, tmp_path):
-    checkpoint_path = tmp_path / "source.pt"
-    checkpoint_path.touch()
-    output_path = tmp_path / "out.pt"
-
-    state_container = {"state": {"initial": True}, "param_groups": ["group"]}
-    checkpoint = {"optimizer": state_container}
-    migrated = {"state": {"migrated": True}, "param_groups": []}
+    ckpt = tmp_path / "source.pt"
+    ckpt.touch()
+    out = tmp_path / "out.pt"
+    migrated = {"state": {"done": True}, "param_groups": []}
+    checkpoint = {"optimizer": {"state": {}, "param_groups": []}}
+    saved = {}
 
-    def fake_load(path, map_location=None):
-        return checkpoint
+    monkeypatch.setattr(migrate_script.torch, "load", lambda *a, **kw: checkpoint)
+    monkeypatch.setattr(migrate_script, "migrate_state_dict", lambda s, _: migrated)
+    monkeypatch.setattr(migrate_script.torch, "save", lambda obj, path: saved.update(obj=obj, path=pathlib.Path(path)))
 
-    def fake_migrate(state, _):
-        return migrated
+    result = runner.invoke(migrate_script.app, [str(ckpt), "heavyball.Mock", "--output", str(out)])
+    assert result.exit_code == 0
+    assert saved["path"] == out
+    assert saved["obj"]["optimizer"] == migrated
 
-    monkeypatch.setattr(migrate_script.torch, "load", fake_load)
-    monkeypatch.setattr(migrate_script, "migrate_state_dict", fake_migrate)
 
+def test_cli_overwrites_input_by_default(monkeypatch, runner, tmp_path):
+    ckpt = tmp_path / "ckpt.pt"
+    ckpt.touch()
     saved = {}
 
-    def fake_save(obj, path):
-        saved["obj"] = obj
-        saved["path"] = pathlib.Path(path)
+    monkeypatch.setattr(migrate_script.torch, "load", lambda *a, **kw: {"optimizer": {"state": {}, "param_groups": []}})
+    monkeypatch.setattr(migrate_script, "migrate_state_dict", lambda s, _: {"state": {}, "param_groups": []})
+    monkeypatch.setattr(migrate_script.torch, "save", lambda obj, path: saved.update(path=pathlib.Path(path)))
 
-    monkeypatch.setattr(migrate_script.torch, "save", fake_save)
+    result = runner.invoke(migrate_script.app, [str(ckpt), "heavyball.Mock"])
+    assert result.exit_code == 0
+    assert saved["path"] == ckpt
 
-    result = runner.invoke(
-        migrate_script.app,
-        [str(checkpoint_path), "heavyball.Mock", "--output", str(output_path)],
-    )
 
+@pytest.mark.parametrize("key", ["optimizer", "model.optimizer", "a.b.c"])
+def test_cli_state_key_parsing(monkeypatch, runner, tmp_path, key):
+    ckpt = tmp_path / "ckpt.pt"
+    ckpt.touch()
+    parts = key.split(".")
+    inner = {"state": {}, "param_groups": []}
+    root = inner
+    for p in reversed(parts):
+        root = {p: root}
+
+    monkeypatch.setattr(migrate_script.torch, "load", lambda *a, **kw: root)
+    monkeypatch.setattr(migrate_script, "migrate_state_dict", lambda s, _: {"state": {}, "param_groups": []})
+    monkeypatch.setattr(migrate_script.torch, "save", lambda *a, **kw: None)
+
+    result = runner.invoke(migrate_script.app, [str(ckpt), "heavyball.Mock", "--state-key", key])
     assert result.exit_code == 0
-    assert saved["path"] == output_path
-    assert saved["obj"]["optimizer"] == migrated
 
 
-def test_cli_migrates_legacy_checkpoint(runner, tmp_path):
-    package_root = pathlib.Path(__file__).resolve().parents[1]
-    heavyball_pkg = package_root / "heavyball"
-    saved_heavyball_modules = {
-        name: sys.modules[name] for name in list(sys.modules) if name == "heavyball" or name.startswith("heavyball.")
-    }
-    for name in list(sys.modules):
-        if name == "heavyball" or name.startswith("heavyball."):
-            sys.modules.pop(name)
+# ====================================================================
+# CLI - real end-to-end (fresh heavyball import)
+# ====================================================================
 
-    spec = importlib.util.spec_from_file_location(
-        "heavyball",
-        heavyball_pkg / "__init__.py",
-        submodule_search_locations=[str(heavyball_pkg)],
-    )
-    heavyball_module = importlib.util.module_from_spec(spec)
-    sys.modules["heavyball"] = heavyball_module
-    spec.loader.exec_module(heavyball_module)
 
-    try:
-        checkpoint_path = tmp_path / "legacy.pt"
-        output_path = tmp_path / "migrated.pt"
-
-        legacy_state = {
-            "state": {
-                0: {
-                    "update_by_adam_exp_avg": torch.ones((2, 2), dtype=torch.float32),
-                    "update_by_adam_exp_avg_sq": torch.full((2, 2), 2.0, dtype=torch.float32),
-                    "is_initialized": [0],
-                },
-                1: {
-                    "update_by_adam_exp_avg": torch.ones((2,), dtype=torch.float32),
-                    "update_by_adam_exp_avg_sq": torch.full((2,), 2.0, dtype=torch.float32),
-                    "is_initialized": [0],
-                },
-            },
-            "param_groups": [
-                {
-                    "params": [0, 1],
-                    "lr": 0.0025,
-                    "betas": [0.9, 0.99],
-                    "eps": 1e-8,
-                    "weight_decay": 0.0,
-                    "warmup_steps": 0,
-                    "multi_tensor": True,
-                    "storage_dtype": "float32",
-                    "mars": False,
-                    "caution": False,
-                    "mars_gamma": 0.0025,
-                    "gradient_clipping": "use_default",
-                    "update_clipping": "use_default",
-                    "palm": "use_default",
-                    "beta2_scale": 0.8,
-                    "__class__": "heavyball.AdamW",
-                }
-            ],
-        }
+def _make_v1_checkpoint(path, shapes, *, group_overrides=None):
+    g = _v1_group(list(range(len(shapes))))
+    g["multi_tensor"] = True
+    g.pop("foreach")
+    g.pop("stochastic_schedule")
+    if group_overrides:
+        g.update(group_overrides)
+    torch.save({"optimizer": {"state": _flat_state(*shapes), "param_groups": [g]}}, path)
+
+
+def _make_v2_checkpoint(path, shapes, *, group_overrides=None):
+    g = _v2_group(list(range(len(shapes))))
+    if group_overrides:
+        g.update(group_overrides)
+    torch.save({"optimizer": {"state": _nested_state(*shapes), "param_groups": [g], "heavyball": _v2_meta()}}, path)
 
-        torch.save({"optimizer": legacy_state}, checkpoint_path)
 
-        result = runner.invoke(
-            migrate_script.app,
-            [str(checkpoint_path), "heavyball.AdamW", "--output", str(output_path)],
-        )
+def _make_v3_checkpoint(path, shapes, *, group_overrides=None):
+    g = _v3_group(list(range(len(shapes))))
+    if group_overrides:
+        g.update(group_overrides)
+    torch.save({"optimizer": {"state": _nested_state(*shapes), "param_groups": [g], "heavyball": _v3_meta()}}, path)
 
+
+def _run_cli_e2e(runner, ckpt, out, class_name):
+    saved = _load_heavyball_fresh()
+    try:
+        result = runner.invoke(migrate_script.app, [str(ckpt), class_name, "--output", str(out)])
         assert result.exit_code == 0, result.stderr or result.stdout
-        assert output_path.exists()
-
-        migrated = torch.load(output_path)
-        migrated_state = migrated["optimizer"]
-
-        for pid, shape in [(0, (2, 2)), (1, (2,))]:
-            assert pid in migrated_state["state"], f"missing state for parameter {pid}"
-            migrated_bucket = migrated_state["state"][pid]
-            assert 0 in migrated_bucket, f"missing transformed view for parameter {pid}"
-            view_state = migrated_bucket[0]
-            assert view_state["update_by_adam_exp_avg_0"].shape == shape
-            assert view_state["update_by_adam_exp_avg_sq_0"].shape == shape
-            assert torch.allclose(view_state["update_by_adam_exp_avg_0"], torch.ones(shape))
-            assert torch.allclose(view_state["update_by_adam_exp_avg_sq_0"], torch.full(shape, 2.0))
-            assert view_state["is_initialized"] == [0]
-
-        assert "heavyball" in migrated_state
-        assert "Migrated checkpoint written to" in result.stdout
+        return torch.load(out)["optimizer"]
     finally:
-        for name in list(sys.modules):
-            if name == "heavyball" or name.startswith("heavyball."):
-                sys.modules.pop(name)
-        sys.modules.update(saved_heavyball_modules)
+        _restore_heavyball(saved)
+
+
+# --- v1 end-to-end ---
+
+
+def test_e2e_v1_adamw(runner, tmp_path):
+    ckpt, out = tmp_path / "v1.pt", tmp_path / "out.pt"
+    _make_v1_checkpoint(ckpt, [(2, 2), (2,)])
+    migrated = _run_cli_e2e(runner, ckpt, out, "heavyball.AdamW")
+    for pid, shape in [(0, (2, 2)), (1, (2,))]:
+        view = migrated["state"][pid][0]
+        assert view["update_by_adam_exp_avg_0"].shape == shape
+        assert view["update_by_adam_exp_avg_sq_0"].shape == shape
+        assert torch.allclose(view["update_by_adam_exp_avg_0"], torch.ones(shape))
+        assert view["is_initialized"] == [0]
+    assert "heavyball" in migrated
+
+
+@pytest.mark.parametrize("old_name,new_name", _DIRECT_RENAMES_NO_LRA)
+def test_e2e_v1_all_direct_renames(runner, tmp_path, old_name, new_name):
+    ckpt, out = tmp_path / "v1.pt", tmp_path / "out.pt"
+    _make_v1_checkpoint(ckpt, [(4,)])
+    migrated = _run_cli_e2e(runner, ckpt, out, f"heavyball.{old_name}")
+    assert 0 in migrated["state"]
+    assert "heavyball" in migrated
+
+
+@pytest.mark.parametrize("old_name,new_name", _DELETED_RENAMES_NO_LRA)
+def test_e2e_v1_all_deleted_renames(runner, tmp_path, old_name, new_name):
+    ckpt, out = tmp_path / "v1.pt", tmp_path / "out.pt"
+    _make_v1_checkpoint(ckpt, [(4,)])
+    migrated = _run_cli_e2e(runner, ckpt, out, f"heavyball.{old_name}")
+    assert 0 in migrated["state"]
+    assert "heavyball" in migrated
+
+
+# PSGDLRA v1 e2e: PSGDLRA computes rank from param numel during __init__,
+# which the migration script's _instantiate_optimizer can't replicate from
+# a state dict alone (rank isn't stored in param_groups). The rename
+# resolution and migration logic for LRA is covered by the unit tests above.
+
+
+@pytest.mark.parametrize("n_params", [1, 3, 5])
+def test_e2e_v1_varying_param_count(runner, tmp_path, n_params):
+    ckpt, out = tmp_path / "v1.pt", tmp_path / "out.pt"
+    shapes = [(i + 2,) for i in range(n_params)]
+    _make_v1_checkpoint(ckpt, shapes)
+    migrated = _run_cli_e2e(runner, ckpt, out, "heavyball.AdamW")
+    for pid in range(n_params):
+        assert pid in migrated["state"]
+
+
+@pytest.mark.parametrize("shape", [(4,), (2, 3), (2, 3, 4)])
+def test_e2e_v1_varying_shapes(runner, tmp_path, shape):
+    ckpt, out = tmp_path / "v1.pt", tmp_path / "out.pt"
+    _make_v1_checkpoint(ckpt, [shape])
+    migrated = _run_cli_e2e(runner, ckpt, out, "heavyball.AdamW")
+    assert migrated["state"][0][0]["update_by_adam_exp_avg_0"].shape == shape
+
+
+# --- v2 end-to-end ---
+
+
+def test_e2e_v2_basic(runner, tmp_path):
+    ckpt, out = tmp_path / "v2.pt", tmp_path / "out.pt"
+    _make_v2_checkpoint(ckpt, [(4,)])
+    migrated = _run_cli_e2e(runner, ckpt, out, "heavyball.AdamW")
+    group = migrated["param_groups"][0]
+    assert group["multi_tensor"] is True
+    assert "foreach" not in group
+    assert "stochastic_schedule" not in group
+    hb = migrated["heavyball"]
+    assert "precond_rng" not in hb
+    assert "stochastic_schedule" not in hb
+
+
+@pytest.mark.parametrize("old_name,new_name", _DIRECT_RENAMES_NO_LRA)
+def test_e2e_v2_all_direct_renames(runner, tmp_path, old_name, new_name):
+    ckpt, out = tmp_path / "v2.pt", tmp_path / "out.pt"
+    _make_v2_checkpoint(ckpt, [(4,)])
+    migrated = _run_cli_e2e(runner, ckpt, out, f"heavyball.{old_name}")
+    assert migrated["param_groups"][0]["multi_tensor"] is True
+    assert "foreach" not in migrated["param_groups"][0]
+
+
+@pytest.mark.parametrize("n_params", [1, 3, 5])
+def test_e2e_v2_varying_param_count(runner, tmp_path, n_params):
+    ckpt, out = tmp_path / "v2.pt", tmp_path / "out.pt"
+    shapes = [(i + 2,) for i in range(n_params)]
+    _make_v2_checkpoint(ckpt, shapes)
+    migrated = _run_cli_e2e(runner, ckpt, out, "heavyball.AdamW")
+    for pid in range(n_params):
+        assert pid in migrated["state"]
+
+
+# --- v3 end-to-end (noop) ---
+
+
+def test_e2e_v3_noop(runner, tmp_path):
+    ckpt, out = tmp_path / "v3.pt", tmp_path / "out.pt"
+    _make_v3_checkpoint(ckpt, [(4,)])
+    migrated = _run_cli_e2e(runner, ckpt, out, "heavyball.AdamW")
+    assert migrated["param_groups"][0]["multi_tensor"] is True
+    assert torch.equal(migrated["state"][0][0]["key_0"], torch.zeros(4))
diff --git a/test/test_param_ecc_compile.py b/test/test_param_ecc_compile.py
index e6fc4ce..6b8c462 100644
--- a/test/test_param_ecc_compile.py
+++ b/test/test_param_ecc_compile.py
@@ -108,7 +108,7 @@ def test_ecc_populated_rne():
     p, ecc, _ = _train_linear("max-autotune-no-cudagraphs", rne=True)
     assert ecc is not None, "param::ecc not found in optimizer state"
     assert ecc.any(), (
-        "param::ecc all zeros with RNE rounding under compile — Inductor likely folded the f32->bf16->f32 roundtrip"
+        "param::ecc all zeros with RNE rounding under compile, Inductor likely folded the f32->bf16->f32 roundtrip"
     )
     clean()
 
diff --git a/test/test_toy_training.py b/test/test_toy_training.py
index 0e2e83a..6a729af 100644
--- a/test/test_toy_training.py
+++ b/test/test_toy_training.py
@@ -29,10 +29,8 @@ def _flatten_tensors(tensors: Iterable[torch.Tensor]):
 
 def _optimizer_params():
     params = []
-    for name in sorted(dir(heavyball)):
-        if name.startswith("_"):
-            continue
-        attr = getattr(heavyball, name)
+    for name in sorted(heavyball.__all__):
+        attr = getattr(heavyball, name, None)
         if not isinstance(attr, type) or not issubclass(attr, optim.Optimizer):
             continue
         if attr is optim.Optimizer:
diff --git a/test/utils.py b/test/utils.py
index 163445f..b00ff8c 100644
--- a/test/utils.py
+++ b/test/utils.py
@@ -34,7 +34,7 @@ def _deduplicate_by_chain(names):
     """Keep one optimizer per unique chain of functions.
 
     Two optimizers that differ only by multi_tensor=True/False have identical
-    chains and test the same code paths — keep whichever appears first.
+    chains and test the same code paths, keep whichever appears first.
     """
     seen = set()
     out = []

From 6f43bf5ad314fff8c7616b433f9882ffb30d5848 Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Mon, 30 Mar 2026 08:47:40 +0000
Subject: [PATCH 08/24] improve interface

---
 heavyball/chainable.py    | 153 ++++++++++++++++++++------------------
 heavyball/utils.py        |  37 +++++----
 test/test_cpu_features.py |  80 ++++++++++++++++++++
 3 files changed, 183 insertions(+), 87 deletions(-)

diff --git a/heavyball/chainable.py b/heavyball/chainable.py
index b37e43d..abd0290 100644
--- a/heavyball/chainable.py
+++ b/heavyball/chainable.py
@@ -277,45 +277,50 @@ def _call(self, state, group, update, grad, param, vars, *args, **kwargs):
 class PrecondGradAccumGuard(FunctionTransform):
     def __init__(self, fn):
         super().__init__(fn, ["precond_grad_accum"])
-        self.steps_taken = 0
-        self.pass_through = None
+        self.steps_taken_key = None
 
-    def _accum(self, state, new):
-        self.steps_taken += 1
+    def _build_val_names(self):
+        super()._build_val_names()
+        self.steps_taken_key = f"_{self.fn_name}_steps_taken_{self.transform_idx}"
+
+    def _accum(self, group, state, new):
+        group[self.steps_taken_key] = group.get(self.steps_taken_key, 0) + 1
         utils.stochastic_add_(state, new)
 
-    def _reset(self, state):
-        if self.steps_taken != 0:
-            self.steps_taken = 0
+    def _reset(self, group, state):
+        if group.get(self.steps_taken_key, 0) != 0:
+            group[self.steps_taken_key] = 0
             utils.zero_(state)
 
     def _init(self, state: dict, group: dict, update: Tensor, grad: Tensor, param: Tensor, *args, **kwargs):
-        if self.pass_through is None:
-            self.pass_through = not group.get("precond_grad_accum", False)
-        if self.pass_through is False:
-            for name in self.names:
-                _zero_guard(state, self.val_name(name), param, _storage_dtype(group))
+        if not group.get("precond_grad_accum", False):
+            return
+        for name in self.names:
+            _zero_guard(state, self.val_name(name), param, _storage_dtype(group))
 
     def _call(self, state, group, update, grad, param, vars, *args, **kwargs):
         base_grad = update if group.get("momentum_into_precond_update", True) else grad
-        if self.pass_through:
+        if not group.get("precond_grad_accum", False):
             return self.fn(state, group, update, grad, param, *args, base_grad, **kwargs)
 
         (vars,) = vars
+        steps_taken = group.get(self.steps_taken_key, 0)
+        accum_state = None
         if group["is_preconditioning"]:
-            if self.steps_taken:
-                self._accum(vars, base_grad)
-                utils.stochastic_multiply_(vars, 1 / self.steps_taken)
+            if steps_taken:
+                self._accum(group, vars, base_grad)
+                utils.stochastic_multiply_(vars, 1 / group[self.steps_taken_key])
+                accum_state = vars
             else:
                 vars = base_grad
         else:
-            self._accum(vars, base_grad)
+            self._accum(group, vars, base_grad)
             vars = base_grad
         try:
             out = self.fn(state, group, update, grad, param, *args, vars, **kwargs)
         finally:
-            if group["is_preconditioning"]:
-                self._reset(vars)
+            if accum_state is not None:
+                self._reset(group, accum_state)
 
         return out
 
@@ -1481,6 +1486,12 @@ def palm_beta2(state, group, update, grad, param):
 
 
 def apply_to_idx(fn, idx):
+    name = fn
+    if isinstance(fn, str):
+        fn = getattr(utils, fn, None)
+        if fn is None or not callable(fn):
+            raise ValueError(f"Unknown function '{name}'")
+
     def _fn(state, group, update, grad, param):
         args = [state, group, update, grad, param]
         return fn(args[idx])
@@ -1859,15 +1870,26 @@ def _step_inner(self, group):
             return
         p, g = zip(*vals)
 
-        for param in p:
-            state = self.state_(param)
-            step = state.get("step", 0)
-            if not isinstance(step, torch.Tensor):
-                step = torch.tensor(step, dtype=torch.int64, device=param.device)
-                state["step"] = step
-            break
-
-        group["step"] = state["step"] = step = step + 1
+        step = group.get("_group_step")
+        if step is None:
+            for param in group["params"]:
+                param_state = self.state.get(param)
+                if not isinstance(param_state, dict):
+                    continue
+                for idx_state in param_state.values():
+                    if isinstance(idx_state, dict) and "step" in idx_state:
+                        step = idx_state["step"]
+                        break
+                if step is not None:
+                    break
+            else:
+                step = 0
+        if isinstance(step, torch.Tensor):
+            step = step.to(device=p[0].device, dtype=torch.int64)
+        else:
+            step = torch.tensor(step, dtype=torch.int64, device=p[0].device)
+        group["_group_step"] = group["step"] = step = step + 1
+        self.state_(p[0])["step"] = step
         group["prev_lr"] = group["lr"] = group["base_lr"] * step / max(step, group["warmup_steps"] + 1)
 
         if not group["multi_tensor"] or len(p) == 1:
@@ -2024,55 +2046,44 @@ def __init__(
 
 class ScheduleFree(BaseOpt):
     def eval(self):
+        return self.train(False)
+
+    def train(self, mode: bool = True):
         z_key = self._find_val_name("z")
         for group in self.param_groups:
-            group["train_mode"] = train_mode = not group.get("train_mode", True)
-            beta1 = utils.get_beta1(group)
-            if beta1 > 0 and not train_mode:
-                for p in group["params"]:
-                    state = self.state_(p)
-                    if z_key in state:
-                        z = utils.promote(state[z_key])
-                        p32 = utils.promote(p.data)
-                        p32.lerp_(end=z, weight=1 - 1 / beta1)
-                        utils.copy_stochastic_(p.data, p32)
-
-    def train(self):
-        z_key = self._find_val_name("z")
-        for group in self.param_groups:
-            group["train_mode"] = train_mode = not group.get("train_mode", False)
+            train_mode = group.get("train_mode", True)
+            if train_mode == mode:
+                continue
+            group["train_mode"] = mode
             beta1 = utils.get_beta1(group)
-            if beta1 > 0 and train_mode:
-                for p in group["params"]:
-                    state = self.state_(p)
-                    if z_key in state:
-                        z = utils.promote(state[z_key])
-                        p32 = utils.promote(p.data)
-                        p32.lerp_(end=z, weight=1 - beta1)
-                        utils.copy_stochastic_(p.data, p32)
+            if beta1 <= 0:
+                continue
+            weight = 1 - beta1 if mode else 1 - 1 / beta1
+            for p in group["params"]:
+                state = self.state_(p)
+                if z_key in state:
+                    z = utils.promote(state[z_key])
+                    p32 = utils.promote(p.data)
+                    p32.lerp_(end=z, weight=weight)
+                    utils.copy_stochastic_(p.data, p32)
+        return self
 
 
 class MSAM(BaseOpt):
     def eval(self):
+        return self.train(False)
+
+    def train(self, mode: bool = True):
         z_key = self._find_val_name("z")
         for group in self.param_groups:
-            group["train_mode"] = train_mode = not group.get("train_mode", True)
-            if not train_mode:
-                for p in group["params"]:
-                    state = self.state_(p)
-                    if z_key in state:
-                        p_copy = p.data.clone()
-                        utils.copy_stochastic_(p.data, state[z_key])
-                        utils.copy_stochastic_(state[z_key], p_copy)
-
-    def train(self):
-        z_key = self._find_val_name("z")
-        for group in self.param_groups:
-            group["train_mode"] = train_mode = not group.get("train_mode", False)
-            if train_mode:
-                for p in group["params"]:
-                    state = self.state_(p)
-                    if z_key in state:
-                        p_copy = p.data.clone()
-                        utils.copy_stochastic_(p.data, state[z_key])
-                        utils.copy_stochastic_(state[z_key], p_copy)
+            train_mode = group.get("train_mode", True)
+            if train_mode == mode:
+                continue
+            group["train_mode"] = mode
+            for p in group["params"]:
+                state = self.state_(p)
+                if z_key in state:
+                    p_copy = p.data.clone()
+                    utils.copy_stochastic_(p.data, state[z_key])
+                    utils.copy_stochastic_(state[z_key], p_copy)
+        return self
diff --git a/heavyball/utils.py b/heavyball/utils.py
index 44b4b28..e8021a0 100644
--- a/heavyball/utils.py
+++ b/heavyball/utils.py
@@ -1590,6 +1590,19 @@ def _handle_closure(self, closure):
         self._fallback_enabled = True
         return self._handle_closure(closure)
 
+    def _cleanup_temporary_tensors(self):
+        for real, views in self.mapping.items():
+            fmt = getattr(real, "_restore_memory_format", None)
+            if fmt is not None:
+                del self.mapping_inverse[_tensor_key(real)]
+                real.data = real.data.to(memory_format=fmt)
+                self.mapping_inverse[_tensor_key(real)] = (real, 0)
+                del real._restore_memory_format
+            for tensor in (real, *views):
+                for key in ("grad", "vector", "hessian_vector", "orig"):
+                    if hasattr(tensor, key):
+                        setattr(tensor, key, None)
+
     def step(self, closure: Optional[Callable] = None):
         if self.precond_schedule is None:
             self._is_preconditioning = False
@@ -1601,22 +1614,14 @@ def step(self, closure: Optional[Callable] = None):
             self.ema_update()
         # we assume that parameters are constant and that there are no excessive recompiles
         with torch.no_grad(), torch._dynamo.utils.disable_cache_limit():
-            for group in self.param_groups:
-                if "param_count" not in group:
-                    group["param_count"] = sum(p.numel() for p in group["params"])
-                group["is_preconditioning"] = self._is_preconditioning
-                self._step(group)
-                for real, views in self.mapping.items():
-                    fmt = getattr(real, "_restore_memory_format", None)
-                    if fmt is not None:
-                        del self.mapping_inverse[_tensor_key(real)]
-                        real.data = real.data.to(memory_format=fmt)
-                        self.mapping_inverse[_tensor_key(real)] = (real, 0)
-                        del real._restore_memory_format
-                    for tensor in (real, *views):
-                        for key in ("grad", "vector", "hessian_vector", "orig"):
-                            if hasattr(tensor, key):
-                                setattr(tensor, key, None)
+            try:
+                for group in self.param_groups:
+                    if "param_count" not in group:
+                        group["param_count"] = sum(p.numel() for p in group["params"])
+                    group["is_preconditioning"] = self._is_preconditioning
+                    self._step(group)
+            finally:
+                self._cleanup_temporary_tensors()
         return loss
 
 
diff --git a/test/test_cpu_features.py b/test/test_cpu_features.py
index 82ed343..0a8b746 100644
--- a/test/test_cpu_features.py
+++ b/test/test_cpu_features.py
@@ -132,3 +132,83 @@ def closure():
     after = [param.detach() for param in model.parameters()]
     diff = torch.cat([(a - b).reshape(-1) for a, b in zip(after, before, strict=True)])
     assert diff.norm().item() > 0.0
+
+
+def test_multiple_param_groups_keep_updating() -> None:
+    p1 = nn.Parameter(torch.zeros(()))
+    p2 = nn.Parameter(torch.zeros(()))
+    opt = heavyball.SGD(
+        [
+            {"params": [p1]},
+            {"params": [p2]},
+        ],
+        lr=0.1,
+        beta=0.0,
+        warmup_steps=0,
+    )
+
+    for _ in range(3):
+        p1.grad = torch.ones_like(p1)
+        p2.grad = torch.full_like(p2, 2.0)
+        opt.step()
+        opt.zero_grad(set_to_none=True)
+
+    assert torch.allclose(p1.detach(), torch.tensor(-0.3))
+    assert torch.allclose(p2.detach(), torch.tensor(-0.6))
+
+
+def test_group_step_does_not_reset_when_active_param_changes() -> None:
+    p1 = nn.Parameter(torch.zeros(()))
+    p2 = nn.Parameter(torch.zeros(()))
+    opt = heavyball.SGD([p1, p2], lr=0.1, beta=0.0, warmup_steps=3)
+
+    p1.grad = torch.ones_like(p1)
+    opt.step()
+    opt.zero_grad(set_to_none=True)
+
+    p2.grad = torch.ones_like(p2)
+    opt.step()
+    opt.zero_grad(set_to_none=True)
+
+    assert p1.item() == pytest.approx(-0.025)
+    assert p2.item() == pytest.approx(-0.05)
+
+
+def test_string_clipping_shorthands_match_public_api() -> None:
+    model, data, target = _make_batch()
+    opt = heavyball.SGD(
+        model.parameters(),
+        lr=1e-3,
+        beta=0.0,
+        gradient_clipping="l2_clip_",
+        update_clipping="trust_region_clip_",
+    )
+
+    loss = _train_once(opt, model, data, target, steps=2)
+    assert torch.isfinite(torch.tensor(loss))
+
+
+@pytest.mark.parametrize("opt_cls", [heavyball.SFAdamW, heavyball.MSAMLaProp])
+def test_mode_switches_are_idempotent(opt_cls) -> None:
+    p = nn.Parameter(torch.tensor([1.0, -1.0]))
+    opt = opt_cls([p], lr=1e-2)
+
+    p.grad = torch.ones_like(p)
+    opt.step()
+    opt.zero_grad(set_to_none=True)
+
+    opt.eval()
+    eval_once = p.detach().clone()
+    opt.eval()
+    eval_twice = p.detach().clone()
+
+    assert torch.allclose(eval_once, eval_twice)
+    assert opt.param_groups[0]["train_mode"] is False
+
+    opt.train()
+    train_once = p.detach().clone()
+    opt.train()
+    train_twice = p.detach().clone()
+
+    assert torch.allclose(train_once, train_twice)
+    assert opt.param_groups[0]["train_mode"] is True

From 97ccdfb98ee31355ea2dd7bc177d0ddfdeb9a676 Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Mon, 30 Mar 2026 11:21:15 +0000
Subject: [PATCH 09/24] migration docs

---
 README.md                          |   7 +-
 docs/heavyball3.md                 | 117 +++++++++++++++++++++++++++++
 heavyball/__init__.py              |  34 +++------
 heavyball/chainable.py             |  30 +++++++-
 heavyball/utils.py                 |   5 +-
 pyproject.toml                     |   2 +-
 scripts/migrate_optimizer_state.py |  14 ++++
 7 files changed, 176 insertions(+), 33 deletions(-)
 create mode 100644 docs/heavyball3.md

diff --git a/README.md b/README.md
index e8bd664..d143e93 100644
--- a/README.md
+++ b/README.md
@@ -204,10 +204,11 @@ HeavyBall includes a diagnostic benchmark suite via [LightBench](https://github.
 for silent optimizer failures across difficulty levels. Results and methodology are documented
 in [docs/benchmark.md](docs/benchmark.md).
 
-## Migrating from 1.x
+## Migrating
 
-See the [2.0.0 migration notes](docs/heavyball2.md) for a full checklist, and `scripts/migrate_optimizer_state.py` for
-checkpoint conversion.
+**From 2.x** See the [3.0.0 migration guide](docs/heavyball3.md) for renamed classes, removed kwargs, and checkpoint conversion.
+
+**From 1.x** See the [2.0.0 migration notes](docs/heavyball2.md), then follow the 3.0.0 guide.
 
 ## Contributing
 
diff --git a/docs/heavyball3.md b/docs/heavyball3.md
new file mode 100644
index 0000000..f4fc2c5
--- /dev/null
+++ b/docs/heavyball3.md
@@ -0,0 +1,117 @@
+# HeavyBall 3.0.0
+
+## Highlights
+
+* Simplified public API: `Foreach*` prefixes removed, short names are now the canonical classes
+* New optimizers: `HyperBallAdamW`, `MuonAdamW`, `PSGDPRO`
+* `Route`-based param dispatch replaces manual `SplitOpt` for mixed-architecture optimizers
+* `ScheduleFree` and `MSAM` mode switches are now idempotent (`eval()` twice is safe)
+* Higher-precision PSGD preconditioner updates
+* `torch.compile`-friendly step with automatic eager fallback for init/preconditioning
+
+---
+
+## Breaking changes
+
+### Class renames
+
+Every `Foreach*` class is renamed to its short form. The old short-form aliases (which existed
+in 2.x) keep working — only the `Foreach*` imports break.
+
+| 2.x name | 3.x name |
+|---|---|
+| `ForeachAdamW` | `AdamW` |
+| `ForeachNAdam` | `NAdam` |
+| `ForeachAdEMAMix` | `AdEMAMix` |
+| `ForeachAdamC` | `AdamC` |
+| `ForeachRMSprop` | `RMSprop` |
+| `ForeachSFAdamW` | `SFAdamW` |
+| `ForeachADOPT` | `ADOPT` |
+| `ForeachMuon` | `Muon` |
+| `ForeachLaProp` | `LaProp` |
+| `ForeachSignLaProp` | `SignLaProp` |
+| `ForeachSOAP` | `SOAP` |
+| `ForeachSOAPNAdam` | `SOAPNAdam` |
+| `ForeachSOAPAdEMAMix` | `SOAPAdEMAMix` |
+| `ForeachSOLP` | `SOLP` |
+| `ForeachPSGDKron` | `PSGDKron` |
+| `ForeachPSGDLRA` | `PSGDLRA` |
+
+### Removed optimizer classes
+
+These were thin subclasses that only set a class-level default. Use the parent class with the
+corresponding constructor argument instead.
+
+| 2.x class | 3.x equivalent |
+|---|---|
+| `PaLMForeachSFAdamW` / `PaLMSFAdamW` | `SFAdamW(..., palm=True)` |
+| `PaLMForeachSOAP` / `PaLMSOAP` / `PalmForEachSoap` | `SOAP(..., palm=True)` |
+| `PrecondScheduleForeachSOAP` / `PrecondScheduleSOAP` | `SOAP(..., use_precond_schedule=True)` |
+| `PrecondSchedulePaLMForeachSOAP` / `PrecondSchedulePaLMSOAP` | `SOAP(..., palm=True, use_precond_schedule=True)` |
+| `ForeachPurePSGD` / `PurePSGD` | `PSGDKron(..., exp_avg_input=False)` |
+| `ForeachCachedPSGDKron` / `CachedPSGDKron` | `PSGDKron(...)` (caching is now the default) |
+| `ForeachDelayedPSGD` / `DelayedPSGD` | `PSGDKron(..., delayed=True)` |
+| `ForeachCachedDelayedPSGDKron` / `CachedDelayedPSGDKron` | `PSGDKron(..., delayed=True)` |
+| `ForeachCachedNewtonPSGD` / `NewtonPSGDKron` | `PSGDKron(..., hessian_approx=True)` |
+| `NewtonHybrid2PSGDKron` | `PSGDKron(..., hessian_approx=True, hvp_interval=2)` |
+| `ForeachDelayedPSGDLRA` / `DelayedPSGDLRA` | `PSGDLRA(..., delayed=True)` |
+| `ForeachNewtonPSGDLRA` / `NewtonPSGDLRA` | `PSGDLRA(..., hessian_approx=True)` |
+| `NewtonHybrid2PSGDLRA` | `PSGDLRA(..., hessian_approx=True, hvp_interval=2)` |
+
+### Renamed parameters
+
+| 2.x parameter | 3.x parameter | Notes |
+|---|---|---|
+| `foreach` | `multi_tensor` | Passing `foreach` emits a `FutureWarning` and remaps automatically |
+
+### Removed parameters
+
+These raise `TypeError` if passed. They were either unused or replaced by better defaults.
+
+| Parameter | Previously on | Notes                                                    |
+|---|---|----------------------------------------------------------|
+| `stochastic_schedule` | SOAP, PSGDKron, PSGDLRA | Deterministic accumulation schedule is now the only mode |
+| `normalize_grads` | SOAP variants | Was unused in the transform pipeline                     |
+| `correct_bias` | SOAP variants | Was unused in the transform pipeline                     |
+| `inverse_free` | PSGDKron | Use `quad_torch` or PSGDPRO for inverse-free PSGD        |
+| `adaptive` | PSGDKron | Removed                                                  |
+
+### Chainable API renames
+
+| 2.x name | 3.x name |
+|---|---|
+| `Branch` | `Parallel` |
+
+### Behavioral changes
+
+* **ScheduleFree / MSAM `eval()` / `train()`**: Now idempotent. Calling `eval()` twice no
+  longer flips back to train mode. Both methods accept a `mode` argument matching
+  `nn.Module.train(mode)` and return `self`.
+* **PSGD dampening**: `dampen_grad` default changed from `2**-13` to `1e-9`, and dampening
+  epsilon uses `torch.finfo(float32).eps` regardless of input dtype. This improves
+  preconditioner accuracy but may change convergence behavior.
+
+---
+
+## Checkpoint migration
+
+Use the migration CLI to convert 1.x or 2.x checkpoints:
+
+```bash
+python scripts/migrate_optimizer_state.py <checkpoint.pt> <OptimizerClass>
+```
+
+Old class names (including all aliases listed above) are resolved automatically.
+The `foreach` → `multi_tensor` key rename in param groups is handled automatically.
+
+---
+
+## Upgrade checklist
+
+1. Replace `from heavyball import Foreach*` with the short name (e.g., `ForeachAdamW` → `AdamW`)
+2. Replace `foreach=` with `multi_tensor=` in constructor calls
+3. Replace removed subclass instantiations with parent + kwargs (see table above)
+4. Remove any `stochastic_schedule`, `normalize_grads`, `correct_bias`, `inverse_free`, or `adaptive` kwargs
+5. Replace `Branch(...)` with `Parallel(...)` in custom chainable code
+6. Migrate checkpoints: `python scripts/migrate_optimizer_state.py <ckpt> heavyball.<Optimizer>`
+7. If you relied on `eval(); eval()` toggling back to train mode, update your code
diff --git a/heavyball/__init__.py b/heavyball/__init__.py
index a7a69ee..d4357c4 100644
--- a/heavyball/__init__.py
+++ b/heavyball/__init__.py
@@ -30,7 +30,7 @@ def __init__(
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
-        super().__init__(params, defaults, multi_tensor, gradient_clipping, update_clipping, fns=(C.heavyball_momentum,))
+        super().__init__(params, defaults, gradient_clipping, update_clipping, fns=(C.heavyball_momentum,))
 
 
 class AdamW(C.BaseOpt):
@@ -58,7 +58,7 @@ def __init__(
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
-        super().__init__(params, defaults, multi_tensor, gradient_clipping, update_clipping, palm, fns=(C.update_by_adam,))
+        super().__init__(params, defaults, gradient_clipping, update_clipping, palm, fns=(C.update_by_adam,))
 
 
 class NAdam(C.BaseOpt):
@@ -88,7 +88,7 @@ def __init__(
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
-        super().__init__(params, defaults, multi_tensor, gradient_clipping, update_clipping, palm, fns=(C.update_by_nadam,))
+        super().__init__(params, defaults, gradient_clipping, update_clipping, palm, fns=(C.update_by_nadam,))
 
 
 class AdEMAMix(C.BaseOpt):
@@ -120,7 +120,7 @@ def __init__(
             raise ValueError("AdEMAMix expects betas with three coefficients.")
 
         params, defaults = C._build_defaults(locals())
-        super().__init__(params, defaults, multi_tensor, gradient_clipping, update_clipping, fns=(C.update_by_ademamix,))
+        super().__init__(params, defaults, gradient_clipping, update_clipping, fns=(C.update_by_ademamix,))
 
 
 class UnscaledAdamW(C.BaseOpt):
@@ -149,7 +149,7 @@ def __init__(
     ):
         params, defaults = C._build_defaults(locals())
         super().__init__(
-            params, defaults, multi_tensor, gradient_clipping, update_clipping, palm, fns=(C.scale_by_unscaled_adam,)
+            params, defaults, gradient_clipping, update_clipping, palm, fns=(C.scale_by_unscaled_adam,)
         )
 
 
@@ -179,7 +179,7 @@ def __init__(
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
-        super().__init__(params, defaults, multi_tensor, gradient_clipping, update_clipping, palm, fns=(C.scale_by_suds,))
+        super().__init__(params, defaults, gradient_clipping, update_clipping, palm, fns=(C.scale_by_suds,))
 
 
 class Scion(C.BaseOpt):
@@ -222,7 +222,7 @@ def __init__(
         defaults.pop("momentum", None)
 
         super().__init__(
-            params, defaults, multi_tensor, gradient_clipping, update_clipping, fns=(C.exp_avg, C.scion_auto_norm)
+            params, defaults, gradient_clipping, update_clipping, fns=(C.exp_avg, C.scion_auto_norm)
         )
 
 
@@ -258,7 +258,7 @@ def __init__(
             max_lr = lr
 
         params, defaults = C._build_defaults(locals())
-        super().__init__(params, defaults, multi_tensor, gradient_clipping, update_clipping, palm, fns=(C.update_by_adamc,))
+        super().__init__(params, defaults, gradient_clipping, update_clipping, palm, fns=(C.update_by_adamc,))
 
 
 class RMSprop(C.BaseOpt):
@@ -295,7 +295,6 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -331,7 +330,6 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -372,7 +370,6 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -413,7 +410,6 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -452,7 +448,6 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -485,7 +480,7 @@ def __init__(
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
-        super().__init__(params, defaults, multi_tensor, gradient_clipping, update_clipping, palm, fns=(C.update_by_adopt,))
+        super().__init__(params, defaults, gradient_clipping, update_clipping, palm, fns=(C.update_by_adopt,))
 
 
 class Muon(C.BaseOpt):
@@ -526,7 +521,6 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -559,7 +553,7 @@ def __init__(
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
-        super().__init__(params, defaults, multi_tensor, gradient_clipping, update_clipping, palm, fns=(C.update_by_laprop,))
+        super().__init__(params, defaults, gradient_clipping, update_clipping, palm, fns=(C.update_by_laprop,))
 
 
 class MuonLaProp(C.BaseOpt):
@@ -590,7 +584,6 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -613,7 +606,6 @@ def _build_soap_defaults(self, locals_dict, fns):
         super().__init__(
             params,
             defaults,
-            locals_dict["multi_tensor"],
             locals_dict["gradient_clipping"],
             locals_dict["update_clipping"],
             locals_dict.get("palm", False),
@@ -773,7 +765,6 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -855,7 +846,6 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -891,7 +881,6 @@ def __init__(
         super().__init__(
             params,
             defaults,
-            multi_tensor,
             gradient_clipping,
             update_clipping,
             palm,
@@ -921,7 +910,6 @@ def _build_psgd_defaults(self, locals_dict, fns, *, default_update_clipping=util
         super().__init__(
             params,
             defaults,
-            locals_dict["multi_tensor"],
             locals_dict["gradient_clipping"],
             update_clipping,
             False,
@@ -1139,7 +1127,7 @@ def __init__(self, specs):
                 all_params.extend(params)
         if not self.optimizers:
             raise ValueError("No optimizers created")
-        super().__init__(all_params, {}, multi_tensor=True)
+        super().__init__(all_params, {"multi_tensor": True})
 
     def _step(self, group):
         pass
diff --git a/heavyball/chainable.py b/heavyball/chainable.py
index abd0290..1c210c3 100644
--- a/heavyball/chainable.py
+++ b/heavyball/chainable.py
@@ -2,6 +2,7 @@
 import copy
 import functools
 import math
+import warnings
 from collections.abc import Iterable as _Iterable
 from typing import Iterable, List, Literal, Optional, Union
 
@@ -180,12 +181,34 @@ def _storage_dtype(group):
 
 _PASSTHROUGH_KWARGS = {"orig_shapes"}
 
+_RENAMED_KWARGS = {"foreach": "multi_tensor"}
+
+_REMOVED_KWARGS = frozenset({
+    "stochastic_schedule",
+    "normalize_grads",
+    "correct_bias",
+    "inverse_free",
+    "adaptive",
+})
+
 
 def _build_defaults(locals_dict):
     d = locals_dict.copy()
     d.pop("self")
     params = d.pop("params")
     kwargs = d.pop("kwargs")
+
+    for old, new in _RENAMED_KWARGS.items():
+        if old in kwargs:
+            warnings.warn(f"'{old}' was renamed to '{new}' in HeavyBall 3.0. "
+                          f"Pass '{new}' instead.", FutureWarning, stacklevel=4)
+            d[new] = kwargs.pop(old)
+
+    hit = _REMOVED_KWARGS & kwargs.keys()
+    if hit:
+        raise TypeError(f"Removed in HeavyBall 3.0: {', '.join(sorted(hit))}. "
+                        f"See docs/heavyball3.md for migration details.")
+
     d.update(kwargs)
     unknown = {k: v for k, v in kwargs.items() if k not in _PASSTHROUGH_KWARGS}
     if unknown:
@@ -1725,14 +1748,14 @@ class ChainOpt(utils.StatefulOptimizer):
         "eps": 1e-8,
     }
 
-    def __init__(self, params, defaults, multi_tensor: bool, *fns):
+    def __init__(self, params, defaults, *fns):
         orig = defaults.pop("orig_shapes", None)
         self._orig_shapes = (
             {k: _ShapeInfo(v) if isinstance(v, tuple) else v for k, v in orig.items()} if orig is not None else None
         )
         base = self.global_defaults.copy()
         base.update({k: v for k, v in defaults.items() if v is not use_default})
-        super().__init__(params, base, multi_tensor)
+        super().__init__(params, base)
         self.fns = fns
         self._eager_chain = self._run_chain
         if self.compile_step:
@@ -1993,7 +2016,6 @@ def __init__(
         self,
         params,
         defaults,
-        multi_tensor: bool = True,
         gradient_clipping: str_or_fn = None,
         update_clipping: str_or_fn = None,
         palm: bool = use_default,
@@ -2041,7 +2063,7 @@ def __init__(
         if default(update_clipping, self.update_clipping) is not None:
             fns = fns + (apply_to_idx(update_clipping, 2),)
 
-        super().__init__(params, defaults, multi_tensor, *fns)
+        super().__init__(params, defaults, *fns)
 
 
 class ScheduleFree(BaseOpt):
diff --git a/heavyball/utils.py b/heavyball/utils.py
index e8021a0..e2207a5 100644
--- a/heavyball/utils.py
+++ b/heavyball/utils.py
@@ -1306,13 +1306,14 @@ class StatefulOptimizer(torch.optim.Optimizer):
         "hessian_approx",
     )
 
-    def __init__(self, params, defaults, multi_tensor: bool = True, use_ema: bool = False):
+    def __init__(self, params, defaults, use_ema: bool = False):
         for attr in self._INSTANCE_ATTRS:
             if attr in defaults:
                 val = defaults.pop(attr)
                 if val is not use_default:
                     setattr(self, attr, val)
-        super().__init__(params, {**defaults, "multi_tensor": multi_tensor})
+        defaults.setdefault("multi_tensor", True)
+        super().__init__(params, defaults)
         self.use_ema = use_ema
         self.mapping = {}
         self.mapping_inverse = {}
diff --git a/pyproject.toml b/pyproject.toml
index 54c4d55..7c2d78d 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -5,7 +5,7 @@ build-backend = "setuptools.build_meta"
 [project]
 name = "heavyball"
 description = "Compile-first PyTorch optimizer library - AdamW, Muon, SOAP/Shampoo, PSGD, Schedule-Free, and 30+ more with torch.compile fusion and composable features"
-version = "2.3.2"
+version = "3.0.0"
 authors = [{ name = "HeavyBall Authors", email = "github.heavyball@nestler.sh" }]
 classifiers = ["Intended Audience :: Developers",
     "Intended Audience :: Science/Research",
diff --git a/scripts/migrate_optimizer_state.py b/scripts/migrate_optimizer_state.py
index 0c0e3e0..162538c 100644
--- a/scripts/migrate_optimizer_state.py
+++ b/scripts/migrate_optimizer_state.py
@@ -24,6 +24,7 @@
 import typer
 
 _CLASS_RENAMES = {
+    # Foreach* internal names → canonical 3.x names
     "ForeachAdamW": "AdamW",
     "ForeachNAdam": "NAdam",
     "ForeachAdEMAMix": "AdEMAMix",
@@ -54,6 +55,19 @@
     "ForeachDelayedPSGDLRA": "PSGDLRA",
     "ForeachNewtonPSGDLRA": "PSGDLRA",
     "NewtonHybrid2PSGDLRA": "PSGDLRA",
+    # 2.x public aliases that pointed to Foreach* classes (now removed)
+    "PaLMSOAP": "SOAP",
+    "PaLMSFAdamW": "SFAdamW",
+    "PalmForEachSoap": "SOAP",
+    "PrecondScheduleSOAP": "SOAP",
+    "PrecondSchedulePaLMSOAP": "SOAP",
+    "PurePSGD": "PSGDKron",
+    "DelayedPSGD": "PSGDKron",
+    "CachedPSGDKron": "PSGDKron",
+    "CachedDelayedPSGDKron": "PSGDKron",
+    "NewtonPSGDKron": "PSGDKron",
+    "DelayedPSGDLRA": "PSGDLRA",
+    "NewtonPSGDLRA": "PSGDLRA",
 }
 
 _REMOVED_GROUP_KEYS = frozenset({"stochastic_schedule"})

From cc981339e5fdcf08a8f8e0a793f4d6f510262d24 Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Mon, 30 Mar 2026 11:21:39 +0000
Subject: [PATCH 10/24] ruff

---
 heavyball/__init__.py     | 39 ++++++++++++++++++------------
 heavyball/chainable.py    | 51 ++++++++++++++++++++-------------------
 heavyball/utils.py        | 10 ++------
 test/test_compile_step.py |  4 +--
 test/test_migrate_cli.py  | 18 +++++++++++---
 test/test_utils_cpu.py    |  1 -
 6 files changed, 68 insertions(+), 55 deletions(-)

diff --git a/heavyball/__init__.py b/heavyball/__init__.py
index d4357c4..46a0f7c 100644
--- a/heavyball/__init__.py
+++ b/heavyball/__init__.py
@@ -148,9 +148,7 @@ def __init__(
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
-        super().__init__(
-            params, defaults, gradient_clipping, update_clipping, palm, fns=(C.scale_by_unscaled_adam,)
-        )
+        super().__init__(params, defaults, gradient_clipping, update_clipping, palm, fns=(C.scale_by_unscaled_adam,))
 
 
 class SUDSAdamW(C.BaseOpt):
@@ -221,9 +219,7 @@ def __init__(
         defaults["scale"] = scale
         defaults.pop("momentum", None)
 
-        super().__init__(
-            params, defaults, gradient_clipping, update_clipping, fns=(C.exp_avg, C.scion_auto_norm)
-        )
+        super().__init__(params, defaults, gradient_clipping, update_clipping, fns=(C.exp_avg, C.scion_auto_norm))
 
 
 class AdamC(C.BaseOpt):
@@ -333,10 +329,13 @@ def __init__(
             gradient_clipping,
             update_clipping,
             palm,
-            fns=(C.scale_by_exp_avg_sq, C.route(
-                (lambda p: p.ndim >= 2, C.update_by_hyperball),
-                default=C.apply_update,
-            )),
+            fns=(
+                C.scale_by_exp_avg_sq,
+                C.route(
+                    (lambda p: p.ndim >= 2, C.update_by_hyperball),
+                    default=C.apply_update,
+                ),
+            ),
         )
 
 
@@ -373,10 +372,12 @@ def __init__(
             gradient_clipping,
             update_clipping,
             palm,
-            fns=(C.route(
-                (lambda p: p.ndim >= 2, (ema, C.orthogonalize_update)),
-                default=C.scale_by_adam,
-            ),),
+            fns=(
+                C.route(
+                    (lambda p: p.ndim >= 2, (ema, C.orthogonalize_update)),
+                    default=C.scale_by_adam,
+                ),
+            ),
         )
 
 
@@ -893,7 +894,9 @@ class PSGDBase(C.BaseOpt):
     cached: bool = False
     exp_avg_input: bool = True
 
-    def _build_psgd_defaults(self, locals_dict, fns, *, default_update_clipping=utils.trust_region_clip_, extra_defaults=None):
+    def _build_psgd_defaults(
+        self, locals_dict, fns, *, default_update_clipping=utils.trust_region_clip_, extra_defaults=None
+    ):
         exp_avg_input = C.default(locals_dict.get("exp_avg_input", C.use_default), self.exp_avg_input)
         update_clipping = C.default(locals_dict["update_clipping"], default_update_clipping)
 
@@ -1204,4 +1207,8 @@ def zero_grad(self, set_to_none: bool = True):
 
 capture_param_shapes = utils.capture_param_shapes
 _BASE_CLASSES = {SOAPBase, PSGDBase}
-__all__ = [k for k, v in globals().items() if isinstance(v, type) and issubclass(v, torch.optim.Optimizer) and v not in _BASE_CLASSES]
+__all__ = [
+    k
+    for k, v in globals().items()
+    if isinstance(v, type) and issubclass(v, torch.optim.Optimizer) and v not in _BASE_CLASSES
+]
diff --git a/heavyball/chainable.py b/heavyball/chainable.py
index 1c210c3..c676931 100644
--- a/heavyball/chainable.py
+++ b/heavyball/chainable.py
@@ -25,7 +25,6 @@ def _key_in_state(state, key):
     return True
 
 
-
 def _guard_in_state(state, key, template_fn):
     if not _key_in_state(state, key):
         state[key] = template_fn()
@@ -150,7 +149,9 @@ def _sel(lst, idx):
                 continue
             group["caution"] = caution
             if fns is not None:
-                u, skip = _inner_chain(_sel(state, idx), group, _sel(update, idx), _sel(grad, idx), _sel(param, idx), *fns)
+                u, skip = _inner_chain(
+                    _sel(state, idx), group, _sel(update, idx), _sel(grad, idx), _sel(param, idx), *fns
+                )
             else:
                 u, skip = _sel(update, idx), False
             results.append((u, skip, idx))
@@ -183,13 +184,15 @@ def _storage_dtype(group):
 
 _RENAMED_KWARGS = {"foreach": "multi_tensor"}
 
-_REMOVED_KWARGS = frozenset({
-    "stochastic_schedule",
-    "normalize_grads",
-    "correct_bias",
-    "inverse_free",
-    "adaptive",
-})
+_REMOVED_KWARGS = frozenset(
+    {
+        "stochastic_schedule",
+        "normalize_grads",
+        "correct_bias",
+        "inverse_free",
+        "adaptive",
+    }
+)
 
 
 def _build_defaults(locals_dict):
@@ -200,14 +203,16 @@ def _build_defaults(locals_dict):
 
     for old, new in _RENAMED_KWARGS.items():
         if old in kwargs:
-            warnings.warn(f"'{old}' was renamed to '{new}' in HeavyBall 3.0. "
-                          f"Pass '{new}' instead.", FutureWarning, stacklevel=4)
+            warnings.warn(
+                f"'{old}' was renamed to '{new}' in HeavyBall 3.0. Pass '{new}' instead.", FutureWarning, stacklevel=4
+            )
             d[new] = kwargs.pop(old)
 
     hit = _REMOVED_KWARGS & kwargs.keys()
     if hit:
-        raise TypeError(f"Removed in HeavyBall 3.0: {', '.join(sorted(hit))}. "
-                        f"See docs/heavyball3.md for migration details.")
+        raise TypeError(
+            f"Removed in HeavyBall 3.0: {', '.join(sorted(hit))}. See docs/heavyball3.md for migration details."
+        )
 
     d.update(kwargs)
     unknown = {k: v for k, v in kwargs.items() if k not in _PASSTHROUGH_KWARGS}
@@ -795,7 +800,9 @@ def _adopt_warmup_2(state, group, update, grad, param, exp_avg, exp_avg_sq):
     u = utils.promote(update)
     easq = utils.promote(exp_avg_sq)
     utils.copy_stochastic_(exp_avg, u / easq.sqrt().clamp_(min=group["eps"]))
-    utils.scale_by_exp_avg_sq_([exp_avg_sq], [update], utils.beta_debias(utils.get_beta2(group), group["step"]), group["eps"])
+    utils.scale_by_exp_avg_sq_(
+        [exp_avg_sq], [update], utils.beta_debias(utils.get_beta2(group), group["step"]), group["eps"]
+    )
 
 
 @zero_guard("exp_avg", "exp_avg_sq")
@@ -930,7 +937,6 @@ def _init_psgd_lra(state, group, update, grad, param, cached: bool = False, prob
     )
 
 
-
 @needs_full_param
 @no_state_no_multi_tensor
 def orthogonalize_update(group, update, grad, param, scale_mode: str = "scale"):  # explore scale_mode="graft"
@@ -1266,9 +1272,7 @@ def _cached_psgd_precond_grad(group, update, Q, Q_cache, grad):
     if group.get("is_cached", False) and Q_cache[0] is not None:
         out = utils.precond_grad_cached_(cached_q=Q_cache, **kwargs)
     else:
-        out = utils.psgd_precond_grad(
-            preconds=Q, store_triu_as_line=group["store_triu_as_line"], **kwargs
-        )
+        out = utils.psgd_precond_grad(preconds=Q, store_triu_as_line=group["store_triu_as_line"], **kwargs)
     group["caution"] = False  # we already cautioned here - shouldn't do it again
     return out
 
@@ -1285,9 +1289,7 @@ def _fused_cached_psgd_precond_grad(group, grad, param, update, Q, Q_cache):
     if group.get("is_cached", False) and Q_cache[0] is not None:
         utils.fused_precond_grad_cached_(cached_q=Q_cache, **kwargs)
     else:
-        utils.fused_psgd_precond_grad(
-            preconds=Q, store_triu_as_line=group["store_triu_as_line"], **kwargs
-        )
+        utils.fused_psgd_precond_grad(preconds=Q, store_triu_as_line=group["store_triu_as_line"], **kwargs)
 
 
 def _update_lra(
@@ -1393,9 +1395,7 @@ def scale_by_delayed_psgd(
     prob: Optional[callable] = None,
 ):
     precond = _cached_psgd_precond_grad(group, update, Q, Q_cache, grad)
-    _update_psgd_precond(
-        cached, Q_cache, group, param, update_to_precond, Q, running_lower_bound, step, prob
-    )
+    _update_psgd_precond(cached, Q_cache, group, param, update_to_precond, Q, running_lower_bound, step, prob)
     return precond
 
 
@@ -1851,7 +1851,8 @@ def fns(self, value):
         self._set_indices(retain=True)
         self._needs_gather = any(getattr(ft, "needs_full_param", False) for ft in _walk_fns(self._fns))
         self._transform_ids = frozenset(
-            ft.transform_idx for ft in _walk_fns(self._fns)
+            ft.transform_idx
+            for ft in _walk_fns(self._fns)
             if ft.transform_idx is not None and getattr(ft, "needs_init", True)
         )
 
diff --git a/heavyball/utils.py b/heavyball/utils.py
index e2207a5..76e6da3 100644
--- a/heavyball/utils.py
+++ b/heavyball/utils.py
@@ -7,11 +7,10 @@
 import itertools
 import math
 import pickle
-import random
 import re
 import string
 import warnings
-from typing import Any, Callable, List, Literal, Optional, Tuple, Union
+from typing import Any, Callable, List, Optional, Tuple, Union
 
 import numpy as np
 import torch
@@ -3172,10 +3171,7 @@ def _psgd_precond_update_(
 
 
 @decorator_knowngood
-
-
 @decorator
-
 @decorator_knowngood
 def _clip(x, norm, clip_at, eps=1e-8):
     x32 = promote(x)
@@ -3564,9 +3560,7 @@ def fused_psgd_precond_grad(
     store_triu_as_line: bool = False,
 ):
     lr, decay = scalar_guard(lr, decay, param[0])
-    _compilable_fused_psgd_precond_grad(
-        ea, param, lr, grad, decay, caution, preconds, store_triu_as_line
-    )
+    _compilable_fused_psgd_precond_grad(ea, param, lr, grad, decay, caution, preconds, store_triu_as_line)
 
 
 @decorator_knowngood
diff --git a/test/test_compile_step.py b/test/test_compile_step.py
index eb7bbaf..ce0a8e5 100644
--- a/test/test_compile_step.py
+++ b/test/test_compile_step.py
@@ -48,6 +48,7 @@ def _make_model():
 def _run_steps(model, optimizer, n=5, seed=0xDEADBEEF):
     torch.manual_seed(seed)
     for _ in range(n):
+
         def closure():
             optimizer.zero_grad(set_to_none=True)
             data = torch.randn(4, 8, device=DEVICE)
@@ -109,6 +110,5 @@ def test_needs_init_clears(opt_name, opt_cls):
     for group in opt.param_groups:
         state = [opt.state_(p) for p in group["params"]]
         assert not opt._needs_init(state), (
-            f"{opt_name}: _needs_init stuck True after {n} steps | "
-            f"compile_step will never engage"
+            f"{opt_name}: _needs_init stuck True after {n} steps | compile_step will never engage"
         )
diff --git a/test/test_migrate_cli.py b/test/test_migrate_cli.py
index d3f3de7..0130305 100644
--- a/test/test_migrate_cli.py
+++ b/test/test_migrate_cli.py
@@ -216,9 +216,17 @@ def test_load_optimizer_class_invalid_raises():
     ("flat_neither", {"state": _flat_state((2,)), "param_groups": [{}]}, 1),
     ("flat_multi_group", {"state": _flat_state((2,), (3,)), "param_groups": [{"foreach": True}, {}]}, 1),
     ("nested_foreach", {"state": _nested_state((2,)), "param_groups": [{"foreach": True}]}, 2),
-    ("nested_foreach_multi_group", {"state": _nested_state((2,), (3,)), "param_groups": [{"foreach": True}, {"foreach": True}]}, 2),
+    (
+        "nested_foreach_multi_group",
+        {"state": _nested_state((2,), (3,)), "param_groups": [{"foreach": True}, {"foreach": True}]},
+        2,
+    ),
     ("nested_multi_tensor", {"state": _nested_state((2,)), "param_groups": [{"multi_tensor": True}]}, 3),
-    ("nested_multi_tensor_multi_group", {"state": _nested_state((2,), (3,)), "param_groups": [{"multi_tensor": True}, {}]}, 3),
+    (
+        "nested_multi_tensor_multi_group",
+        {"state": _nested_state((2,), (3,)), "param_groups": [{"multi_tensor": True}, {}]},
+        3,
+    ),
     ("empty_state_multi_tensor", {"state": {}, "param_groups": [{"multi_tensor": True}]}, 3),
     ("empty_state_foreach", {"state": {}, "param_groups": [{"foreach": True}]}, 1),
     ("empty_state_bare", {"state": {}, "param_groups": [{}]}, 1),
@@ -246,7 +254,11 @@ def test_detect_version(name, sd, expected):
     ("empty_group", {}, {}),
     ("params_only", {"params": [0]}, {}),
     ("all_removed", {"params": [0], "stochastic_schedule": None}, {}),
-    ("kitchen_sink", {"params": [0, 1], "foreach": True, "stochastic_schedule": True, "lr": 0.01, "betas": [0.9, 0.99]}, {"multi_tensor": True, "lr": 0.01, "betas": (0.9, 0.99)}),
+    (
+        "kitchen_sink",
+        {"params": [0, 1], "foreach": True, "stochastic_schedule": True, "lr": 0.01, "betas": [0.9, 0.99]},
+        {"multi_tensor": True, "lr": 0.01, "betas": (0.9, 0.99)},
+    ),
 ]
 
 
diff --git a/test/test_utils_cpu.py b/test/test_utils_cpu.py
index 621056c..b9af3d7 100644
--- a/test/test_utils_cpu.py
+++ b/test/test_utils_cpu.py
@@ -1,5 +1,4 @@
 import os
-import random
 import warnings
 from copy import deepcopy
 

From 164ba3ad3fba67fa64e95ee72c3316573456fd39 Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Mon, 30 Mar 2026 18:57:09 +0000
Subject: [PATCH 11/24] reduce python overhead

---
 README.md                |   7 +-
 heavyball/chainable.py   | 378 +++++++++++++++++++++++++++++----------
 heavyball/utils.py       | 122 ++++++++-----
 test/test_distributed.py |  39 +++-
 4 files changed, 394 insertions(+), 152 deletions(-)

diff --git a/README.md b/README.md
index d143e93..3ae2ebd 100644
--- a/README.md
+++ b/README.md
@@ -128,9 +128,10 @@ Available modes: `bf16+8`, `bf16+16`, `fp16+8`, `fp16+16`.
 
 HeavyBall works with both DDP and FSDP. First-order optimizers are elementwise and operate directly on FSDP shards with
 no repartitioning. Second-order methods (Muon, SOAP, PSGD) need the full parameter to compute their update, so HeavyBall
-auto-detects FSDP-sharded parameters on the first step and repartitions them: each weight matrix is assigned to one rank
-in round-robin, which reconstructs the full parameter, computes the update, and broadcasts the result. This saves both
-compute and memory compared to DDP-style redundant updates, at the cost of communication.
+auto-detects FSDP-sharded parameters on the first step and repartitions them with a metadata-first `all_to_all_single`
+exchange: each weight matrix is deterministically assigned to one rank, shard metadata is exchanged up front, the owner
+reconstructs the full parameter, computes the update once, and returns the updated shards. This saves both compute and
+memory compared to DDP-style redundant updates, at the cost of communication.
 
 ```python
 from torch.distributed.fsdp import FullyShardedDataParallel as FSDP
diff --git a/heavyball/chainable.py b/heavyball/chainable.py
index c676931..5204dca 100644
--- a/heavyball/chainable.py
+++ b/heavyball/chainable.py
@@ -755,12 +755,12 @@ def orthogonalize_grad_to_param(group, update, grad, param):
 def update_by_schedule_free(group, update, grad, param, z):
     # Compute weight_sum once per step, not per param in no-multi_tensor mode.
     if group.get("_sf_step") is not group["step"]:
-        weight = abs(group["lr"]) ** group["weight_lr_power"] * max(group["step"], 1) ** group["r"]
+        weight = abs(group["lr"]) ** group["weight_lr_power"] * group["step"].clamp(min=1) ** group["r"]
         group["weight_sum"] = group.get("weight_sum", 0) + weight
         group["_sf_step"] = group["step"]
 
     weight_sum = group["weight_sum"]
-    weight = abs(group["lr"]) ** group["weight_lr_power"] * max(group["step"], 1) ** group["r"]
+    weight = abs(group["lr"]) ** group["weight_lr_power"] * group["step"].clamp(min=1) ** group["r"]
     try:
         ckp1 = weight / weight_sum
     except ZeroDivisionError:
@@ -881,6 +881,7 @@ def scale_by_adopt(group, update, grad, param, exp_avg, exp_avg_sq):
 
 
 def _init_psgd_kron(state, group, update, grad, param, cached: bool = False, prob: Optional[callable] = None):
+    tmp = utils.get_temporary(group, param) or {}
     Q = utils.init_Q_exprs(
         grad,
         group["precond_init_scale"],
@@ -889,8 +890,8 @@ def _init_psgd_kron(state, group, update, grad, param, cached: bool = False, pro
         group["max_size_triangular"],
         group["min_ndim_triangular"],
         group["memory_save_mode"],
-        getattr(param, "hessian_vector", None),
-        getattr(param, "vector", None),
+        tmp.get("hessian_vector"),
+        tmp.get("vector"),
         dtype=getattr(torch, group["q_dtype"]),
     )
     state["Q"] = utils.triu_to_line(Q) if group["store_triu_as_line"] else Q
@@ -924,6 +925,7 @@ def _init_psgd_pro_kron(state, group, update, grad, param, cached: bool = False,
 
 
 def _init_psgd_lra(state, group, update, grad, param, cached: bool = False, prob: Optional[callable] = None):
+    tmp = utils.get_temporary(group, param) or {}
     state["U"], state["V"], state["d"] = utils.init_lra(
         grad,
         group["param_count"],
@@ -931,8 +933,8 @@ def _init_psgd_lra(state, group, update, grad, param, cached: bool = False, prob
         group["precond_init_scale_scale"],
         group["precond_init_scale_power"],
         group["rank"],
-        getattr(param, "hessian_vector", None),
-        getattr(param, "vector", None),
+        tmp.get("hessian_vector"),
+        tmp.get("vector"),
         dtype=getattr(torch, group["q_dtype"]),
     )
 
@@ -1169,12 +1171,10 @@ def _update_psgd_precond(
     if not group["is_preconditioning"]:
         return
 
-    if utils.hasattr_none(param, "vector"):
-        vector, hessian_vector = param.vector, param.hessian_vector
-        del param.vector
-        del param.hessian_vector
-    else:
+    if (utils.get_temporary(group, param) or {}).get("vector") is None:
         vector, hessian_vector = utils.dampen_grad(grad, group["dampening"])
+    else:
+        vector, hessian_vector = utils.take_temporary(group, param, "vector", "hessian_vector")
 
     precond = utils.psgd_update_precond(
         hessian_vector,
@@ -1298,12 +1298,10 @@ def _update_lra(
     if not group["is_preconditioning"]:
         return utils.multi_flatten((U, 1), (V, 1), (d, 0))
 
-    if utils.hasattr_none(params[0], "hessian_vector"):
-        vector = utils.flatten([p.vector for p in params])
-        hessian_vector = utils.flatten([p.hessian_vector for p in params])
-        for p in params:
-            del p.vector
-            del p.hessian_vector
+    if (utils.get_temporary(group, params[0]) or {}).get("hessian_vector") is not None:
+        vector_hv = [utils.take_temporary(group, p, "vector", "hessian_vector") for p in params]
+        vector = utils.flatten([v for v, _ in vector_hv])
+        hessian_vector = utils.flatten([hv for _, hv in vector_hv])
     else:
         vector, hessian_vector = utils.dampen_multiple(grads)
     precond_step = group["precond_step"] = group.get("precond_step", -1) + 1
@@ -1523,15 +1521,70 @@ def _fn(state, group, update, grad, param):
     return _fn
 
 
+_FSDP_HEADER_WIDTH = 4
+_FSDP_BUCKET_BYTES = 32 << 20
+_FSDP_DTYPE_CODES = {
+    torch.float64: 0,
+    torch.float32: 1,
+    torch.float16: 2,
+    torch.bfloat16: 3,
+    torch.int64: 4,
+    torch.int32: 5,
+    torch.int16: 6,
+    torch.int8: 7,
+    torch.uint8: 8,
+    torch.bool: 9,
+}
+
+
 class _ShapeInfo:
-    __slots__ = ("orig_shape", "offset", "total", "group", "owner")
+    __slots__ = ("orig_shape", "offset", "total", "group", "owner", "param_idx")
 
-    def __init__(self, orig_shape, offset=0, total=None, group=None, owner=None):
+    def __init__(self, orig_shape, offset=0, total=None, group=None, owner=None, param_idx=None):
         self.orig_shape = orig_shape
         self.offset = offset
         self.total = total if total is not None else math.prod(orig_shape)
         self.group = group
         self.owner = owner
+        self.param_idx = param_idx
+
+
+class _FSDPBucket:
+    __slots__ = ("device", "dtype", "send_entries", "send_splits", "recv_entries", "recv_splits")
+
+    def __init__(self, device, dtype, send_entries, send_splits, recv_entries, recv_splits):
+        self.device = device
+        self.dtype = dtype
+        self.send_entries = send_entries
+        self.send_splits = send_splits
+        self.recv_entries = recv_entries
+        self.recv_splits = recv_splits
+
+
+class _FSDPState:
+    __slots__ = ("items", "buckets")
+
+    def __init__(self, items, buckets):
+        self.items = items
+        self.buckets = buckets
+
+
+def _dtype_code(dtype):
+    if dtype not in _FSDP_DTYPE_CODES:
+        raise TypeError(f"Unsupported FSDP shard dtype: {dtype}")
+    return _FSDP_DTYPE_CODES[dtype]
+
+
+def _assign_fsdp_owners(entries, shard_sizes, world_size):
+    loads = [0] * world_size
+    owners = []
+    for i, (p, _, total, _) in enumerate(entries):
+        active = shard_sizes[i].nonzero().squeeze(-1).tolist()
+        candidates = active or list(range(world_size))
+        owner = min(candidates, key=loads.__getitem__)
+        loads[owner] += total * p.element_size()
+        owners.append(owner)
+    return owners
 
 
 def _detect_orig_shapes(params):
@@ -1554,8 +1607,6 @@ def _detect_orig_shapes(params):
         for param, spi, shape in zip(obj._params, obj._shard_param_infos, obj._shapes):
             lookup[id(param)] = (tuple(shape), spi)
 
-    _dist = torch.distributed.is_initialized() and torch.distributed.get_world_size() > 1
-
     # optimizer param order is stable across ranks
     fsdp_entries = [
         (p, s, math.prod(s), spi)
@@ -1563,47 +1614,178 @@ def _detect_orig_shapes(params):
         for s, spi in [lookup.get(id(p), (None, None))]
         if id(p) in fsdp_ids and s is not None
     ]
-
-    groups = {}
-    if _dist and fsdp_entries:
-        rank = torch.distributed.get_rank()
-        ws = torch.distributed.get_world_size()
-        n = len(fsdp_entries)
-        flags = torch.zeros(n, ws, dtype=torch.int32, device=fsdp_entries[0][0].device)
-        for i, (p, orig, total, spi) in enumerate(fsdp_entries):
-            if spi.in_shard and spi.numel_in_shard is not None and spi.numel_in_shard < total:
-                flags[i, rank] = 1
-        torch.distributed.all_reduce(flags)
-        pg_cache = {}
-        for i in range(n):
-            ranks = flags[i].nonzero().squeeze(-1).tolist()
-            if len(ranks) >= 2:
-                key = tuple(ranks)
-                if key not in pg_cache:
-                    pg_cache[key] = torch.distributed.new_group(ranks)
-                groups[i] = (pg_cache[key], ranks)
-
-    # owner must be precomputed (different ranks see different subsets in _reshape_params)
     result = {}
-    split_idx = 0
-    for i, (p, orig, total, spi) in enumerate(fsdp_entries):
-        sg = groups.get(i)
-        if sg:
-            pg, ranks = sg
-            owner = ranks[split_idx % len(ranks)]
-            split_idx += 1
-            if spi.in_shard:
-                result[id(p)] = _ShapeInfo(orig, spi.intra_param_start_idx, total, pg, owner)
-        elif spi.in_shard:
-            result[id(p)] = _ShapeInfo(orig, spi.intra_param_start_idx, total)
+    ws = torch.distributed.get_world_size() if torch.distributed.is_initialized() else 1
+    if ws > 1 and fsdp_entries:
+        rank = torch.distributed.get_rank()
+        shard_sizes = torch.zeros(len(fsdp_entries), ws, dtype=torch.int64, device=fsdp_entries[0][0].device)
+        for i, (p, _, _, spi) in enumerate(fsdp_entries):
+            shard_sizes[i, rank] = p.numel() if spi.in_shard else 0
+        torch.distributed.all_reduce(shard_sizes)
+        owners = _assign_fsdp_owners(fsdp_entries, shard_sizes, ws)
+    else:
+        owners = [None] * len(fsdp_entries)
+    for param_idx, ((p, orig, total, spi), owner) in enumerate(zip(fsdp_entries, owners)):
+        offset = 0 if spi.intra_param_start_idx is None else spi.intra_param_start_idx
+        result[id(p)] = _ShapeInfo(orig, offset, total, owner=owner, param_idx=param_idx)
     return result
 
 
-def _reduce_gather(shard, offset, total, pg, dst):
-    full = shard.new_zeros(total)
-    full[offset : offset + shard.numel()] = shard
-    torch.distributed.reduce(full, dst=dst, group=pg)
-    return full
+def _exchange_split_sizes(splits, device):
+    send = torch.tensor(splits, dtype=torch.int64, device=device)
+    recv = torch.empty_like(send)
+    torch.distributed.all_to_all_single(recv, send)
+    return recv.tolist()
+
+
+def _all_to_all_variable(sendbuf, recv_splits, send_splits):
+    recv = sendbuf.new_empty(sum(recv_splits))
+    torch.distributed.all_to_all_single(recv, sendbuf, output_split_sizes=recv_splits, input_split_sizes=send_splits)
+    return recv
+
+
+def _fsdp_bucket_schedule(items):
+    buckets, current, lookup = [], {}, {}
+    for p, info, _ in items:
+        key = (p.device, p.dtype)
+        idx = current.get(key)
+        size = info.total * p.element_size()
+        if idx is None or (buckets[idx][2] and buckets[idx][2] + size > _FSDP_BUCKET_BYTES):
+            idx = len(buckets)
+            buckets.append([p.device, p.dtype, 0])
+            current[key] = idx
+        buckets[idx][2] += size
+        lookup[info.param_idx] = idx
+    return [(device, dtype) for device, dtype, _ in buckets], lookup
+
+
+def _exchange_fsdp_shards(schedule, bucket_lookup, items, tensor_getter, keep_state=False):
+    ws = torch.distributed.get_world_size()
+    per_bucket = [[] for _ in schedule]
+    for p, info, shard in items:
+        tensor = tensor_getter(p, shard)
+        if tensor is None or tensor.numel() == 0:
+            continue
+        flat = tensor.reshape(-1)
+        bucket_idx = bucket_lookup[info.param_idx]
+        device, dtype = schedule[bucket_idx]
+        if flat.device != device or flat.dtype != dtype:
+            raise RuntimeError(f"FSDP bucket mismatch for param {info.param_idx}: expected {(device, dtype)}, got {(flat.device, flat.dtype)}")
+        per_bucket[bucket_idx].append((info.owner, info.param_idx, info.offset, flat, shard))
+
+    received, states = {}, []
+    for (device, dtype), bucket_entries in zip(schedule, per_bucket):
+        by_dst = [[] for _ in range(ws)]
+        for entry in bucket_entries:
+            by_dst[entry[0]].append(entry)
+
+        send_meta_splits = [len(dst_entries) * _FSDP_HEADER_WIDTH for dst_entries in by_dst]
+        send_payload_splits = [sum(flat.numel() for _, _, _, flat, _ in dst_entries) for dst_entries in by_dst]
+        recv_meta_splits = _exchange_split_sizes(send_meta_splits, device)
+        recv_payload_splits = _exchange_split_sizes(send_payload_splits, device)
+
+        code = _dtype_code(dtype)
+        meta = [
+            value
+            for dst_entries in by_dst
+            for _, param_idx, offset, flat, _ in dst_entries
+            for value in (param_idx, offset, flat.numel(), code)
+        ]
+        payload = [flat for dst_entries in by_dst for _, _, _, flat, _ in dst_entries]
+        send_meta = torch.tensor(meta, dtype=torch.int64, device=device) if meta else torch.empty(0, dtype=torch.int64, device=device)
+        send_payload = torch.cat(payload) if payload else torch.empty(0, dtype=dtype, device=device)
+
+        recv_meta = _all_to_all_variable(send_meta, recv_meta_splits, send_meta_splits)
+        recv_entries = [[] for _ in range(ws)]
+        meta_offset = 0
+        for src, count in enumerate(recv_meta_splits):
+            if count == 0:
+                continue
+            if count % _FSDP_HEADER_WIDTH:
+                raise RuntimeError(f"Malformed FSDP metadata split: {count}")
+            rows = recv_meta[meta_offset : meta_offset + count].view(-1, _FSDP_HEADER_WIDTH).cpu().tolist()
+            meta_offset += count
+            for param_idx, offset, length, got in rows:
+                if got != code:
+                    raise RuntimeError(f"FSDP dtype mismatch for bucket {dtype}: expected {code}, got {got}")
+                recv_entries[src].append((param_idx, offset, length))
+
+        recv_payload = _all_to_all_variable(send_payload, recv_payload_splits, send_payload_splits)
+        payload_offset = 0
+        for src_entries in recv_entries:
+            for param_idx, offset, length in src_entries:
+                chunk = recv_payload[payload_offset : payload_offset + length]
+                received.setdefault(param_idx, []).append((offset, chunk))
+                payload_offset += length
+        if payload_offset != recv_payload.numel():
+            raise RuntimeError("FSDP payload unpack mismatch")
+
+        if keep_state:
+            states.append(_FSDPBucket(device, dtype, by_dst, send_payload_splits, recv_entries, recv_payload_splits))
+
+    return received, states
+
+
+def _reshape_fsdp_params(items):
+    rank = torch.distributed.get_rank()
+    schedule, bucket_lookup = _fsdp_bucket_schedule(items)
+    params, buckets = _exchange_fsdp_shards(schedule, bucket_lookup, items, lambda _, shard: shard, keep_state=True)
+    grads, _ = _exchange_fsdp_shards(schedule, bucket_lookup, items, lambda p, _: p.grad)
+
+    for p, info, shard in items:
+        p.grad = None
+        if info.owner != rank:
+            continue
+
+        pieces = params.get(info.param_idx, ())
+        total = sum(chunk.numel() for _, chunk in pieces)
+        if total != info.total:
+            raise RuntimeError(f"FSDP parameter assembly mismatch for param {info.param_idx}: {total} != {info.total}")
+
+        full = shard.new_empty(info.total)
+        for offset, chunk in pieces:
+            full[offset : offset + chunk.numel()].copy_(chunk)
+        p.data = full.view(info.orig_shape)
+
+        grad_pieces = grads.get(info.param_idx, ())
+        if not grad_pieces:
+            continue
+        grad_total = sum(chunk.numel() for _, chunk in grad_pieces)
+        if grad_total != info.total:
+            raise RuntimeError(f"FSDP grad assembly mismatch for param {info.param_idx}: {grad_total} != {info.total}")
+        grad = full.new_empty(info.total, dtype=grad_pieces[0][1].dtype)
+        for offset, chunk in grad_pieces:
+            grad[offset : offset + chunk.numel()].copy_(chunk)
+        p.grad = grad.view(info.orig_shape)
+
+    return _FSDPState(items, buckets)
+
+
+def _restore_fsdp_params(state):
+    by_param = {info.param_idx: (p, info, shard) for p, info, shard in state.items}
+    for bucket in state.buckets:
+        payload = []
+        for dst, recv_entries in enumerate(bucket.recv_entries):
+            for param_idx, offset, length in recv_entries:
+                p, info, _ = by_param[param_idx]
+                flat = p.data.reshape(-1)
+                if flat.numel() != info.total:
+                    raise RuntimeError(f"FSDP return path expects full param {param_idx}, got {flat.numel()}")
+                payload.append(flat[offset : offset + length])
+        send_payload = torch.cat(payload) if payload else torch.empty(0, dtype=bucket.dtype, device=bucket.device)
+        recv_payload = _all_to_all_variable(send_payload, bucket.send_splits, bucket.recv_splits)
+
+        payload_offset = 0
+        for send_entries in bucket.send_entries:
+            for _, _, _, flat, shard in send_entries:
+                shard.copy_(recv_payload[payload_offset : payload_offset + flat.numel()])
+                payload_offset += flat.numel()
+        if payload_offset != recv_payload.numel():
+            raise RuntimeError("FSDP return payload unpack mismatch")
+
+    for p, _, shard in state.items:
+        p.data = shard
+        p.grad = None
 
 
 def _view_param(p, shape):
@@ -1615,57 +1797,55 @@ def _view_param(p, shape):
 def _reshape_params(params, orig_shapes, gather=True):
     if not orig_shapes:
         return [], []
-    rank = torch.distributed.get_rank() if torch.distributed.is_initialized() else 0
+    dist_ready = torch.distributed.is_initialized() and torch.distributed.get_world_size() > 1
     views, gathers = [], []
 
     for p in params:
         info = orig_shapes.get(id(p))
-        if info is None or p.data.shape == info.orig_shape:
+        if info is None:
             continue
 
-        if info.group is not None and gather:
+        if gather and dist_ready and info.owner is not None:
             shard = p.data
-            full = _reduce_gather(shard, info.offset, info.total, info.group, info.owner)
-            if rank == info.owner:
-                p.data = full.view(info.orig_shape)
-                if p.grad is not None:
-                    p.grad = _reduce_gather(p.grad, info.offset, info.total, info.group, info.owner).view(
-                        info.orig_shape
-                    )
-            else:
-                del full
-                if p.grad is not None:
-                    _reduce_gather(p.grad, info.offset, info.total, info.group, info.owner)
-                p.grad = None
             gathers.append((p, info, shard))
+            continue
+
+        if p.data.shape == info.orig_shape:
+            continue
+
+        orig, numel = info.orig_shape, p.data.numel()
+        if numel == info.total:
+            target = orig
+        elif numel > 0 and len(orig) >= 2:
+            inner = math.prod(orig[1:])
+            target = (numel // inner, *orig[1:]) if numel % inner == 0 else None
         else:
-            orig, numel = info.orig_shape, p.data.numel()
-            if numel == info.total:
-                target = orig
-            elif numel > 0 and len(orig) >= 2:
-                inner = math.prod(orig[1:])
-                target = (numel // inner, *orig[1:]) if numel % inner == 0 else None
-            else:
-                continue
-            if target is not None:
-                flat = p.data.shape
-                _view_param(p, target)
-                views.append((p, flat))
+            continue
+        if target is not None:
+            flat = p.data.shape
+            _view_param(p, target)
+            views.append((p, flat))
+
+    if gathers:
+        gathers = _reshape_fsdp_params(gathers)
 
     return views, gathers
 
 
 def _restore_params(views, gathers):
-    rank = torch.distributed.get_rank() if torch.distributed.is_initialized() else 0
-    for p, info, shard in gathers:
-        if rank == info.owner:
-            full = p.data.flatten()
-        else:
-            full = shard.new_empty(info.total)
-        torch.distributed.broadcast(full, src=info.owner, group=info.group)
-        shard.copy_(full[info.offset : info.offset + shard.numel()])
-        p.data = shard
-        p.grad = None
+    if isinstance(gathers, _FSDPState):
+        _restore_fsdp_params(gathers)
+    else:
+        rank = torch.distributed.get_rank() if torch.distributed.is_initialized() else 0
+        for p, info, shard in gathers:
+            if rank == info.owner:
+                full = p.data.flatten()
+            else:
+                full = shard.new_empty(info.total)
+            torch.distributed.broadcast(full, src=info.owner, group=info.group)
+            shard.copy_(full[info.offset : info.offset + shard.numel()])
+            p.data = shard
+            p.grad = None
     for p, flat in views:
         _view_param(p, flat)
 
@@ -1868,7 +2048,7 @@ def _find_val_name(self, name):
     def _step(self, group):
         if "base_lr" not in group:
             group["base_lr"] = group["lr"]
-        if "prev_lr" in group and group["prev_lr"] != group["lr"]:
+        if "base_lr" in group and group["base_lr"] != group["lr"]:
             utils.warn_once(
                 f"Learning rate changed between steps. This is an experimental feature and "
                 f"only supported with multi_tensor=True (currently multi_tensor={group['multi_tensor']})."
@@ -1911,10 +2091,10 @@ def _step_inner(self, group):
         if isinstance(step, torch.Tensor):
             step = step.to(device=p[0].device, dtype=torch.int64)
         else:
-            step = torch.tensor(step, dtype=torch.int64, device=p[0].device)
+            step = utils.scalar_guard(step, p[0])
         group["_group_step"] = group["step"] = step = step + 1
         self.state_(p[0])["step"] = step
-        group["prev_lr"] = group["lr"] = group["base_lr"] * step / max(step, group["warmup_steps"] + 1)
+        group["prev_lr"] = group["lr"] = group["base_lr"] * step / step.clamp(min=group["warmup_steps"] + 1)
 
         if not group["multi_tensor"] or len(p) == 1:
             for param, grad in zip(p, g):
@@ -1923,7 +2103,7 @@ def _step_inner(self, group):
             self._chain(group, g, p, caution)
 
         group["caution"] = caution
-        group["lr"] = group["prev_lr"]
+        group["lr"] = group["base_lr"]
         group["step"] = None
 
     def _run_chain(self, state, group, g, p, caution):
diff --git a/heavyball/utils.py b/heavyball/utils.py
index 76e6da3..e9c6791 100644
--- a/heavyball/utils.py
+++ b/heavyball/utils.py
@@ -1269,6 +1269,28 @@ def hasattr_none(obj, name):
     return getattr(obj, name, None) is not None
 
 
+def set_temporary(group: dict, tensor: Tensor, **kwargs):
+    if not kwargs:
+        return
+    state = group.setdefault("_tmp", {}).setdefault(id(tensor), {"tensor": tensor})
+    state.update(kwargs)
+
+
+def get_temporary(group: dict, tensor: Tensor):
+    tmp = group.get("_tmp")
+    return None if tmp is None else tmp.get(id(tensor))
+
+
+def take_temporary(group: dict, tensor: Tensor, *keys):
+    state = get_temporary(group, tensor)
+    if state is None:
+        return None if len(keys) == 1 else (None,) * len(keys)
+    out = tuple(state.pop(key, None) for key in keys)
+    if len(state) == 1:
+        group["_tmp"].pop(id(tensor), None)
+    return out[0] if len(keys) == 1 else out
+
+
 class ExactHVPFailed(ValueError):
     pass
 
@@ -1385,21 +1407,29 @@ def split_p_and_g_in_group(
         should_promote: bool = True,
         raw: bool = False,
     ):
+        tmp = group.get("_tmp")
         for p in group["params"]:
-            grad = getattr(p, "grad", None)
+            if raw:
+                grad = getattr(p, "grad", None)
+                if grad is None and skip_none:
+                    continue
+                p.grad = None
+                yield p, grad
+                continue
+
+            state = None if tmp is None else tmp.get(id(p))
+            grad = None if state is None else state.pop("grad", None)
+            if grad is None:
+                grad = getattr(p, "grad", None)
             if grad is None and skip_none:
                 continue
 
             p.grad = None
 
-            if raw:
-                yield p, grad
-                continue
-
             if group.get("merge_dims", False) and not p.data.is_contiguous():
                 for fmt in (torch.channels_last, torch.channels_last_3d):
                     if p.data.is_contiguous(memory_format=fmt):
-                        p._restore_memory_format = fmt
+                        set_temporary(group, p, restore_memory_format=fmt)
                         break
                 p.data = p.data.contiguous()
 
@@ -1407,20 +1437,23 @@ def split_p_and_g_in_group(
             for i, pv in enumerate(p_views):
                 self.mapping_inverse[_tensor_key(pv)] = (p, i)
 
-            vector = getattr(p, "vector", None)
-            hessian_vector = getattr(p, "hessian_vector", None)
-            p.vector = None
-            p.hessian_vector = None
-
-            grad, vs, hvs = [
-                [None] * len(p_views) if x is None else merge_group(group, x)  #
-                for x in (grad, vector, hessian_vector)
-            ]
+            if state is None:
+                vector = hessian_vector = None
+            else:
+                vector = state.pop("vector", None)
+                hessian_vector = state.pop("hessian_vector", None)
+                if len(state) == 1:
+                    tmp.pop(id(p), None)
+            grad = itertools.repeat(None, len(p_views)) if grad is None else merge_group(group, grad)
+            vs = itertools.repeat(None, len(p_views)) if vector is None else merge_group(group, vector)
+            hvs = itertools.repeat(None, len(p_views)) if hessian_vector is None else merge_group(group, hessian_vector)
 
             for pv, g, v, hv in zip(p_views, grad, vs, hvs):
                 g = promote_detach(g, should_promote)
-                pv.vector = promote_detach(v, should_promote)
-                pv.hessian_vector = promote_detach(hv, should_promote)
+                v = promote_detach(v, should_promote)
+                hv = promote_detach(hv, should_promote)
+                if v is not None or hv is not None:
+                    set_temporary(group, pv, vector=v, hessian_vector=hv)
                 yield pv, g
 
     def state_size(self) -> int:
@@ -1494,10 +1527,10 @@ def _finite_differences_hvp(self, closure):
         for group in self.param_groups:
             for p, g in self.split_p_and_g_in_group(group, skip_none=True, raw=True):
                 grads.append(g)
-                p.vector = torch.randn_like(p)
-                p.orig = p.data.clone()
+                vector = torch.randn_like(p)
+                set_temporary(group, p, vector=vector, orig=p.data.clone())
                 # scale taken from https://github.com/lixilinx/psgd_torch/blob/1943e66596111e78157ca1b72b31c1dfdf0653ef/preconditioned_stochastic_gradient_descent.py#L2161
-                stochastic_add_(p.data, p.vector, torch.finfo(torch.float32).eps ** 0.5)
+                stochastic_add_(p.data, vector, torch.finfo(torch.float32).eps ** 0.5)
 
         with torch.enable_grad():
             closure()
@@ -1506,22 +1539,22 @@ def _finite_differences_hvp(self, closure):
         # this costs more memory, but the imprecision seems too severe to use the other method
         for group in self.param_groups:
             for p, g in self.split_p_and_g_in_group(group, skip_none=True, raw=True):
-                p.grad = grads.pop(0)
-                stochastic_add_divide_(g, p.grad, -1, torch.finfo(torch.float32).eps ** 0.5)
-                p.hessian_vector = g
-                p.data.copy_(p.orig)
-                del p.orig
+                grad = grads.pop(0)
+                set_temporary(group, p, grad=grad, hessian_vector=g)
+                stochastic_add_divide_(g, grad, -1, torch.finfo(torch.float32).eps ** 0.5)
+                p.data.copy_(take_temporary(group, p, "orig"))
         return loss
 
     def _double_backward_hvp(self, closure):
         with torch.enable_grad(), patch_backward():
             loss = closure()
 
-        params, grads = [], []
+        params, grads, groups = [], [], []
         for group in self.param_groups:
             for p, g in self.split_p_and_g_in_group(group, skip_none=True, raw=True):
                 params.append(p)
                 grads.append(g)
+                groups.append(group)
 
         if not params:
             raise ValueError("No parameter has gradients")
@@ -1534,10 +1567,8 @@ def _double_backward_hvp(self, closure):
                 raise ExactHVPFailed(str(e.args))
 
         unused = []
-        for p, g, v, hv in zip(params, grads, vs, hvs):
-            p.hessian_vector = detach(hv)
-            p.grad = detach(g)
-            p.vector = detach(v)
+        for group, p, g, v, hv in zip(groups, params, grads, vs, hvs):
+            set_temporary(group, p, grad=detach(g), vector=detach(v), hessian_vector=detach(hv))
             if hv is None:
                 unused.append(list(p.shape))
 
@@ -1591,17 +1622,18 @@ def _handle_closure(self, closure):
         return self._handle_closure(closure)
 
     def _cleanup_temporary_tensors(self):
-        for real, views in self.mapping.items():
-            fmt = getattr(real, "_restore_memory_format", None)
-            if fmt is not None:
-                del self.mapping_inverse[_tensor_key(real)]
-                real.data = real.data.to(memory_format=fmt)
-                self.mapping_inverse[_tensor_key(real)] = (real, 0)
-                del real._restore_memory_format
-            for tensor in (real, *views):
-                for key in ("grad", "vector", "hessian_vector", "orig"):
-                    if hasattr(tensor, key):
-                        setattr(tensor, key, None)
+        for group in self.param_groups:
+            tmp = group.pop("_tmp", None)
+            if tmp is None:
+                continue
+            for state in tmp.values():
+                fmt = state.get("restore_memory_format")
+                if fmt is None:
+                    continue
+                tensor = state["tensor"]
+                self.mapping_inverse.pop(_tensor_key(tensor), None)
+                tensor.data = tensor.data.to(memory_format=fmt)
+                self.mapping_inverse[_tensor_key(tensor)] = (tensor, 0)
 
     def step(self, closure: Optional[Callable] = None):
         if self.precond_schedule is None:
@@ -2172,10 +2204,10 @@ def update_param_(
         grad = [None] * len(param)
     _compilable_update_(param, update, decay, lr, caution, grad)
 
-
-def precond_schedule(step, precond_scheduler):
-    precond_prob = max(step, 1) ** precond_scheduler[0]
-    precond_prob = math.log10(precond_prob)
+@decorator_knowngood
+def precond_schedule(step: Tensor, precond_scheduler):
+    precond_prob = step.clamp(min=1) ** precond_scheduler[0]
+    precond_prob = torch.log10(precond_prob)
     precond_prob = precond_prob ** precond_scheduler[1] + 1
     return 1 / precond_prob
 
diff --git a/test/test_distributed.py b/test/test_distributed.py
index 1663f13..d96d9d1 100644
--- a/test/test_distributed.py
+++ b/test/test_distributed.py
@@ -50,6 +50,8 @@
     if n in REPRESENTATIVE_OPTS and n not in _FSDP_SKIP
 ]
 
+_OWNER_EDGE_OPTS = [n for n in ["Muon"] if n in REPRESENTATIVE_OPTS and n not in _FSDP_SKIP]
+
 
 def _set_cache(cache_dir, compile_mode="default"):
     os.environ["TORCHINDUCTOR_CACHE_DIR"] = cache_dir
@@ -101,6 +103,14 @@ def _make_integration_model():
     )
 
 
+def _make_owner_edge_model():
+    return nn.Sequential(
+        nn.Linear(32, 32, bias=False),
+        nn.ReLU(),
+        nn.Linear(32, 1, bias=False),
+    )
+
+
 def _make_data(dim=32, n=4):
     torch.manual_seed(_DATA_SEED)
     return [torch.randn(4, dim, device="cuda") for _ in range(n)]
@@ -118,6 +128,10 @@ def _make_integration_data():
     return _make_data(64, 8)
 
 
+def _make_owner_edge_data():
+    return _make_data(32, 6)
+
+
 def _train(model, opt, data):
     for x in data:
         model(x).mean().backward()
@@ -263,7 +277,7 @@ def _assert_close(ref, result, label, rtol=0, atol=0):
             assert False, f"{label}: param {i} diverged beyond 1 ULP ({n} elements, max |diff|={worst:.2e})"
 
 
-def _run_fsdp_test(opt_name, tmp_path, model_fn, data_fn, label):
+def _run_fsdp_test(opt_name, tmp_path, model_fn, data_fn, label, world_size=2, tol=None):
     cache_dir = tempfile.mkdtemp(prefix=f"hb_{label}_{opt_name}_")
     ref_path = str(tmp_path / "ref.pt")
     mp.spawn(_ref_worker, args=(opt_name, ref_path, cache_dir, None, model_fn, data_fn), nprocs=1, join=True)
@@ -271,12 +285,14 @@ def _run_fsdp_test(opt_name, tmp_path, model_fn, data_fn, label):
     result_path = str(tmp_path / "result.pt")
     mp.spawn(
         _fsdp_worker,
-        args=(2, str(tmp_path / "store"), opt_name, result_path, cache_dir, None, model_fn, data_fn),
-        nprocs=2,
+        args=(world_size, str(tmp_path / "store"), opt_name, result_path, cache_dir, None, model_fn, data_fn),
+        nprocs=world_size,
         join=True,
     )
-    tol = dict(rtol=1e-2, atol=1e-4) if opt_name in _FSDP_PSGD else {}
-    _assert_close(ref, torch.load(result_path, weights_only=True), f"{label}/{opt_name}", **tol)
+    base_tol = dict(rtol=1e-2, atol=1e-4) if opt_name in _FSDP_PSGD else {}
+    if tol is not None:
+        base_tol.update({k: max(base_tol.get(k, 0), v) for k, v in tol.items()})
+    _assert_close(ref, torch.load(result_path, weights_only=True), f"{label}/{opt_name}", **base_tol)
 
 
 @pytest.mark.parametrize("opt_name", REPRESENTATIVE_OPTS)
@@ -336,3 +352,16 @@ def test_fsdp_misaligned(opt_name, tmp_path):
 @pytest.mark.parametrize("opt_name", _INTEGRATION_OPTS)
 def test_fsdp_integration(opt_name, tmp_path):
     _run_fsdp_test(opt_name, tmp_path, _make_integration_model, _make_integration_data, "FSDP-integ")
+
+
+@pytest.mark.parametrize("opt_name", _OWNER_EDGE_OPTS)
+def test_fsdp_owner_edge(opt_name, tmp_path):
+    _run_fsdp_test(
+        opt_name,
+        tmp_path,
+        _make_owner_edge_model,
+        _make_owner_edge_data,
+        "FSDP-owner3",
+        world_size=3,
+        tol=dict(atol=5e-8),
+    )

From 94a5974f25b8c2947f679a04c41adfe0a6efd7a5 Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Mon, 30 Mar 2026 18:59:16 +0000
Subject: [PATCH 12/24] ruff

---
 heavyball/chainable.py | 10 ++++++++--
 heavyball/utils.py     |  1 +
 2 files changed, 9 insertions(+), 2 deletions(-)

diff --git a/heavyball/chainable.py b/heavyball/chainable.py
index 5204dca..5b79a31 100644
--- a/heavyball/chainable.py
+++ b/heavyball/chainable.py
@@ -1670,7 +1670,9 @@ def _exchange_fsdp_shards(schedule, bucket_lookup, items, tensor_getter, keep_st
         bucket_idx = bucket_lookup[info.param_idx]
         device, dtype = schedule[bucket_idx]
         if flat.device != device or flat.dtype != dtype:
-            raise RuntimeError(f"FSDP bucket mismatch for param {info.param_idx}: expected {(device, dtype)}, got {(flat.device, flat.dtype)}")
+            raise RuntimeError(
+                f"FSDP bucket mismatch for param {info.param_idx}: expected {(device, dtype)}, got {(flat.device, flat.dtype)}"
+            )
         per_bucket[bucket_idx].append((info.owner, info.param_idx, info.offset, flat, shard))
 
     received, states = {}, []
@@ -1692,7 +1694,11 @@ def _exchange_fsdp_shards(schedule, bucket_lookup, items, tensor_getter, keep_st
             for value in (param_idx, offset, flat.numel(), code)
         ]
         payload = [flat for dst_entries in by_dst for _, _, _, flat, _ in dst_entries]
-        send_meta = torch.tensor(meta, dtype=torch.int64, device=device) if meta else torch.empty(0, dtype=torch.int64, device=device)
+        send_meta = (
+            torch.tensor(meta, dtype=torch.int64, device=device)
+            if meta
+            else torch.empty(0, dtype=torch.int64, device=device)
+        )
         send_payload = torch.cat(payload) if payload else torch.empty(0, dtype=dtype, device=device)
 
         recv_meta = _all_to_all_variable(send_meta, recv_meta_splits, send_meta_splits)
diff --git a/heavyball/utils.py b/heavyball/utils.py
index e9c6791..8ecad17 100644
--- a/heavyball/utils.py
+++ b/heavyball/utils.py
@@ -2204,6 +2204,7 @@ def update_param_(
         grad = [None] * len(param)
     _compilable_update_(param, update, decay, lr, caution, grad)
 
+
 @decorator_knowngood
 def precond_schedule(step: Tensor, precond_scheduler):
     precond_prob = step.clamp(min=1) ** precond_scheduler[0]

From c2676bd678296ee9501204cabb49b0d0634e0f05 Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Tue, 31 Mar 2026 10:28:36 +0000
Subject: [PATCH 13/24] add optimizer step benchmark

---
 benchmarks/bench_optimizer_step.py | 67 ++++++++++++++++++++++++++++++
 heavyball/utils.py                 |  7 +++-
 2 files changed, 72 insertions(+), 2 deletions(-)
 create mode 100644 benchmarks/bench_optimizer_step.py

diff --git a/benchmarks/bench_optimizer_step.py b/benchmarks/bench_optimizer_step.py
new file mode 100644
index 0000000..06d2c73
--- /dev/null
+++ b/benchmarks/bench_optimizer_step.py
@@ -0,0 +1,67 @@
+import cProfile
+import pstats
+from enum import StrEnum
+from math import prod
+from time import perf_counter
+import numpy as np
+import torch
+import typer
+
+import heavyball
+
+app = typer.Typer(add_completion=False, pretty_exceptions_enable=False)
+
+DEFAULT_SHAPES = ((128, 128),) * 4 + ((512, 128),) * 2 + ((512,),) * 2 + ((128,),) * 4
+
+
+class DType(StrEnum):
+    float16 = "float16"
+    bfloat16 = "bfloat16"
+    float32 = "float32"
+
+
+def parse_shape(text: str) -> tuple[int, ...]:
+    try:
+        shape = tuple(map(int, text.lower().replace("x", " ").split()))
+    except ValueError as e:
+        raise typer.BadParameter(f"invalid shape: {text!r}") from e
+    if not shape:
+        raise typer.BadParameter(f"invalid shape: {text!r}")
+    return shape
+
+
+@app.command()
+def main(optimizer: str = "AdamW", dtype: DType = DType.float32, shape: list[str] | None = None,
+        compile_step: bool = False, update_precond: bool | None = None, steps: int = 300, warmup: int = 20,
+        windows: int = 6, seed: int = 0, ):
+    shapes = DEFAULT_SHAPES if shape is None else tuple(map(parse_shape, shape))
+    torch_dtype = getattr(torch, dtype)
+    kwargs = {"compile_step": compile_step}
+    if update_precond is not None:
+        kwargs["preconditioner_update_probability"] = float(update_precond)
+
+    gen = torch.Generator(device="cuda").manual_seed(seed)
+    params = []
+    for dims in shapes:
+        param = torch.nn.Parameter(torch.randn(dims, device="cuda", dtype=torch_dtype, generator=gen))
+        param.grad = torch.randn(dims, device="cuda", dtype=torch_dtype, generator=gen)
+        params.append(param)
+
+    step = getattr(heavyball, optimizer)(params, **kwargs).step
+    for _ in range(warmup):
+        step()
+
+    times = []
+    for _ in range(windows):
+        torch.cuda.synchronize()
+        start = perf_counter()
+        for _ in range(steps):
+            step()
+        torch.cuda.synchronize()
+        times.append((perf_counter() - start) / steps)
+
+    print(f"{len(shapes)} tensors, {sum(prod(s) for s in shapes)} total params")
+    print(f'Median Time: {np.median(times) * 1e6:.3f}µs')
+
+if __name__ == "__main__":
+    app()
diff --git a/heavyball/utils.py b/heavyball/utils.py
index 8ecad17..5da9d51 100644
--- a/heavyball/utils.py
+++ b/heavyball/utils.py
@@ -1318,6 +1318,7 @@ class StatefulOptimizer(torch.optim.Optimizer):
     fallback_to_finite_differences: bool = True
     _fallback_enabled: bool = False
     hvp_interval: int = 1  # grad is faster initially, hvp later
+    auto_set_grad_to_none: bool = False
 
     _INSTANCE_ATTRS = (
         "compile_step",
@@ -1413,7 +1414,8 @@ def split_p_and_g_in_group(
                 grad = getattr(p, "grad", None)
                 if grad is None and skip_none:
                     continue
-                p.grad = None
+                if self.auto_set_grad_to_none:
+                    p.grad = None
                 yield p, grad
                 continue
 
@@ -1424,7 +1426,8 @@ def split_p_and_g_in_group(
             if grad is None and skip_none:
                 continue
 
-            p.grad = None
+            if self.auto_set_grad_to_none:
+                p.grad = None
 
             if group.get("merge_dims", False) and not p.data.is_contiguous():
                 for fmt in (torch.channels_last, torch.channels_last_3d):

From 6afa484747a8e3bc9e8cc969349b86cd795f90dc Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Tue, 31 Mar 2026 16:07:49 +0000
Subject: [PATCH 14/24] run ortho in scion, round ns iteration

---
 heavyball/utils.py | 28 ++++++++++++++--------------
 1 file changed, 14 insertions(+), 14 deletions(-)

diff --git a/heavyball/utils.py b/heavyball/utils.py
index 5da9d51..099da96 100644
--- a/heavyball/utils.py
+++ b/heavyball/utils.py
@@ -656,7 +656,7 @@ def _scion_bias_rms_direction(x: Tensor, eps: float = 1e-8) -> Tensor:
 
 def _scion_spectral_direction(x: Tensor) -> Tensor:
     flat = x.reshape(x.shape[0], -1)
-    inplace_orthogonal_(flat)
+    flat = inplace_orthogonal_(flat)
     normalized = flat.reshape_as(x)
     in_dim = max(flat.shape[1], 1)
     scale = math.sqrt(x.shape[0] / in_dim)
@@ -665,7 +665,7 @@ def _scion_spectral_direction(x: Tensor) -> Tensor:
 
 def _scion_spectral_conv_direction(x: Tensor) -> Tensor:
     flat = x.reshape(x.shape[0], -1)
-    inplace_orthogonal_(flat)
+    flat = inplace_orthogonal_(flat)
     normalized = flat.reshape_as(x)
     out_channels, in_channels = x.shape[:2]
     spatial = math.prod(x.shape[2:]) if x.ndim > 2 else 1
@@ -774,7 +774,7 @@ def _compilable_grafting(magnitude, direction):
 def _compilable_orthogonal_(x: Tensor, mode: str | ZerothPowerMode, out: Tensor | None, scale_mode: str):
     if not isinstance(mode, ZerothPowerMode):
         mode = ZerothPowerMode(mode)
-    if not isinstance(scale_mode, ZerothPowerMode):
+    if not isinstance(scale_mode, OrthoScaleMode):
         scale_mode = OrthoScaleMode(scale_mode)
     if mode == ZerothPowerMode.newtonschulz or x.shape[0] != x.shape[1]:
         y = zeropower_via_newtonschulz5(x, 5)
@@ -2147,17 +2147,17 @@ def stochastic_round_list_(ref: List[Tensor], source: List[Tensor]):
 def stochastic_round_(ref: Tensor, source: Tensor | None = None):
     if source is None:
         source = ref
-    if ref.dtype != torch.bfloat16:
-        return source.to(ref.dtype)
-    if source.dtype == torch.bfloat16:
-        return source
-    if source.dtype in (torch.float16, torch.float32, torch.float64):
-        source = source.to(torch.float32).view(dtype=torch.int32)
-        noise = sum(torch.randint_like(source, low=0, high=(1 << 16)) for _ in range(dither_steps))
-        noise = noise + source - (dither_steps - 1) * (1 << 15)  # center | x - (N-1)*delta/2
-        noise = noise.bitwise_and(-65536)  # FFFF0000 mask, preserves sign+exp+7 mantissa bits
-        return noise.view(dtype=torch.float32).bfloat16()
-    return source.to(ref.dtype)
+        dtype = torch.bfloat16
+    else:
+        dtype = ref.dtype
+    if dtype != torch.bfloat16 or source.dtype not in (torch.float16, torch.float32, torch.float64):
+        return source.to(dtype)
+
+    source = source.to(torch.float32).view(dtype=torch.int32)
+    noise = sum(torch.randint_like(source, low=0, high=(1 << 16)) for _ in range(dither_steps))
+    noise = noise + source - (dither_steps - 1) * (1 << 15)  # center | x - (N-1)*delta/2
+    noise = noise.bitwise_and(-65536)  # FFFF0000 mask, preserves sign+exp+7 mantissa bits
+    return noise.view(dtype=torch.float32).bfloat16()
 
 
 @decorator_knowngood

From e387c8af051b41aed053da90f96f5e5fe7e6f360 Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Tue, 31 Mar 2026 19:25:22 +0000
Subject: [PATCH 15/24] compile more

---
 benchmarks/bench_optimizer_step.py | 36 +++++++++++++++++++++---------
 heavyball/chainable.py             |  1 -
 heavyball/utils.py                 |  9 ++++----
 3 files changed, 30 insertions(+), 16 deletions(-)

diff --git a/benchmarks/bench_optimizer_step.py b/benchmarks/bench_optimizer_step.py
index 06d2c73..07ca682 100644
--- a/benchmarks/bench_optimizer_step.py
+++ b/benchmarks/bench_optimizer_step.py
@@ -1,5 +1,3 @@
-import cProfile
-import pstats
 from enum import StrEnum
 from math import prod
 from time import perf_counter
@@ -11,7 +9,7 @@
 
 app = typer.Typer(add_completion=False, pretty_exceptions_enable=False)
 
-DEFAULT_SHAPES = ((128, 128),) * 4 + ((512, 128),) * 2 + ((512,),) * 2 + ((128,),) * 4
+DEFAULT_SHAPES = ((2048, 2048),) * 32
 
 
 class DType(StrEnum):
@@ -20,6 +18,11 @@ class DType(StrEnum):
     float32 = "float32"
 
 
+class Library(StrEnum):
+    heavyball = "heavyball"
+    torch = "torch"
+
+
 def parse_shape(text: str) -> tuple[int, ...]:
     try:
         shape = tuple(map(int, text.lower().replace("x", " ").split()))
@@ -31,13 +34,25 @@ def parse_shape(text: str) -> tuple[int, ...]:
 
 
 @app.command()
-def main(optimizer: str = "AdamW", dtype: DType = DType.float32, shape: list[str] | None = None,
-        compile_step: bool = False, update_precond: bool | None = None, steps: int = 300, warmup: int = 20,
-        windows: int = 6, seed: int = 0, ):
+def main(
+    optimizer: str = "AdamW",
+    library: Library = Library.heavyball,
+    dtype: DType = DType.float32,
+    shape: list[str] | None = None,
+    compile_step: bool = False,
+    fused: bool | None = None,
+    update_precond: bool | None = None,
+    steps: int = 300,
+    warmup: int = 20,
+    windows: int = 6,
+    seed: int = 0,
+):
     shapes = DEFAULT_SHAPES if shape is None else tuple(map(parse_shape, shape))
     torch_dtype = getattr(torch, dtype)
-    kwargs = {"compile_step": compile_step}
-    if update_precond is not None:
+    kwargs = {"compile_step": compile_step} if library is Library.heavyball else {}
+    if fused is not None and library is Library.torch:
+        kwargs["fused"] = fused
+    if update_precond is not None and library is Library.heavyball:
         kwargs["preconditioner_update_probability"] = float(update_precond)
 
     gen = torch.Generator(device="cuda").manual_seed(seed)
@@ -47,7 +62,8 @@ def main(optimizer: str = "AdamW", dtype: DType = DType.float32, shape: list[str
         param.grad = torch.randn(dims, device="cuda", dtype=torch_dtype, generator=gen)
         params.append(param)
 
-    step = getattr(heavyball, optimizer)(params, **kwargs).step
+    module = heavyball if library is Library.heavyball else torch.optim
+    step = getattr(module, optimizer)(params, **kwargs).step
     for _ in range(warmup):
         step()
 
@@ -61,7 +77,7 @@ def main(optimizer: str = "AdamW", dtype: DType = DType.float32, shape: list[str
         times.append((perf_counter() - start) / steps)
 
     print(f"{len(shapes)} tensors, {sum(prod(s) for s in shapes)} total params")
-    print(f'Median Time: {np.median(times) * 1e6:.3f}µs')
+    print(f"Median Time: {np.median(times) * 1e6:.3f}µs")
 
 if __name__ == "__main__":
     app()
diff --git a/heavyball/chainable.py b/heavyball/chainable.py
index 5b79a31..e8d8b2e 100644
--- a/heavyball/chainable.py
+++ b/heavyball/chainable.py
@@ -1182,7 +1182,6 @@ def _update_psgd_precond(
         Q,
         group["store_triu_as_line"],
         utils.get_beta2(group),
-        group["ortho_method"],
         vector,
         running_lower_bound,
         group["lower_bound_beta"],
diff --git a/heavyball/utils.py b/heavyball/utils.py
index 099da96..04fe270 100644
--- a/heavyball/utils.py
+++ b/heavyball/utils.py
@@ -2813,15 +2813,15 @@ def max_eigenvalue_spd(A_outer: Tensor, power_iter: int = 4) -> Tensor:
 
     def _inner():
         x = A_outer.index_select(0, max_idx).flatten().contiguous()
-        A = stochastic_round_(A_outer / x_norm)
+        A = promote(A_outer) / x_norm
         x = x / x_norm
 
         def _mv(x):
-            return promote((x.to(A.dtype) @ A.mT) @ A.mT)
+            return promote((x @ A.mT) @ A.mT)
 
         for _ in range(power_iter):
             x = F.normalize(_mv(x), dim=0)
-        return (x @ _mv(x)).to(x_norm.dtype).sqrt() * x_norm
+        return (x @ _mv(x)).sqrt() * x_norm
 
     return cond(x_norm > 0, _inner, lambda: x_norm.squeeze().clone()).squeeze()
 
@@ -3006,14 +3006,13 @@ def _update_lb(ell: Tensor, lb_state: Tensor, beta: Tensor) -> Tensor:
     return ell
 
 
-@decorator
+@functools.partial(decorator_knowngood, fullgraph=False)
 def psgd_update_precond(
     G: Tensor,
     precond_lr: float,
     oq: "TriuOrLine",
     store_triu_as_line: bool,
     beta2: float,
-    ortho_method: Optional[str],
     V: Tensor,
     running_lower_bound: List[Tensor],
     lower_bount_beta: float,

From 2c77d49d39f29695602f13fd44dd00408a8e2455 Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Wed, 1 Apr 2026 09:17:29 +0000
Subject: [PATCH 16/24] update benchmark matrix

---
 assets/benchmark_matrix.png | Bin 2496725 -> 1160757 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/assets/benchmark_matrix.png b/assets/benchmark_matrix.png
index 8300fcafd11de224451ad0f2c8894d883177bc79..26a7839c3aff36118840f9909658c104c666fc44 100644
GIT binary patch
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From e7b25bce538b74f48b330f06f17b470ac0e3d5b0 Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Wed, 1 Apr 2026 09:18:02 +0000
Subject: [PATCH 17/24] PSGDKronAdam

---
 heavyball/__init__.py  | 98 ++++++++++++++++++++++++++++++++++++------
 heavyball/chainable.py | 69 ++++++++++++++++++++++++++++-
 heavyball/helpers.py   | 23 ----------
 heavyball/utils.py     | 69 +++++++++++++++++++++++++++--
 4 files changed, 219 insertions(+), 40 deletions(-)

diff --git a/heavyball/__init__.py b/heavyball/__init__.py
index 46a0f7c..0877d66 100644
--- a/heavyball/__init__.py
+++ b/heavyball/__init__.py
@@ -7,6 +7,8 @@
 from . import chainable as C
 from . import utils
 
+ShapeMap = dict[int, tuple[int, ...]]
+
 
 class SGD(C.BaseOpt):
     def __init__(
@@ -27,6 +29,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
@@ -55,6 +58,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
@@ -85,6 +89,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
@@ -114,6 +119,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         if len(betas) != 3:
@@ -145,6 +151,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
@@ -174,6 +181,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
@@ -202,6 +210,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         if lr < 0:
@@ -245,6 +254,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         if max_lr is None:
@@ -285,6 +295,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
@@ -320,6 +331,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
@@ -362,6 +374,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
@@ -405,6 +418,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
@@ -443,6 +457,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
@@ -478,6 +493,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
@@ -508,6 +524,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
@@ -551,6 +568,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
@@ -579,6 +597,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
@@ -656,6 +675,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         self._build_soap_defaults(locals(), fns=(C.scale_by_soap,))
@@ -694,6 +714,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         self._build_soap_defaults(locals(), fns=(C.scale_by_soap_nadam,))
@@ -733,6 +754,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         self._build_soap_defaults(locals(), fns=(C.scale_by_soap_ademamix,))
@@ -760,6 +782,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
@@ -814,6 +837,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         self._build_soap_defaults(locals(), fns=(C.scale_by_soap_laprop,))
@@ -841,6 +865,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
@@ -876,6 +901,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         params, defaults = C._build_defaults(locals())
@@ -899,7 +925,6 @@ def _build_psgd_defaults(
     ):
         exp_avg_input = C.default(locals_dict.get("exp_avg_input", C.use_default), self.exp_avg_input)
         update_clipping = C.default(locals_dict["update_clipping"], default_update_clipping)
-
         locals_dict = {**locals_dict, "exp_avg_input": exp_avg_input, "update_clipping": update_clipping}
         params, defaults = C._build_defaults(locals_dict)
 
@@ -927,10 +952,6 @@ class PSGDKron(PSGDBase):
     Source available at https://github.com/evanatyourservice/kron_torch/blob/97a2b5ee8a1a4c29e4780bbf6c521e545189eff9/kron_torch/kron.py
     """
 
-    delayed: bool = False
-    cached: bool = False
-    exp_avg_input: bool = True
-
     def __init__(
         self,
         params,
@@ -958,7 +979,6 @@ def __init__(
         exp_avg_input: Optional[bool] = C.use_default,
         gradient_clipping: C.str_or_fn = C.use_default,
         update_clipping: C.str_or_fn = C.use_default,  #
-        ortho_method: Optional[str] = None,
         precond_grad_accum: bool = False,
         lower_bound_beta: float = 0.9,
         dampening: float = 1e-9,
@@ -976,6 +996,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         delayed = C.default(delayed, self.delayed)
@@ -986,6 +1007,62 @@ def __init__(
         )
 
 
+class PSGDKronAdam(PSGDBase):
+    """
+    Adam in the approximate eigenspace induced by the PSGD-Kron preconditioner.
+    Uses cached orthogonal factors from the PSGD preconditioner, applies Adam in that basis, then maps back.
+    """
+
+    def __init__(
+        self,
+        params,
+        lr=0.001,
+        beta=None,
+        betas=(0.9, 0.999),
+        eps: float = 1e-8,
+        weight_decay=0.0,
+        preconditioner_update_probability=C.use_default,
+        max_size_triangular=2048,
+        min_ndim_triangular=2,
+        memory_save_mode=None,
+        momentum_into_precond_update=True,
+        warmup_steps: int = 0,
+        merge_dims: bool = False,
+        split: bool = False,
+        store_triu_as_line: bool = True,
+        multi_tensor: bool = True,
+        q_dtype="float32",
+        storage_dtype: str = "float32",
+        mars: bool = False,
+        caution: bool = False,
+        mars_gamma: float = 0.0025,
+        gradient_clipping: C.str_or_fn = C.use_default,
+        update_clipping: C.str_or_fn = C.use_default,
+        precond_grad_accum: bool = False,
+        lower_bound_beta: float = 0.9,
+        dampening: float = 1e-9,
+        precond_update_power_iterations: int = 2,
+        precond_init_scale=None,
+        precond_init_scale_scale: float = 1,
+        precond_init_scale_power: Optional[float] = None,
+        precond_lr: float = 0.1,
+        finite_differences: bool = C.use_default,
+        fallback_to_finite_differences: bool = C.use_default,
+        hvp_interval: int = C.use_default,
+        hessian_approx: bool = C.use_default,
+        compile_step: bool = C.use_default,
+        promote: bool = C.use_default,
+        ecc: str | None = None,
+        param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
+        **kwargs,
+    ):
+        self._build_psgd_defaults(
+            {**locals(), "exp_avg_input": False},
+            fns=(C.scale_by_psgd_eigen_adam,),
+        )
+
+
 class PSGDPRO(PSGDBase):
     """
     PSGD with Q0.5EQ1.5 (PRO/Procrustes) preconditioner update.
@@ -993,9 +1070,6 @@ class PSGDPRO(PSGDBase):
     Reference: https://github.com/lixilinx/psgd_torch
     """
 
-    cached: bool = False
-    exp_avg_input: bool = True
-
     def __init__(
         self,
         params,
@@ -1033,6 +1107,7 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         cached = C.default(cached, self.cached)
@@ -1055,9 +1130,6 @@ class PSGDLRA(PSGDBase):
     algorithms and will produce different results.
     """
 
-    delayed: bool = False
-    exp_avg_input: bool = True
-
     def __init__(
         self,
         params,
@@ -1092,10 +1164,10 @@ def __init__(
         promote: bool = C.use_default,
         ecc: str | None = None,
         param_ecc: str | None = None,
+        orig_shapes: ShapeMap | None = None,
         **kwargs,
     ):
         delayed = C.default(delayed, self.delayed)
-
         if rank is None:
             utils.warn_once(
                 f"{rank=}. It will be set to log2(param_count). This requires `params` to be of type list. Currently, {type(params)=}"
diff --git a/heavyball/chainable.py b/heavyball/chainable.py
index e8d8b2e..0cf091b 100644
--- a/heavyball/chainable.py
+++ b/heavyball/chainable.py
@@ -197,7 +197,7 @@ def _storage_dtype(group):
 
 def _build_defaults(locals_dict):
     d = locals_dict.copy()
-    d.pop("self")
+    d.pop("self", None)
     params = d.pop("params")
     kwargs = d.pop("kwargs")
 
@@ -903,6 +903,26 @@ def _init_psgd_kron(state, group, update, grad, param, cached: bool = False, pro
     state["Q_cache"] = [torch.empty_like(q) for q in Q]
 
 
+def _init_psgd_eigen_kron(state, group, update, grad, param, prob: Optional[callable] = None):
+    tmp = utils.get_temporary(group, param) or {}
+    Q = utils.init_Q_exprs(
+        grad,
+        group["precond_init_scale"],
+        group["precond_init_scale_scale"],
+        group["precond_init_scale_power"],
+        group["max_size_triangular"],
+        group["min_ndim_triangular"],
+        group["memory_save_mode"],
+        tmp.get("hessian_vector"),
+        tmp.get("vector"),
+        dtype=getattr(torch, group["q_dtype"]),
+    )
+    state["Q"] = utils.triu_to_line(Q) if group["store_triu_as_line"] else Q
+    state["Q_basis"] = utils.get_psgd_eigenbasis(Q)
+    state["running_lower_bound"] = [torch.zeros((1,), device=q.device, dtype=torch.float64) for q in Q]
+    state["step"] = torch.zeros((), device=param.device, dtype=torch.float64)
+
+
 def _init_psgd_pro_kron(state, group, update, grad, param, cached: bool = False, prob: Optional[callable] = None):
     Q = utils.init_Q_exprs(
         grad,
@@ -1373,6 +1393,53 @@ def scale_by_psgd(
     return _cached_psgd_precond_grad(group, update, Q, Q_cache, grad)
 
 
+@needs_full_param
+@SqueezeGrad
+@PrecondGradAccumGuard
+@zero_guard("exp_avg", "exp_avg_sq")
+@general_guard("Q", "Q_basis", "running_lower_bound", "step", init_fn=_init_psgd_eigen_kron, skip_first=False)
+@no_state_no_multi_tensor
+def scale_by_psgd_eigen_adam(
+    group,
+    update,
+    grad,
+    param,
+    update_to_precond,
+    exp_avg,
+    exp_avg_sq,
+    Q,
+    Q_basis,
+    running_lower_bound: List[Tensor],
+    step: Tensor,
+    prob: Optional[callable] = None,
+):
+    basis = Q_basis
+    if basis is None:
+        basis = utils.get_psgd_eigenbasis(utils.line_to_triu(Q) if group["store_triu_as_line"] else Q)
+
+    projected = utils.project(utils.promote(update), basis, False)
+    precond = utils.adam_(
+        exp_avg,
+        exp_avg_sq,
+        projected,
+        utils.get_beta1(group),
+        utils.get_beta2(group),
+        group["step"],
+        group["eps"],
+    )[0]
+    precond = utils.project(precond, basis, True)
+
+    if group["is_preconditioning"]:
+        _update_psgd_precond(False, None, group, param, update_to_precond, Q, running_lower_bound, step, prob)
+        utils.update_psgd_eigenbasis(
+            utils.line_to_triu(Q) if group["store_triu_as_line"] else Q,
+            Q_basis,
+            exp_avg,
+        )
+
+    return precond
+
+
 @needs_full_param
 @SqueezeGrad
 @PrecondGradAccumGuard
diff --git a/heavyball/helpers.py b/heavyball/helpers.py
index 23a4e77..71a2cdb 100644
--- a/heavyball/helpers.py
+++ b/heavyball/helpers.py
@@ -178,7 +178,6 @@ class BoTorchSampler(SimpleAPIBaseSampler):
     """
     A significantly more efficient implementation of `BoTorchSampler` from Optuna - keeps more on the GPU / in torch
     The original is available at https://github.com/optuna/optuna-integration/blob/156a8bc081322791015d2beefff9373ed7b24047/optuna_integration/botorch/botorch.py under the MIT License
-    The original API is kept for backward compatibility, but many arguments are ignored to improve maintainability.
     """
 
     def __init__(
@@ -186,18 +185,12 @@ def __init__(
         search_space: Optional[dict[str, BaseDistribution]] = None,
         *,
         candidates_func: Optional[Callable[..., Tensor]] = None,
-        constraints_func: Optional[Callable[..., Tensor]] = None,
         n_startup_trials: int = 10,
-        consider_running_trials: bool = False,
         independent_sampler: Optional[BaseSampler] = None,
         seed: int | None = None,
         device: torch.device | str | None = None,
         trial_chunks: int = 128,
     ):
-        if constraints_func is not None:
-            raise NotImplementedError("constraints_func is currently not supported by BoTorchSampler.")
-        if consider_running_trials:
-            raise NotImplementedError("consider_running_trials is currently not supported by BoTorchSampler.")
         if candidates_func is not None and not callable(candidates_func):
             raise TypeError("candidates_func must be callable.")
         self._candidates_func = candidates_func
@@ -206,7 +199,6 @@ def __init__(
         self._seed = seed
         self.trial_chunks = trial_chunks
 
-        self._study_id: int | None = None
         self.search_space = {} if search_space is None else dict(search_space)
         if isinstance(device, str):
             device = torch.device(device)
@@ -643,12 +635,9 @@ def __init__(
         search_space: dict[str, BaseDistribution],
         *,
         seed: int | None = None,
-        constant_liar: bool = False,
         independent_sampler: BaseSampler | None = None,
     ) -> None:
         super().__init__(search_space, seed)
-        if constant_liar:
-            raise NotImplementedError("constant_liar is not supported by HEBOSampler.")
         self._hebo = HEBO(_convert_to_hebo_design_space(search_space), scramble_seed=self._seed)
         self._independent_sampler = independent_sampler or optuna.samplers.RandomSampler(seed=seed)
         self._rng = np.random.default_rng(seed)
@@ -716,7 +705,6 @@ def __init__(
         upper: np.ndarray,
         seed: Optional[int] = None,
         population_size: Optional[int] = None,
-        learning_rate: Optional[float] = None,
         last_n: int = 4096,
         loco_step_size: float = 0.1,
         device: str | None = None,
@@ -733,7 +721,6 @@ def __init__(
         self.last_n = last_n
         self.batchnorm_decay = batchnorm_decay
         self.score_decay = score_decay
-        self._learning_rate = learning_rate or 1.0 / np.sqrt(n_dimension)
         self._mean = torch.from_numpy(mean).to(device)
         self._sigma = torch.from_numpy(inv_sigma).to(device)
         self._lower = torch.from_numpy(lower).to(device)
@@ -832,20 +819,16 @@ def __init__(
         search_space: Dict[str, BaseDistribution],
         x0: Optional[Dict[str, Any]] = None,
         sigma0: Optional[float] = None,
-        lr: Optional[float] = None,
         n_startup_trials: int = 1,
         independent_sampler: Optional[BaseSampler] = None,
-        warn_independent_sampling: bool = True,
         seed: Optional[int] = None,
         population_size: Optional[int] = None,
     ) -> None:
         self.search_space = search_space
         self._x0 = x0
         self._sigma0 = sigma0
-        self._lr = lr
         self._independent_sampler = independent_sampler or optuna.samplers.RandomSampler(seed=seed)
         self._n_startup_trials = n_startup_trials
-        self._warn_independent_sampling = warn_independent_sampling
         self._optimizer: Optional[FastINGO] = None
         self._seed = seed
         self._population_size = population_size
@@ -906,7 +889,6 @@ def sample_relative(
             return {}
 
         if len(search_space) == 1:
-            self._warn_independent_sampling = False
             return {}
 
         trans = SearchSpaceTransform(search_space)
@@ -949,7 +931,6 @@ def _init_optimizer(
             upper=upper_bounds,
             seed=self._seed,
             population_size=population_size,
-            learning_rate=self._lr,
         )
 
     def sample_independent(
@@ -1022,10 +1003,7 @@ def __init__(
         search_space: Optional[dict[str, BaseDistribution]] = None,
         *,
         seed: int | None = None,
-        constraints_func: Optional[Callable[..., Any]] = None,
     ) -> None:
-        if constraints_func is not None:
-            raise NotImplementedError("constraints_func is not supported by AutoSampler.")
         if samplers is None:
             if search_space is None:
                 raise ValueError("AutoSampler requires a search_space when using the default sampler schedule.")
@@ -1036,7 +1014,6 @@ def __init__(
         self._rng = LazyRandomState(seed)
         self._random_sampler = RandomSampler(seed=seed)
         self._thread_local_sampler = ThreadLocalSampler()
-        self._constraints_func = constraints_func
         self._completed_trials = 0
         self._current_index = -1
 
diff --git a/heavyball/utils.py b/heavyball/utils.py
index 04fe270..70ef148 100644
--- a/heavyball/utils.py
+++ b/heavyball/utils.py
@@ -884,6 +884,68 @@ def get_orthogonal_matrix_QR(GG: List[Tensor], Q: List[Tensor], *exp_avg: Tensor
             copy_stochastic_(q, q_new)
 
 
+def _transform_projected_state(old_qs: List[Optional[Tensor]], new_qs: List[Optional[Tensor]], *states: Tensor):
+    if not states:
+        return
+
+    ref = states[0]
+    if ref is None or ref.dim() == 0:
+        return
+
+    assert ref.ndim < 13, "ref.ndim must be less than 13"
+    in_str = einsum_base[: ref.dim()]
+    out_str = einsum_base[ref.dim() : 2 * ref.dim()]
+
+    old_basis = ",".join([o + i for q, i, o in zip(old_qs, in_str, in_str.upper()) if q is not None])
+    if not old_basis:
+        return
+
+    new_basis = ",".join([i + o for q, i, o in zip(new_qs, in_str.upper(), out_str) if q is not None])
+    out_str = "".join([o if o in new_basis else i for i, o in zip(in_str, out_str)])
+    subscripts = f"{in_str},{old_basis},{new_basis}->{out_str}"
+    old_basis = [promote(q) for q in old_qs if q is not None]
+    new_basis = [promote(q) for q in new_qs if q is not None]
+
+    for state in states:
+        new = compiled_einsum(subscripts, promote(state), *old_basis, *new_basis)
+        copy_stochastic_(state, new)
+
+@decorator_knowngood
+def get_psgd_eigenbasis(Q: List[Tensor], prev: Optional[List[Optional[Tensor]]] = None):
+    prev = [None] * len(Q) if prev is None else prev
+    out = []
+
+    for q, old_basis in zip(Q, prev):
+        if q.ndim < 2:
+            out.append(None)
+            continue
+
+        basis = msign(promote(q)).mT.to(dtype=q.dtype)
+        projected = promote(q) @ promote(basis)
+        sort_idx = torch.argsort(compiled_einsum("ij,ij->j", projected, projected), descending=True)
+        basis = basis.index_select(1, sort_idx)
+
+        if old_basis is not None:
+            signs = compiled_einsum("ij,ij->j", promote(old_basis), promote(basis))
+            signs = torch.where(signs < 0, -torch.ones_like(signs), torch.ones_like(signs)).to(dtype=basis.dtype)
+            basis = basis * signs.view(1, -1)
+
+        out.append(basis)
+
+    return out
+
+@decorator_knowngood
+def update_psgd_eigenbasis(Q: List[Tensor], Q_basis: List[Optional[Tensor]], *states: Tensor):
+    new_basis = get_psgd_eigenbasis(Q, Q_basis)
+    _transform_projected_state(Q_basis, new_basis, *states)
+
+    for i, (old_basis, new_basis_i) in enumerate(zip(Q_basis, new_basis)):
+        if old_basis is None or new_basis_i is None:
+            Q_basis[i] = new_basis_i
+        else:
+            copy_stochastic_(old_basis, new_basis_i)
+
+
 def get_orthogonal_matrix(mat, max_eps: float = 1e-3, min_eps: float = 1e-30):
     """
     Computes the eigenbases of the preconditioner using torch.linalg.eigh decomposition.
@@ -1318,7 +1380,7 @@ class StatefulOptimizer(torch.optim.Optimizer):
     fallback_to_finite_differences: bool = True
     _fallback_enabled: bool = False
     hvp_interval: int = 1  # grad is faster initially, hvp later
-    auto_set_grad_to_none: bool = False
+    consume_grad: bool = True
 
     _INSTANCE_ATTRS = (
         "compile_step",
@@ -1326,6 +1388,7 @@ class StatefulOptimizer(torch.optim.Optimizer):
         "fallback_to_finite_differences",
         "hvp_interval",
         "hessian_approx",
+        "consume_grad"
     )
 
     def __init__(self, params, defaults, use_ema: bool = False):
@@ -1414,7 +1477,7 @@ def split_p_and_g_in_group(
                 grad = getattr(p, "grad", None)
                 if grad is None and skip_none:
                     continue
-                if self.auto_set_grad_to_none:
+                if self.consume_grad:
                     p.grad = None
                 yield p, grad
                 continue
@@ -1426,7 +1489,7 @@ def split_p_and_g_in_group(
             if grad is None and skip_none:
                 continue
 
-            if self.auto_set_grad_to_none:
+            if self.consume_grad:
                 p.grad = None
 
             if group.get("merge_dims", False) and not p.data.is_contiguous():

From 076c34048a4b3e41aaf86b60d6c4457255061370 Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Wed, 1 Apr 2026 12:15:55 +0000
Subject: [PATCH 18/24] add benchmark

---
 README.md          | 16 ++++++++++++++--
 docs/heavyball3.md | 11 +++++++++++
 2 files changed, 25 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index 3ae2ebd..fe611d5 100644
--- a/README.md
+++ b/README.md
@@ -21,21 +21,25 @@ Requires PyTorch >= 2.2.
 
 ```python
 from heavyball import AdamW
+
 opt = AdamW(model.parameters(), lr=1e-3)
 ```
 
 ```python
 from heavyball import SOAP  # Shampoo-based preconditioning
+
 opt = SOAP(model.parameters(), lr=3e-3)
 ```
 
 ```python
 from heavyball import Muon
+
 opt = Muon(model.parameters(), lr=0.02, ecc="bf16+8", mars=True, caution=True)
 ```
 
 ```python
 from heavyball import SplitOpt, Muon, AdamW
+
 opt = SplitOpt([
     {'params': matrices, 'optimizer': Muon, 'lr': 0.02},
     {'params': vectors, 'optimizer': AdamW, 'lr': 1e-3},
@@ -44,6 +48,8 @@ opt = SplitOpt([
 
 The API matches `torch.optim`, with the same parameter groups, same `step()`/`zero_grad()` interface. See [
 `examples/`](examples/) for training scripts.
+By default, HeavyBall consumes gradients during `step()` and clears `p.grad` once it has used it. Pass
+`consume_grad=False` if your training loop needs gradients to remain attached after the optimizer step.
 
 ## Optimizers
 
@@ -160,10 +166,12 @@ updates.
 ```python
 import heavyball.chainable as C
 
+
 def graft(outputs, eps=1e-8):
     adam_update, sgd_update = outputs
     return [s * (a.norm() / s.norm().add(eps)) for a, s in zip(adam_update, sgd_update)]
 
+
 class GraftedAdam(C.BaseOpt):
     def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8,
                  weight_decay=0, warmup_steps=0, multi_tensor=True):
@@ -201,13 +209,17 @@ Custom optimizers built via the chainable API inherit this behavior.
 
 ## Benchmarks
 
-HeavyBall includes a diagnostic benchmark suite via [LightBench](https://github.com/HomebrewML/LightBench) that tests
+HeavyBall includes a benchmark suite via [LightBench](https://github.com/HomebrewML/LightBench) that tests
 for silent optimizer failures across difficulty levels. Results and methodology are documented
 in [docs/benchmark.md](docs/benchmark.md).
 
+[`benchmarks/bench_release_optimizers.py`](benchmarks/bench_release_optimizers.py) measures optimizer latency, with
+AdamW step times dropping from 10.63 ms in HeavyBall 2 to 4.15 ms in HeavyBall 3.
+
 ## Migrating
 
-**From 2.x** See the [3.0.0 migration guide](docs/heavyball3.md) for renamed classes, removed kwargs, and checkpoint conversion.
+**From 2.x** See the [3.0.0 migration guide](docs/heavyball3.md) for renamed classes, removed kwargs, and checkpoint
+conversion.
 
 **From 1.x** See the [2.0.0 migration notes](docs/heavyball2.md), then follow the 3.0.0 guide.
 
diff --git a/docs/heavyball3.md b/docs/heavyball3.md
index f4fc2c5..ec33e95 100644
--- a/docs/heavyball3.md
+++ b/docs/heavyball3.md
@@ -7,10 +7,17 @@
 * `Route`-based param dispatch replaces manual `SplitOpt` for mixed-architecture optimizers
 * `ScheduleFree` and `MSAM` mode switches are now idempotent (`eval()` twice is safe)
 * Higher-precision PSGD preconditioner updates
+* New `consume_grad` option: `step()` clears `p.grad` after consuming it by default; set `consume_grad=False` to keep gradients attached after the step
 * `torch.compile`-friendly step with automatic eager fallback for init/preconditioning
 
 ---
 
+## Release benchmarks
+
+HeavyBall 3 was benchmarked against HeavyBall 2 and `torch.optim` with
+[`benchmarks/bench_release_optimizers.py`](../benchmarks/bench_release_optimizers.py), with compiled AdamW step latency
+dropping from 10.63 ms in HeavyBall 2 to 4.15 ms in HeavyBall 3.
+
 ## Breaking changes
 
 ### Class renames
@@ -87,6 +94,9 @@ These raise `TypeError` if passed. They were either unused or replaced by better
 * **ScheduleFree / MSAM `eval()` / `train()`**: Now idempotent. Calling `eval()` twice no
   longer flips back to train mode. Both methods accept a `mode` argument matching
   `nn.Module.train(mode)` and return `self`.
+* **Gradient lifetime**: `consume_grad=True` is available on all optimizers and clears `p.grad`
+  during `step()` once the gradient has been consumed. Set `consume_grad=False` if your code
+  reads gradients after stepping or relies on them remaining attached.
 * **PSGD dampening**: `dampen_grad` default changed from `2**-13` to `1e-9`, and dampening
   epsilon uses `torch.finfo(float32).eps` regardless of input dtype. This improves
   preconditioner accuracy but may change convergence behavior.
@@ -115,3 +125,4 @@ The `foreach` → `multi_tensor` key rename in param groups is handled automatic
 5. Replace `Branch(...)` with `Parallel(...)` in custom chainable code
 6. Migrate checkpoints: `python scripts/migrate_optimizer_state.py <ckpt> heavyball.<Optimizer>`
 7. If you relied on `eval(); eval()` toggling back to train mode, update your code
+8. If your training loop reads `p.grad` after `step()`, pass `consume_grad=False`

From d23dcb14fbc578bb195e449ec611ba59dd2fe4ce Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Wed, 1 Apr 2026 12:16:39 +0000
Subject: [PATCH 19/24] more tests

---
 README.md                        |  2 +-
 docs/heavyball3.md               |  2 +-
 test/test_chainable_cpu.py       |  1 +
 test/test_helpers_cpu.py         | 17 +++++++++++++
 test/test_optimizer_cpu_smoke.py | 43 ++++++++++++++++++++++++++++++++
 5 files changed, 63 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index fe611d5..0c5f0b3 100644
--- a/README.md
+++ b/README.md
@@ -213,7 +213,7 @@ HeavyBall includes a benchmark suite via [LightBench](https://github.com/Homebre
 for silent optimizer failures across difficulty levels. Results and methodology are documented
 in [docs/benchmark.md](docs/benchmark.md).
 
-[`benchmarks/bench_release_optimizers.py`](benchmarks/bench_release_optimizers.py) measures optimizer latency, with
+[`benchmarks/bench_release_optimizers.py`](benchmarks/bench_optimizer_step.py) measures optimizer latency, with
 AdamW step times dropping from 10.63 ms in HeavyBall 2 to 4.15 ms in HeavyBall 3.
 
 ## Migrating
diff --git a/docs/heavyball3.md b/docs/heavyball3.md
index ec33e95..9f6c856 100644
--- a/docs/heavyball3.md
+++ b/docs/heavyball3.md
@@ -15,7 +15,7 @@
 ## Release benchmarks
 
 HeavyBall 3 was benchmarked against HeavyBall 2 and `torch.optim` with
-[`benchmarks/bench_release_optimizers.py`](../benchmarks/bench_release_optimizers.py), with compiled AdamW step latency
+[`benchmarks/bench_optimizer_step.py`](../benchmarks/bench_release_optimizers.py), with compiled AdamW step latency
 dropping from 10.63 ms in HeavyBall 2 to 4.15 ms in HeavyBall 3.
 
 ## Breaking changes
diff --git a/test/test_chainable_cpu.py b/test/test_chainable_cpu.py
index 64e24c6..1f36885 100644
--- a/test/test_chainable_cpu.py
+++ b/test/test_chainable_cpu.py
@@ -92,6 +92,7 @@ def state_fn(_x):
     "OrthoLaProp",
     "LaPropOrtho",
     "PSGDKron",
+    "PSGDKronAdam",
     "PSGDLRA",
     "PSGDPRO",
     "SUDSAdamW",
diff --git a/test/test_helpers_cpu.py b/test/test_helpers_cpu.py
index bc5952c..5a7ed4e 100644
--- a/test/test_helpers_cpu.py
+++ b/test/test_helpers_cpu.py
@@ -3,6 +3,7 @@
 import numpy as np
 import optuna
 import pandas as pd
+import pytest
 import torch
 from optuna.distributions import FloatDistribution, IntDistribution
 from optuna.samplers import RandomSampler
@@ -81,6 +82,22 @@ def _dummy_candidates(params, values, *_args):
     assert 0.0 <= suggestion["width"] <= 1.0
 
 
+def test_helper_samplers_reject_removed_compat_kwargs():
+    search_space = {"width": FloatDistribution(0.0, 1.0)}
+
+    with pytest.raises(TypeError):
+        helpers.BoTorchSampler(search_space, consider_running_trials=True)
+
+    with pytest.raises(TypeError):
+        helpers.HEBOSampler(search_space, constant_liar=True)
+
+    with pytest.raises(TypeError):
+        helpers.ImplicitNaturalGradientSampler(search_space, warn_independent_sampling=False)
+
+    with pytest.raises(TypeError):
+        helpers.AutoSampler(search_space=search_space, constraints_func=lambda *_args: None)
+
+
 def test_hebo_sampler_observe_and_sample(monkeypatch):
     class DummyHEBO:
         def __init__(self, *_args, **_kwargs):
diff --git a/test/test_optimizer_cpu_smoke.py b/test/test_optimizer_cpu_smoke.py
index 80b82c7..7875d5f 100644
--- a/test/test_optimizer_cpu_smoke.py
+++ b/test/test_optimizer_cpu_smoke.py
@@ -1,9 +1,11 @@
+import functools
 import inspect
 
 import pytest
 import torch
 
 import heavyball
+from heavyball import chainable as C
 from heavyball.utils import StatefulOptimizer
 
 DEVICE = torch.device("cuda" if torch.cuda.is_available() else "cpu")
@@ -80,3 +82,44 @@ def closure():
         clone = opt_cls(model.parameters())
         clone.load_state_dict(state_dict)
         assert clone.state_dict()["state"].keys() == state_dict["state"].keys()
+
+
+def test_optimizer_keeps_constructor_compatibility_features():
+    param = torch.nn.Parameter(torch.randn(4, 4, device=DEVICE))
+
+    with pytest.warns(FutureWarning, match="renamed to 'multi_tensor'"):
+        optimizer = heavyball.AdamW([param], foreach=True)
+    assert optimizer.param_groups[0]["multi_tensor"] is True
+
+    with pytest.raises(TypeError, match="Removed in HeavyBall"):
+        heavyball.SOAP([param], normalize_grads=True)
+
+    with pytest.warns(UserWarning, match="Working with uncaptured keyword arguments"):
+        heavyball.AdamW([param], totally_fake=True)
+
+
+def test_optimizer_accepts_explicit_orig_shapes():
+    param = torch.nn.Parameter(torch.randn(4, 4, device=DEVICE))
+    shapes = heavyball.capture_param_shapes([param])
+    optimizer = heavyball.AdamW([param], orig_shapes=shapes)
+    assert "orig_shapes" not in optimizer.param_groups[0]
+
+
+def test_subclass_defaults_still_apply():
+    class ScheduledSOAP(heavyball.SOAP):
+        use_precond_schedule = True
+
+    class DelayedPSGDKron(heavyball.PSGDKron):
+        delayed = True
+        exp_avg_input = False
+
+    param = torch.nn.Parameter(torch.randn(4, 4, device=DEVICE))
+
+    soap = ScheduledSOAP([param])
+    assert "precondition_frequency" not in soap.param_groups[0]
+    assert "precond_scheduler" not in soap.param_groups[0]
+
+    psgd = DelayedPSGDKron([param])
+    first_fn = psgd.fns[0]
+    assert isinstance(first_fn, functools.partial)
+    assert first_fn.func.get_fn() is C.scale_by_delayed_psgd.get_fn()

From 324bade93929319e315cdabf36ee38678c25d119 Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Wed, 1 Apr 2026 12:16:53 +0000
Subject: [PATCH 20/24] ruff

---
 benchmarks/bench_optimizer_step.py | 2 ++
 heavyball/utils.py                 | 4 +++-
 2 files changed, 5 insertions(+), 1 deletion(-)

diff --git a/benchmarks/bench_optimizer_step.py b/benchmarks/bench_optimizer_step.py
index 07ca682..62ced5e 100644
--- a/benchmarks/bench_optimizer_step.py
+++ b/benchmarks/bench_optimizer_step.py
@@ -1,6 +1,7 @@
 from enum import StrEnum
 from math import prod
 from time import perf_counter
+
 import numpy as np
 import torch
 import typer
@@ -79,5 +80,6 @@ def main(
     print(f"{len(shapes)} tensors, {sum(prod(s) for s in shapes)} total params")
     print(f"Median Time: {np.median(times) * 1e6:.3f}µs")
 
+
 if __name__ == "__main__":
     app()
diff --git a/heavyball/utils.py b/heavyball/utils.py
index 70ef148..cdaeffe 100644
--- a/heavyball/utils.py
+++ b/heavyball/utils.py
@@ -910,6 +910,7 @@ def _transform_projected_state(old_qs: List[Optional[Tensor]], new_qs: List[Opti
         new = compiled_einsum(subscripts, promote(state), *old_basis, *new_basis)
         copy_stochastic_(state, new)
 
+
 @decorator_knowngood
 def get_psgd_eigenbasis(Q: List[Tensor], prev: Optional[List[Optional[Tensor]]] = None):
     prev = [None] * len(Q) if prev is None else prev
@@ -934,6 +935,7 @@ def get_psgd_eigenbasis(Q: List[Tensor], prev: Optional[List[Optional[Tensor]]]
 
     return out
 
+
 @decorator_knowngood
 def update_psgd_eigenbasis(Q: List[Tensor], Q_basis: List[Optional[Tensor]], *states: Tensor):
     new_basis = get_psgd_eigenbasis(Q, Q_basis)
@@ -1388,7 +1390,7 @@ class StatefulOptimizer(torch.optim.Optimizer):
         "fallback_to_finite_differences",
         "hvp_interval",
         "hessian_approx",
-        "consume_grad"
+        "consume_grad",
     )
 
     def __init__(self, params, defaults, use_ema: bool = False):

From 62606277f2e9c68b36427cccc519f32d88b03c30 Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Wed, 1 Apr 2026 13:53:08 +0000
Subject: [PATCH 21/24] rename to LATHER + fix algorithm

---
 README.md                  | 10 +++++--
 docs/heavyball3.md         | 26 +++++++++++++++---
 heavyball/__init__.py      |  8 +++---
 heavyball/chainable.py     | 12 ++++-----
 heavyball/utils.py         | 54 +++++++++++++++++++++++++-------------
 test/test_chainable_cpu.py |  2 +-
 6 files changed, 76 insertions(+), 36 deletions(-)

diff --git a/README.md b/README.md
index 0c5f0b3..5c15e1a 100644
--- a/README.md
+++ b/README.md
@@ -4,7 +4,7 @@
 
 HeavyBall is an optimizer library for PyTorch where every optimizer is assembled from composable, compiled building
 blocks. It includes API-compatible replacements for `torch.optim.AdamW`, `SGD`, and `RMSprop`, alongside Muon, SOAP (
-Shampoo), PSGD (Kronecker), ADOPT, Schedule-Free, LaProp, and others.
+Shampoo), PSGD (Kronecker), LATHER, ADOPT, Schedule-Free, LaProp, and others.
 
 The building blocks, over 100 functions in [`utils.py`](heavyball/utils.py), are each compiled with
 `torch.compile(fullgraph=True)` and fuse into Triton kernels. Features like MARS gradient correction,
@@ -31,6 +31,12 @@ from heavyball import SOAP  # Shampoo-based preconditioning
 opt = SOAP(model.parameters(), lr=3e-3)
 ```
 
+```python
+from heavyball import LATHER  # Lie-group Adam Through Harmonic Eigenbasis Rotations
+
+opt = LATHER(model.parameters(), lr=1e-3)
+```
+
 ```python
 from heavyball import Muon
 
@@ -76,7 +82,7 @@ Muon, MuonAdamW, MuonLaProp, HyperBallAdamW, OrthoLaProp, LaPropOrtho
 SOAP, SOAPNAdam, SOAPAdEMAMix, SOLP
 
 **PSGD (Kronecker):**
-PSGDKron, PSGDPRO
+PSGDKron, LATHER, PSGDPRO
 
 **PSGD (Low-Rank):**
 PSGDLRA
diff --git a/docs/heavyball3.md b/docs/heavyball3.md
index 9f6c856..592f381 100644
--- a/docs/heavyball3.md
+++ b/docs/heavyball3.md
@@ -3,20 +3,22 @@
 ## Highlights
 
 * Simplified public API: `Foreach*` prefixes removed, short names are now the canonical classes
-* New optimizers: `HyperBallAdamW`, `MuonAdamW`, `PSGDPRO`
+* New optimizers: `HyperBallAdamW`, `MuonAdamW`, `LATHER`, `PSGDPRO`
+* `LATHER` expands to "Lie-group Adam Through Harmonic Eigenbasis Rotations"
 * `Route`-based param dispatch replaces manual `SplitOpt` for mixed-architecture optimizers
 * `ScheduleFree` and `MSAM` mode switches are now idempotent (`eval()` twice is safe)
 * Higher-precision PSGD preconditioner updates
 * New `consume_grad` option: `step()` clears `p.grad` after consuming it by default; set `consume_grad=False` to keep gradients attached after the step
+* `orig_shapes` is now an explicit documented optimizer argument; use `capture_param_shapes(...)` before wrapping models with sharding backends that do not preserve original parameter shapes
 * `torch.compile`-friendly step with automatic eager fallback for init/preconditioning
 
 ---
 
 ## Release benchmarks
 
-HeavyBall 3 was benchmarked against HeavyBall 2 and `torch.optim` with
-[`benchmarks/bench_optimizer_step.py`](../benchmarks/bench_release_optimizers.py), with compiled AdamW step latency
-dropping from 10.63 ms in HeavyBall 2 to 4.15 ms in HeavyBall 3.
+HeavyBall 3.0.0 was benchmarked against HeavyBall 2.0.0 and `torch.optim` with
+[`benchmarks/bench_release_optimizers.py`](../benchmarks/bench_release_optimizers.py), with compiled AdamW step latency
+dropping from 10.63 ms in HeavyBall 2.0.0 to 4.15 ms in HeavyBall 3.0.0, a 2.56x speedup.
 
 ## Breaking changes
 
@@ -83,6 +85,18 @@ These raise `TypeError` if passed. They were either unused or replaced by better
 | `inverse_free` | PSGDKron | Use `quad_torch` or PSGDPRO for inverse-free PSGD        |
 | `adaptive` | PSGDKron | Removed                                                  |
 
+### Helper sampler kwargs
+
+These compatibility kwargs were removed from `heavyball.helpers` samplers and now raise
+`TypeError`.
+
+| Class | Removed kwargs |
+|---|---|
+| `BoTorchSampler` | `constraints_func`, `consider_running_trials` |
+| `HEBOSampler` | `constant_liar` |
+| `ImplicitNaturalGradientSampler` | `lr`, `warn_independent_sampling` |
+| `AutoSampler` | `constraints_func` |
+
 ### Chainable API renames
 
 | 2.x name | 3.x name |
@@ -97,6 +111,9 @@ These raise `TypeError` if passed. They were either unused or replaced by better
 * **Gradient lifetime**: `consume_grad=True` is available on all optimizers and clears `p.grad`
   during `step()` once the gradient has been consumed. Set `consume_grad=False` if your code
   reads gradients after stepping or relies on them remaining attached.
+* **Sharded parameter shapes**: Built-in optimizers now expose `orig_shapes` explicitly. Use
+  `capture_param_shapes()` before wrapping parameters if your sharding backend hides original
+  shapes.
 * **PSGD dampening**: `dampen_grad` default changed from `2**-13` to `1e-9`, and dampening
   epsilon uses `torch.finfo(float32).eps` regardless of input dtype. This improves
   preconditioner accuracy but may change convergence behavior.
@@ -126,3 +143,4 @@ The `foreach` → `multi_tensor` key rename in param groups is handled automatic
 6. Migrate checkpoints: `python scripts/migrate_optimizer_state.py <ckpt> heavyball.<Optimizer>`
 7. If you relied on `eval(); eval()` toggling back to train mode, update your code
 8. If your training loop reads `p.grad` after `step()`, pass `consume_grad=False`
+9. Remove obsolete compatibility kwargs from `heavyball.helpers` samplers
diff --git a/heavyball/__init__.py b/heavyball/__init__.py
index 0877d66..db48ee3 100644
--- a/heavyball/__init__.py
+++ b/heavyball/__init__.py
@@ -1007,10 +1007,10 @@ def __init__(
         )
 
 
-class PSGDKronAdam(PSGDBase):
+class LATHER(PSGDBase):
     """
-    Adam in the approximate eigenspace induced by the PSGD-Kron preconditioner.
-    Uses cached orthogonal factors from the PSGD preconditioner, applies Adam in that basis, then maps back.
+    Lie-group Adam Through Harmonic Eigenbasis Rotations.
+    Runs Adam in the approximate eigenspace induced by the PSGD-Kron preconditioner, then maps back.
     """
 
     def __init__(
@@ -1059,7 +1059,7 @@ def __init__(
     ):
         self._build_psgd_defaults(
             {**locals(), "exp_avg_input": False},
-            fns=(C.scale_by_psgd_eigen_adam,),
+            fns=(C.scale_by_lather,),
         )
 
 
diff --git a/heavyball/chainable.py b/heavyball/chainable.py
index 0cf091b..24cb333 100644
--- a/heavyball/chainable.py
+++ b/heavyball/chainable.py
@@ -1184,7 +1184,7 @@ def _update_psgd_precond(
     running_lower_bound,
     step,
     prob: Optional[callable] = None,
-) -> Optional[Tensor]:
+) -> None:
     if prob is None:
         prob = utils.precond_update_prob_schedule()
 
@@ -1196,7 +1196,7 @@ def _update_psgd_precond(
     else:
         vector, hessian_vector = utils.take_temporary(group, param, "vector", "hessian_vector")
 
-    precond = utils.psgd_update_precond(
+    utils.psgd_update_precond(
         hessian_vector,
         group["precond_lr"],
         Q,
@@ -1215,10 +1215,8 @@ def _update_psgd_precond(
         float_prob = prob(group["step"])
     group["is_cached"] = should_use_cache = cached and float_prob < 0.5
 
-    if precond is not None:
-        return precond
     if not should_use_cache or not cached:
-        return None
+        return
 
     Q_resolved = utils.line_to_triu(Q) if group["store_triu_as_line"] else Q
     for i, (c_, q_) in enumerate(zip(Q_cache, Q_resolved)):
@@ -1233,7 +1231,7 @@ def _update_psgd_precond(
             torch.matmul(q_.T, q_, out=c_)
         else:
             torch.mul(q_, q_, out=c_)
-    return None
+    return
 
 
 def _update_psgd_pro_precond(
@@ -1399,7 +1397,7 @@ def scale_by_psgd(
 @zero_guard("exp_avg", "exp_avg_sq")
 @general_guard("Q", "Q_basis", "running_lower_bound", "step", init_fn=_init_psgd_eigen_kron, skip_first=False)
 @no_state_no_multi_tensor
-def scale_by_psgd_eigen_adam(
+def scale_by_lather(
     group,
     update,
     grad,
diff --git a/heavyball/utils.py b/heavyball/utils.py
index cdaeffe..d7aa7c0 100644
--- a/heavyball/utils.py
+++ b/heavyball/utils.py
@@ -106,8 +106,18 @@ def _fn(*args, **kwargs):
     return _fn
 
 
+def decorator_no_fullgraph(func: Callable):
+    return decorator_knowngood(func, fullgraph=False)
+
+
 einsum_base = string.ascii_lowercase
 
+no_compile_qr = torch.compiler.disable(torch.linalg.qr)
+no_compile_solve = torch.compiler.disable(torch.linalg.solve)
+no_compile_svd = torch.compiler.disable(torch.linalg.svd)
+no_compile_lobpcg = torch.compiler.disable(torch.lobpcg)
+no_compile_solve_triangular = torch.compiler.disable(torch.linalg.solve_triangular)
+
 
 @decorator_knowngood
 def compiled_einsum(expr, *args):
@@ -770,7 +780,7 @@ def _compilable_grafting(magnitude, direction):
     return direction * (magnitude.norm() / direction.norm().clamp(min=1e-6))
 
 
-@decorator_knowngood
+@decorator_no_fullgraph
 def _compilable_orthogonal_(x: Tensor, mode: str | ZerothPowerMode, out: Tensor | None, scale_mode: str):
     if not isinstance(mode, ZerothPowerMode):
         mode = ZerothPowerMode(mode)
@@ -783,12 +793,12 @@ def _compilable_orthogonal_(x: Tensor, mode: str | ZerothPowerMode, out: Tensor
     elif mode == ZerothPowerMode.legacy_newtonschulz:
         y = legacy_zeropower_via_newtonschulz5(x, 5)
     elif mode == ZerothPowerMode.qr:
-        y = torch.linalg.qr(promote(x)).Q
+        y = no_compile_qr(promote(x)).Q
     elif mode == ZerothPowerMode.svd:
-        u, _s, vt = torch.linalg.svd(promote(x))
+        u, _s, vt = no_compile_svd(promote(x))
         y = u @ vt
     elif mode == ZerothPowerMode.legacy_svd:
-        u, _s, vt = torch.linalg.svd(promote(x))
+        u, _s, vt = no_compile_svd(promote(x))
         y = u @ vt.T
     else:
         raise NotImplementedError(f"Unknown zeroth_power_mode: {mode}")
@@ -815,7 +825,7 @@ def _compilable_scatter_set(target, source, index):
     target[:] = source.contiguous()[index].reshape_as(target)
 
 
-# @decorator_knowngood
+@decorator_no_fullgraph
 def get_orthogonal_matrix_QR(GG: List[Tensor], Q: List[Tensor], *exp_avg: Tensor):
     """
     Computes the eigenbases of the preconditioner using one round of power iteration
@@ -911,7 +921,7 @@ def _transform_projected_state(old_qs: List[Optional[Tensor]], new_qs: List[Opti
         copy_stochastic_(state, new)
 
 
-@decorator_knowngood
+@decorator_no_fullgraph
 def get_psgd_eigenbasis(Q: List[Tensor], prev: Optional[List[Optional[Tensor]]] = None):
     prev = [None] * len(Q) if prev is None else prev
     out = []
@@ -921,22 +931,31 @@ def get_psgd_eigenbasis(Q: List[Tensor], prev: Optional[List[Optional[Tensor]]]
             out.append(None)
             continue
 
-        basis = msign(promote(q)).mT.to(dtype=q.dtype)
-        projected = promote(q) @ promote(basis)
+        q32 = promote(q)
+        if old_basis is None:
+            old_basis32 = torch.eye(q.shape[-1], device=q.device, dtype=q32.dtype)
+        else:
+            old_basis32 = promote(old_basis)
+
+        Y = q32.mT @ (q32 @ old_basis32)
+        basis_raw = no_compile_qr(Y, mode="reduced").Q.to(dtype=q.dtype)
+        projected = q32 @ promote(basis_raw)
         sort_idx = torch.argsort(compiled_einsum("ij,ij->j", projected, projected), descending=True)
-        basis = basis.index_select(1, sort_idx)
+        basis_raw = basis_raw.index_select(1, sort_idx)
 
-        if old_basis is not None:
-            signs = compiled_einsum("ij,ij->j", promote(old_basis), promote(basis))
-            signs = torch.where(signs < 0, -torch.ones_like(signs), torch.ones_like(signs)).to(dtype=basis.dtype)
-            basis = basis * signs.view(1, -1)
+        if old_basis is None:
+            basis = basis_raw
+        else:
+            signs = compiled_einsum("ij,ij->j", old_basis32, promote(basis_raw))
+            signs = torch.where(signs < 0, -torch.ones_like(signs), torch.ones_like(signs)).to(dtype=basis_raw.dtype)
+            basis = basis_raw * signs.view(1, -1)
 
         out.append(basis)
 
     return out
 
 
-@decorator_knowngood
+@decorator_no_fullgraph
 def update_psgd_eigenbasis(Q: List[Tensor], Q_basis: List[Optional[Tensor]], *states: Tensor):
     new_basis = get_psgd_eigenbasis(Q, Q_basis)
     _transform_projected_state(Q_basis, new_basis, *states)
@@ -2769,14 +2788,13 @@ def psgd_calc_A_and_conjB(G: Tensor, Q, conjB: Tensor | None):  # conjB ("V", "v
         conjB = torch.randn_like(G)
     exprA = cached_precond_grad_expr(ndim_tuple(Q), G.ndim)  # calcA expr and cached precond expr are the same
     A = casted_einsum(exprA, *Q, G)
-    solve = torch.compiler.disable(torch.linalg.solve_triangular)
     transposed_shape = original_shape = conjB.shape
     prev_i = -1
     qs, conjB = _psgd_calc_scalars_(Q, conjB)
     for i, tri_q in qs:
         conjB, transposed_shape = _reshape_conjB(conjB, transposed_shape, original_shape, prev_i, i)
         prev_i = i
-        conjB = solve(tri_q, conjB, upper=True, left=False)
+        conjB = no_compile_solve_triangular(tri_q, conjB, upper=True, left=False)
     conjB, _ = _reshape_conjB(conjB, transposed_shape, original_shape, prev_i, -1)
     return A, conjB
 
@@ -2785,7 +2803,7 @@ def max_singular_value_exact(A, use_lobpcg: bool = False):
     try:
         if use_lobpcg:
             A = A @ A.T
-            eigval, _ = torch.compiler.disable(torch.lobpcg)(A, k=1, largest=True)
+            eigval, _ = no_compile_lobpcg(A, k=1, largest=True)
             return eigval[0].sqrt()
         else:
             return torch.linalg.svd(promote(A), driver="gesvdj")[1].max().to(A.dtype)  # == linalg.matrix_norm(A, ord=2)
@@ -3071,7 +3089,7 @@ def _update_lb(ell: Tensor, lb_state: Tensor, beta: Tensor) -> Tensor:
     return ell
 
 
-@functools.partial(decorator_knowngood, fullgraph=False)
+@decorator_no_fullgraph
 def psgd_update_precond(
     G: Tensor,
     precond_lr: float,
diff --git a/test/test_chainable_cpu.py b/test/test_chainable_cpu.py
index 1f36885..ed2da33 100644
--- a/test/test_chainable_cpu.py
+++ b/test/test_chainable_cpu.py
@@ -92,7 +92,7 @@ def state_fn(_x):
     "OrthoLaProp",
     "LaPropOrtho",
     "PSGDKron",
-    "PSGDKronAdam",
+    "LATHER",
     "PSGDLRA",
     "PSGDPRO",
     "SUDSAdamW",

From 9ee5a569425268161bb057e3e529fff77c8ba1a8 Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Wed, 1 Apr 2026 14:26:18 +0000
Subject: [PATCH 22/24] LATHER warm start

---
 heavyball/chainable.py | 16 +++++++-------
 heavyball/utils.py     | 47 +++++++++++++++++++++++++-----------------
 2 files changed, 35 insertions(+), 28 deletions(-)

diff --git a/heavyball/chainable.py b/heavyball/chainable.py
index 24cb333..1aabc00 100644
--- a/heavyball/chainable.py
+++ b/heavyball/chainable.py
@@ -917,11 +917,13 @@ def _init_psgd_eigen_kron(state, group, update, grad, param, prob: Optional[call
         tmp.get("vector"),
         dtype=getattr(torch, group["q_dtype"]),
     )
-    state["Q"] = utils.triu_to_line(Q) if group["store_triu_as_line"] else Q
-    state["Q_basis"] = utils.get_psgd_eigenbasis(Q)
     state["running_lower_bound"] = [torch.zeros((1,), device=q.device, dtype=torch.float64) for q in Q]
     state["step"] = torch.zeros((), device=param.device, dtype=torch.float64)
 
+    _update_psgd_precond(False, None, group, param, update, Q, state["running_lower_bound"], state["step"], prob)
+    state["Q"] = utils.triu_to_line(Q) if group["store_triu_as_line"] else Q
+    state["Q_basis"] = utils.init_psgd_eigenbasis(Q)
+
 
 def _init_psgd_pro_kron(state, group, update, grad, param, cached: bool = False, prob: Optional[callable] = None):
     Q = utils.init_Q_exprs(
@@ -1395,7 +1397,7 @@ def scale_by_psgd(
 @SqueezeGrad
 @PrecondGradAccumGuard
 @zero_guard("exp_avg", "exp_avg_sq")
-@general_guard("Q", "Q_basis", "running_lower_bound", "step", init_fn=_init_psgd_eigen_kron, skip_first=False)
+@general_guard("Q", "Q_basis", "running_lower_bound", "step", init_fn=_init_psgd_eigen_kron, skip_first=True)
 @no_state_no_multi_tensor
 def scale_by_lather(
     group,
@@ -1411,11 +1413,7 @@ def scale_by_lather(
     step: Tensor,
     prob: Optional[callable] = None,
 ):
-    basis = Q_basis
-    if basis is None:
-        basis = utils.get_psgd_eigenbasis(utils.line_to_triu(Q) if group["store_triu_as_line"] else Q)
-
-    projected = utils.project(utils.promote(update), basis, False)
+    projected = utils.project(utils.promote(update), Q_basis, False)
     precond = utils.adam_(
         exp_avg,
         exp_avg_sq,
@@ -1425,7 +1423,7 @@ def scale_by_lather(
         group["step"],
         group["eps"],
     )[0]
-    precond = utils.project(precond, basis, True)
+    precond = utils.project(precond, Q_basis, True)
 
     if group["is_preconditioning"]:
         _update_psgd_precond(False, None, group, param, update_to_precond, Q, running_lower_bound, step, prob)
diff --git a/heavyball/utils.py b/heavyball/utils.py
index d7aa7c0..4006633 100644
--- a/heavyball/utils.py
+++ b/heavyball/utils.py
@@ -113,6 +113,7 @@ def decorator_no_fullgraph(func: Callable):
 einsum_base = string.ascii_lowercase
 
 no_compile_qr = torch.compiler.disable(torch.linalg.qr)
+no_compile_eigh = torch.compiler.disable(torch.linalg.eigh)
 no_compile_solve = torch.compiler.disable(torch.linalg.solve)
 no_compile_svd = torch.compiler.disable(torch.linalg.svd)
 no_compile_lobpcg = torch.compiler.disable(torch.lobpcg)
@@ -922,49 +923,57 @@ def _transform_projected_state(old_qs: List[Optional[Tensor]], new_qs: List[Opti
 
 
 @decorator_no_fullgraph
-def get_psgd_eigenbasis(Q: List[Tensor], prev: Optional[List[Optional[Tensor]]] = None):
-    prev = [None] * len(Q) if prev is None else prev
+def init_psgd_eigenbasis(Q: List[Tensor]):
     out = []
 
-    for q, old_basis in zip(Q, prev):
+    for q in Q:
         if q.ndim < 2:
             out.append(None)
             continue
 
         q32 = promote(q)
+        evals, basis = no_compile_eigh(q32.mT @ q32)
+        sort_idx = torch.argsort(evals, descending=True)
+        out.append(basis.index_select(1, sort_idx).to(dtype=q.dtype))
+
+    return out
+
+
+@decorator_no_fullgraph
+def get_psgd_eigenbasis(Q: List[Tensor], prev: List[Optional[Tensor]]):
+    out = []
+
+    for q, old_basis in zip(Q, prev):
+        if q.ndim < 2:
+            out.append(None)
+            continue
         if old_basis is None:
-            old_basis32 = torch.eye(q.shape[-1], device=q.device, dtype=q32.dtype)
-        else:
-            old_basis32 = promote(old_basis)
+            raise ValueError(
+                "get_psgd_eigenbasis requires a previous basis for matrix blocks; use init_psgd_eigenbasis"
+            )
 
+        q32 = promote(q)
+        old_basis32 = promote(old_basis)
         Y = q32.mT @ (q32 @ old_basis32)
         basis_raw = no_compile_qr(Y, mode="reduced").Q.to(dtype=q.dtype)
         projected = q32 @ promote(basis_raw)
         sort_idx = torch.argsort(compiled_einsum("ij,ij->j", projected, projected), descending=True)
         basis_raw = basis_raw.index_select(1, sort_idx)
-
-        if old_basis is None:
-            basis = basis_raw
-        else:
-            signs = compiled_einsum("ij,ij->j", old_basis32, promote(basis_raw))
-            signs = torch.where(signs < 0, -torch.ones_like(signs), torch.ones_like(signs)).to(dtype=basis_raw.dtype)
-            basis = basis_raw * signs.view(1, -1)
-
+        signs = compiled_einsum("ij,ij->j", old_basis32, promote(basis_raw))
+        signs = torch.where(signs < 0, -torch.ones_like(signs), torch.ones_like(signs)).to(dtype=basis_raw.dtype)
+        basis = basis_raw * signs.view(1, -1)
         out.append(basis)
 
     return out
 
 
 @decorator_no_fullgraph
-def update_psgd_eigenbasis(Q: List[Tensor], Q_basis: List[Optional[Tensor]], *states: Tensor):
+def update_psgd_eigenbasis(Q: List[Tensor], Q_basis: List[Tensor], *states: Tensor):
     new_basis = get_psgd_eigenbasis(Q, Q_basis)
     _transform_projected_state(Q_basis, new_basis, *states)
 
     for i, (old_basis, new_basis_i) in enumerate(zip(Q_basis, new_basis)):
-        if old_basis is None or new_basis_i is None:
-            Q_basis[i] = new_basis_i
-        else:
-            copy_stochastic_(old_basis, new_basis_i)
+        copy_stochastic_(old_basis, new_basis_i)
 
 
 def get_orthogonal_matrix(mat, max_eps: float = 1e-3, min_eps: float = 1e-30):

From ad178b80d1258d610519087eb6e9c236711e9c33 Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Wed, 1 Apr 2026 15:35:22 +0000
Subject: [PATCH 23/24] align LATHER with SOAP

---
 heavyball/utils.py | 78 +++++++++++++++++++++++++---------------------
 1 file changed, 43 insertions(+), 35 deletions(-)

diff --git a/heavyball/utils.py b/heavyball/utils.py
index 4006633..0101df7 100644
--- a/heavyball/utils.py
+++ b/heavyball/utils.py
@@ -932,9 +932,7 @@ def init_psgd_eigenbasis(Q: List[Tensor]):
             continue
 
         q32 = promote(q)
-        evals, basis = no_compile_eigh(q32.mT @ q32)
-        sort_idx = torch.argsort(evals, descending=True)
-        out.append(basis.index_select(1, sort_idx).to(dtype=q.dtype))
+        out.append(_stable_symmetric_basis(q32.mT @ q32, out_device=q.device, out_dtype=q.dtype))
 
     return out
 
@@ -973,9 +971,50 @@ def update_psgd_eigenbasis(Q: List[Tensor], Q_basis: List[Tensor], *states: Tens
     _transform_projected_state(Q_basis, new_basis, *states)
 
     for i, (old_basis, new_basis_i) in enumerate(zip(Q_basis, new_basis)):
+        if old_basis is None:  # happens only if ndim < 2
+            continue
         copy_stochastic_(old_basis, new_basis_i)
 
 
+def _stable_symmetric_basis(
+    m: Tensor,
+    max_eps: float = 1e-3,
+    min_eps: float = 1e-30,
+    *,
+    out_device=None,
+    out_dtype=None,
+):
+    out_device = m.device if out_device is None else out_device
+    out_dtype = m.dtype if out_dtype is None else out_dtype
+    m = promote(m.data)
+
+    eps = min_eps
+    while True:
+        try:
+            eye = torch.eye(m.shape[0], device=m.device, dtype=m.dtype)
+            _eigval, eigvec = no_compile_eigh(m + eps * eye)
+            return torch.flip(eigvec, [1]).to(device=out_device, dtype=out_dtype)
+        except torch.OutOfMemoryError:
+            if m.device.type == "cpu":
+                raise
+            if torch.cuda.is_available():
+                torch.cuda.synchronize(m.device)
+            clean()
+            m = m.cpu()
+        except RuntimeError as e:
+            if torch.cuda.is_available() and ("CUDA" in str(e) or "illegal memory access" in str(e)):
+                torch.cuda.synchronize(m.device)
+                clean()
+                m = m.cpu()
+            elif m.dtype != torch.double:
+                m = m.double()
+            elif eps < max_eps:
+                eps = eps ** (2 / 3)
+            else:
+                raise
+        clean()
+
+
 def get_orthogonal_matrix(mat, max_eps: float = 1e-3, min_eps: float = 1e-30):
     """
     Computes the eigenbases of the preconditioner using torch.linalg.eigh decomposition.
@@ -987,38 +1026,7 @@ def get_orthogonal_matrix(mat, max_eps: float = 1e-3, min_eps: float = 1e-30):
             final.append(None)
             continue
 
-        device, dtype = m.device, m.dtype
-        m = promote(m.data)
-
-        eps = min_eps
-        while True:
-            try:
-                eye = torch.eye(m.shape[0], device=m.device, dtype=m.dtype)
-                _eigval, eigvec = torch.linalg.eigh(m + eps * eye)
-                eigvec = eigvec.to(device=device, dtype=dtype)
-                break
-            except torch.OutOfMemoryError:
-                if m.device.type == "cpu":
-                    raise
-                if torch.cuda.is_available():
-                    torch.cuda.synchronize(m.device)
-                clean()
-                m = m.cpu()
-            except RuntimeError as e:
-                if torch.cuda.is_available() and ("CUDA" in str(e) or "illegal memory access" in str(e)):
-                    torch.cuda.synchronize(m.device)
-                    clean()
-                    m = m.cpu()
-                elif m.dtype != torch.double:
-                    m = m.double()
-                elif eps < max_eps:
-                    eps = eps ** (2 / 3)
-                else:
-                    raise
-            clean()
-
-        eigvec = torch.flip(eigvec, [1])
-        final.append(eigvec)
+        final.append(_stable_symmetric_basis(m, max_eps=max_eps, min_eps=min_eps))
 
     return final
 

From fbe977706c8c863578e2b94459ba42400e0b31ad Mon Sep 17 00:00:00 2001
From: ClashLuke <39779310+ClashLuke@users.noreply.github.com>
Date: Wed, 1 Apr 2026 15:54:10 +0000
Subject: [PATCH 24/24] first step works with store_triu_as_line

---
 heavyball/chainable.py | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/heavyball/chainable.py b/heavyball/chainable.py
index 1aabc00..100c7c2 100644
--- a/heavyball/chainable.py
+++ b/heavyball/chainable.py
@@ -920,8 +920,10 @@ def _init_psgd_eigen_kron(state, group, update, grad, param, prob: Optional[call
     state["running_lower_bound"] = [torch.zeros((1,), device=q.device, dtype=torch.float64) for q in Q]
     state["step"] = torch.zeros((), device=param.device, dtype=torch.float64)
 
+    line, group["store_triu_as_line"] = group["store_triu_as_line"], False
     _update_psgd_precond(False, None, group, param, update, Q, state["running_lower_bound"], state["step"], prob)
-    state["Q"] = utils.triu_to_line(Q) if group["store_triu_as_line"] else Q
+    group["store_triu_as_line"] = line
+    state["Q"] = utils.triu_to_line(Q) if line else Q
     state["Q_basis"] = utils.init_psgd_eigenbasis(Q)