diff --git a/index.bs b/index.bs
index 14778685..6e7fe0e0 100644
--- a/index.bs
+++ b/index.bs
@@ -739,6 +739,11 @@ interface MLOperand {};
 </dl>
 </div>
 
+To get the <dfn for="MLOperand">rank</dfn> of an {{MLOperand}} |operand|, run the following steps:
+<div algorithm=rank class=algorithm-steps>
+    1. Return the size of |operand|.{{MLOperand/[[descriptor]]}}.{{MLOperandDescriptor/dimensions}}.
+</div>
+
 Since the {{MLOperand/[[builder]]}} object is bound by the {{MLGraphBuilder/constructor()}} constructor to an {{MLContext}} object, an {{MLOperand}} is also always bound to the same {{MLContext}} object.
 
 #### Creating {{MLOperand}} #### {#api-mloperand-create}
@@ -763,6 +768,16 @@ To <dfn>check dimensions</dfn> given |dimensions| and |type|, run the following
     1. Return `true`.
 </div>
 
+To <dfn for="MLOperand">validate MLOperand</dfn> given |operand| and |builder|, run the following steps:
+<div class=algorithm-steps>
+    1. If |operand|.{{MLOperand/[[builder]]}} is not an instance of {{MLGraphBuilder}}, return `false`.
+    1. If |builder| is not `undefined` and is not equal to |operand|.{{MLOperand/[[builder]]}}, return `false`.
+    1. Let |desc| be |operand|.{{MLOperand/[[descriptor]]}}.
+    1. If |desc| is not an [=object=] that [=implements=] {{MLOperandDescriptor}}, return `false`.
+    1. If |desc|.{{MLOperandDescriptor/dimensions}} [=map/exists=] and invoking <a>check dimensions</a> given |desc|.{{MLOperandDescriptor/dimensions}} and |desc|.{{MLOperandDescriptor/type}} returns `false`, then return `false`.
+    1. Return `true`.
+</div>
+
 ### The MLActivation interface ### {#api-mlactivation}
 
 Objects implementing the {{MLActivation}} interface represent activation function types.
@@ -1418,7 +1433,7 @@ partial interface MLGraphBuilder {
   MLOperand concat(sequence<MLOperand> inputs, unsigned long axis);
 };
 </script>
-<div algorithm=concat>
+<div>
     **Arguments:**
         - *inputs*: a sequence of {{MLOperand}}. All input tensors must have the
             same shape, except for the size of the dimension to concatenate on.
@@ -1429,6 +1444,37 @@ partial interface MLGraphBuilder {
     that all the inputs concatenated along. The size of that dimension is
     computed as the sum of all the input sizes of the same dimension.
 </div>
+<div algorithm=concat>
+    The {{MLGraphBuilder/concat(inputs, axis)}} steps are:
+    <div class="note">
+        The permissions and context validity have been checked by [[#api-mlgraphbuilder-constructor]] steps.
+    </div>
+    1. Let |inputs| be the first argument.
+        1. [=Assert=]: the type of |inputs| is sequence of {{MLOperand}} objects.
+        1. [=Assert=]: the type of |axis| is `unsigned long`.
+        1. [=Assert=]: the shape, i.e. {{MLOperandDescriptor/dimensions}}) of each operand in |inputs| is the same, except on the dimension given by |axis| on which they are concatenated.
+        1. [=Assert=]: the {{MLOperandDescriptor/type}} of each operand in |inputs| is the same.
+        1. If any of the following steps fail, then throw a "{{DataError}}" {{DOMException}} and stop.
+            1. If |inputs| is not an array of [=objects=], fail.
+            1. If |axis| is not a positive integer [=number=], fail.
+            1. If |axis| is greater than or equal to the <a>rank</a> of |inputs|, fail.
+            1. Let |desc| be |inputs|[0].{{MLOperand/[[descriptor]]}}.
+            1. Let |desc|.{{MLOperandDescriptor/dimensions}}[|axis|] be `0`.
+            1. For each |index| between 0 and the <a>rank</a> of |inputs|:
+                1. If running <a>validate MLOperand</a> given |inputs|[|index|] and [=this=]  returns `false`, then fail.
+                1. For each |dim| between 0 and the <a>rank</a> of |inputs|[|index|]:
+                    <div class="note">
+                        If the shape of each corresponding dimension and type of the operands, except for those of the dimension given by |axis|, is not the same, fail.
+                    </div>
+                    1. If |dim| is not equal to |axis| and if |inputs|[|index|].{{MLOperandDescriptor/dimensions}}[|dim|] is not equal to |inputs|[0].{{MLOperandDescriptor/dimensions}}[|dim|], fail.
+                    1. If |inputs|[|dim|].{{MLOperandDescriptor/type}} is not equal to |inputs|[0].{{MLOperandDescriptor/type}}.
+                    1. If |dim| is equal to |axis|, add to |desc|.{{MLOperandDescriptor/dimensions}}[|axis|] the value of |inputs|[|index|].{{MLOperandDescriptor/dimensions}}[|dim|].
+        1. Let |output| be the result of invoking the <a>create MLOperand</a> steps given [=this=] and |desc|.
+            1. If that throws an error, re-throw the error and stop.
+        1. Make a request to the underlying platform to create an operator for this method with |inputs| connected as input and |output| connected as output and store a reference to the [=implementation-defined=] platform object to |output|.{{MLOperand/[[operand]]}}.
+            1. If that fails, throw a "{{DataError}}" {{DOMException}} and stop.
+        1. Return |output|.
+</div>
 
 ### The conv2d() method ### {#api-mlgraphbuilder-conv2d}
 Compute a 2-D convolution given 4-D input and filter tensors