AF2 Structure Module Study Notes

This repository contains personal study notes on the AlphaFold 2 (AF2) structure module, with a focus on the invariant point attention (IPA) mechanism and related geometric machinery.

The maintained sources are native LaTeX (.tex) files, and the primary way to read the notes is via the compiled PDF files.

References

• Jumper, J. et al. (2021). Highly accurate protein structure prediction with AlphaFold. Nature, 596(7873), 583–589.
  Article and open-access PDF: https://www.nature.com/articles/s41586-021-03819-2

LaTeX Files (sources) and PDFs (outputs)

LaTeX sources live in the tex/ directory, and compiled PDFs live in the pdf/ directory:

• tex/af2_structure_module_full_walkthrough.tex / pdf/af2_structure_module_full_walkthrough.pdf
  Self-contained walkthrough of the AF2 structure module: frames, Algorithm 20, IPA (Algorithm 22), BackboneUpdate, FAPE, torsions, rigid groups, and overall loss.

• tex/af2_ipa_point_features_detailed_explanation.tex / pdf/af2_ipa_point_features_detailed_explanation.pdf
  Detailed explanation of point features in IPA: scalar vs point Q/K/V, local vs global coordinates, frames, distance term in logits, point-valued outputs, and invariance.

• tex/af2_ipa_point_features_alternative_explanation.tex / pdf/af2_ipa_point_features_alternative_explanation.pdf
  Alternative, more streamlined exposition of point features and how they fit into a “dot product + biases” view of attention.

• tex/af2_ipa_viewed_as_standard_self_attention_at_its_core.tex / pdf/af2_ipa_viewed_as_standard_self_attention_at_its_core.pdf
  IPA interpreted as standard self-attention with additional bias terms (pair bias and geometric bias), emphasizing that Q/K/V + softmax remains the core.

• tex/af2_ipa_invariance_and_equivariance_local_vs_global_coordinates_explanation.tex / pdf/af2_ipa_invariance_and_equivariance_local_vs_global_coordinates_explanation.pdf
  Focused on local vs global coordinates, rigid transforms, and why IPA’s logits and outputs are invariant to global SE(3) motions while BackboneUpdate is equivariant.

• tex/af2_structure_module_algo20_transitionMLP_dropout_layernorm_deep_dive.tex / pdf/af2_structure_module_algo20_transitionMLP_dropout_layernorm_deep_dive.pdf
  Deep dive on Algorithm 20: Transition MLP + dropout + LayerNorm.

• tex/rotations_and_invariance_background.tex / pdf/rotations_and_invariance_background.pdf
  General 3D geometry background: rotations, dot-product invariance, preserved quantities, and rigid motions in SE(3).

• tex/af2_local_global_rigid_transforms_vs_change_of_basis.tex / pdf/af2_local_global_rigid_transforms_vs_change_of_basis.pdf
  Clarifies why AF2’s local–global frame maps are per-residue rigid transforms (elements of $\mathrm{SE}(3)$), not mere linear change-of-basis operations on a single vector space.

• tex/af2_local_global_frames_visual_intuition.tex / pdf/af2_local_global_frames_visual_intuition.pdf
  Visual, coordinate-level intuition for why AF2 attaches local frames to residues and how this yields rotationally invariant geometric features.

Building the PDFs

From the tex/ directory, you can compile any note with pdflatex (or xelatex):

cd tex
pdflatex af2_structure_module_full_walkthrough.tex
pdflatex af2_ipa_point_features_detailed_explanation.tex
# etc.