fix: broadcast vectors for grad calculation (#1535)

Co-authored-by: José Valim <[email protected]>

Author: polvalente

nx/lib/nx.ex

@@ -5420,9 +5420,13 @@ defmodule Nx do
       {_, [], 0} ->
         fun.(left, right)
 
-      {[devec_left, devec_right], canonical_vectorized_axes, _offset} ->
-        devec_left
-        |> fun.(devec_right)
+      {[devec_left, devec_right], canonical_vectorized_axes, offset} ->
+        leading_names = Keyword.keys(canonical_vectorized_axes)
+        l = %{devec_left | names: leading_names ++ Enum.drop(devec_left.names, offset)}
+        r = %{devec_right | names: leading_names ++ Enum.drop(devec_right.names, offset)}
+
+        l
+        |> fun.(r)
         |> vectorize(canonical_vectorized_axes)
     end
   end

nx/lib/nx/defn/expr.ex

@@ -1394,6 +1394,10 @@ defmodule Nx.Defn.Expr do
 
   ## Constant helpers and related optimizations
 
+  defp constant(%{vectorized_axes: [_ | _]} = out, number) do
+    tensor(Nx.fill(out, number, type: out.type))
+  end
+
   defp constant(%{shape: shape, type: type} = out, number) do
     number =
       cond do
@@ -1661,7 +1665,7 @@ defmodule Nx.Defn.Expr do
 
   defp counter_to_name(counter), do: [?a + counter]
 
-  defp to_type_shape(%{type: type, shape: shape}) do
+  defp to_type_shape(%{vectorized_axes: [], type: type, shape: shape}) do
     brackets =
       shape
       |> Tuple.to_list()

nx/lib/nx/defn/grad.ex

@@ -19,10 +19,10 @@ defmodule Nx.Defn.Grad do
     {:env, env} = Function.info(fun, :env)
     ids = stop_grads(env, ids)
 
-    # save vectorized axes before devectorizing
-    expr = to_grad |> fun.()
+    expr = fun.(to_grad)
 
-    transformed_expr = transform.(expr) |> validate_expr!() |> Nx.devectorize(keep_names: false)
+    transformed_expr =
+      expr |> transform.() |> validate_expr!()
 
     {parents, nodes} = parents_tree(transformed_expr, ids)
 
@@ -33,23 +33,17 @@ defmodule Nx.Defn.Grad do
       Composite.traverse(
         to_grad,
         {nodes, grads},
-        fn %{vectorized_axes: vectorized_axes} = node, acc ->
-          node
-          |> Nx.devectorize(keep_names: false)
-          |> to_grad(to_grad_ids, parents, acc)
-          |> then(fn {node, acc} ->
-            {Nx.vectorize(node, vectorized_axes), acc}
-          end)
+        fn node, acc ->
+          to_grad(node, to_grad_ids, parents, acc)
         end
       )
 
     {expr, graded}
   end
 
-  defp constant(float, shape) do
-    shape = Nx.shape(shape)
+  defp constant(float, %T{shape: shape} = t) do
     names = List.duplicate(nil, tuple_size(shape))
-    Expr.constant(%T{shape: shape, type: {:f, 32}, names: names}, float, [])
+    Expr.constant(%T{t | names: names, type: {:f, 32}}, float, [])
   end
 
   defp validate_expr!(%T{data: %Expr{}} = expr) do
@@ -94,47 +88,88 @@ defmodule Nx.Defn.Grad do
                [:equal, :greater, :greater_equal, :less, :less_equal, :not_equal, :argsort]
 
   defp parents_tree(expr, nodes) do
-    Composite.reduce(expr, {%{}, nodes}, &recur_parents_tree/2)
+    Composite.reduce(
+      expr,
+      {%{}, nodes},
+      &recur_parents_tree(
+        Nx.devectorize(&1, keep_names: true),
+        &2,
+        Keyword.keys(&1.vectorized_axes)
+      )
+    )
   end
 
-  defp recur_parents_tree(%T{data: %Expr{id: id, op: op}} = t, {parents, nodes}) do
+  defp recur_parents_tree(%T{data: %Expr{id: id, op: op}} = t, {parents, nodes}, vectorized_names) do
     case nodes do
-      %{^id => _} -> {parents, nodes}
-      %{} -> parents_args(op, t, id, {parents, Map.put(nodes, id, t)})
+      %{^id => _} ->
+        {parents, nodes}
+
+      %{} ->
+        # We use this to compute the proper axis sizes for the tensor
+        nodes = Map.put(nodes, id, {t, vectorized_names})
+
+        parents_args(op, t, id, {parents, nodes}, vectorized_names)
     end
   end
 
-  defp parents_args(:metadata, %{data: %{args: [_, %{stop_grad: true}]}}, _id, acc) do
+  defp parents_args(
+         :metadata,
+         %{data: %{args: [_, %{stop_grad: true}]}},
+         _id,
+         acc,
+         _parent_vectorized_names
+       ) do
     acc
   end
 
-  defp parents_args(:optional, %{data: %{args: [call, _expr, callback]}} = t, id, acc) do
+  defp parents_args(
+         :optional,
+         %{data: %{args: [call, _expr, callback]}} = t,
+         id,
+         acc,
+         parent_vectorized_names
+       ) do
     expr = apply(callback, call.data.args)
 
     # Now traverse over the optional expression where args are the new parameters.
     # Once we access the parameter itself, we point the parameter to the arg.
-    {parents, nodes} =
-      Composite.reduce(expr, acc, fn expr, {parents, nodes} ->
-        parents = Map.update(parents, expr.data.id, [id], &[id | &1])
-        recur_parents_tree(expr, {parents, nodes})
+    {{parents, nodes}, _} =
+      Composite.reduce(expr, {acc, parent_vectorized_names}, fn
+        expr, {{parents, nodes}, expr_vectorized_names} ->
+          arg_vectorized_names = compute_arg_vectorized_names(expr, expr_vectorized_names)
+          parents = Map.update(parents, expr.data.id, [id], &[id | &1])
+
+          acc =
+            recur_parents_tree(
+              expr,
+              {parents, nodes},
+              arg_vectorized_names
+            )
+
+          {acc, expr_vectorized_names}
       end)
 
-    {parents, Map.put(nodes, id, put_in(t.data.args, [call, expr, callback]))}
+    updated_node =
+      {put_in(t.data.args, [call, expr, callback]), parent_vectorized_names}
+
+    {parents, Map.put(nodes, id, updated_node)}
   end
 
   # We register cond as a special node to avoid pretraversing it.
   # Instead we traverse it early on on the grad computation.
-  defp parents_args(:cond, _, id, {parents, nodes}) do
+  defp parents_args(:cond, _, id, {parents, nodes}, _parent_vectorized_names) do
     {Map.update(parents, __MODULE__, [id], &[id | &1]), nodes}
   end
 
-  defp parents_args(op, t, parent_id, acc) do
+  defp parents_args(op, t, parent_id, acc, parent_vectorized_names) do
     reduce_args(op, t, acc, fn arg, {parents, nodes} ->
       if arg.data.op in @constants do
         {parents, nodes}
       else
+        arg_vectorized_names = compute_arg_vectorized_names(t, parent_vectorized_names)
         parents = Map.update(parents, arg.data.id, [parent_id], &[parent_id | &1])
-        recur_parents_tree(arg, {parents, nodes})
+
+        recur_parents_tree(arg, {parents, nodes}, arg_vectorized_names)
       end
     end)
   end
@@ -191,10 +226,27 @@ defmodule Nx.Defn.Grad do
     case nodes do
       %{^id => _} ->
         {nodes, grads} = traverse_parents(id, to_grad_ids, parents, {nodes, grads})
-        {ans, nodes} = Map.pop!(nodes, id)
+        {{ans, vectorized_names}, nodes} = Map.pop!(nodes, id)
         %T{data: %Expr{op: op, args: args}} = ans
         {gs, grads} = Map.pop(grads, id)
 
+        {args, ans} =
+          if vectorized_names != [] do
+            args =
+              Enum.map(args, fn
+                %T{} = arg ->
+                  revectorize_node(arg, vectorized_names)
+
+                opt ->
+                  opt
+              end)
+
+            ans = Nx.vectorize(ans, vectorized_names)
+            {args, ans}
+          else
+            {args, ans}
+          end
+
         case gs do
           nil ->
             {nodes, grads}
@@ -213,6 +265,22 @@ defmodule Nx.Defn.Grad do
     end
   end
 
+  defp compute_arg_vectorized_names(%{vectorized_axes: vectorized_axes}, []),
+    do: Keyword.keys(vectorized_axes)
+
+  defp compute_arg_vectorized_names(
+         %{vectorized_axes: vectorized_axes, names: names},
+         parent_names
+       ) do
+    Keyword.keys(vectorized_axes) ++ Enum.filter(names, &(&1 in parent_names))
+  end
+
+  defp revectorize_node(node, vectorized_names) do
+    vectorized_names = compute_arg_vectorized_names(node, vectorized_names)
+
+    Nx.vectorize(node, vectorized_names)
+  end
+
   defp update_grads(:elem, [%{type: {:tuple, size}} = tuple, pos], _ans, g, _to_grad_ids, grads) do
     update_in(grads[tuple.data.id], fn tuple ->
       tuple = tuple || Tuple.duplicate([], size)

nx/test/nx/defn/grad_test.exs

@@ -4256,21 +4256,97 @@ defmodule Nx.Defn.GradTest do
   end
 
   describe "vectorization" do
-    test "supports vectorization" do
+    test "supports combination of vectorized and non-vectorized tensors" do
+      x = Nx.tensor([[1, 2, 3], [4, 5, 6]]) |> Nx.vectorize(:x)
+      y = 1
+
+      grad = Nx.Defn.grad(y, fn y -> Nx.add(x, y) end)
+
+      assert grad == Nx.tensor([3.0, 3.0]) |> Nx.vectorize([:x])
+    end
+
+    test "supports combination of vectorized and non-vectorized tensors over composed function" do
+      x = Nx.tensor([[1, 2, 3], [4, 5, 6]], names: [:x, :y]) |> Nx.vectorize(:x)
+      y = 1
+
+      grad = Nx.Defn.grad(y, fn y -> Nx.add(y, Nx.sin(x)) end)
+      assert grad == Nx.tensor([3.0, 3.0]) |> Nx.vectorize([:x])
+
+      grad = Nx.Defn.grad(x, fn x -> Nx.add(y, Nx.sin(x)) end)
+      assert grad == Nx.cos(x)
+    end
+
+    # Skipping this as it's not supported yet.
+    @tag :skip
+    test "edge case where the same name changes meaning" do
+      x = Nx.tensor([[1], [2], [3]]) |> Nx.vectorize(x: 3)
+
+      grad =
+        Nx.Defn.grad(x, fn t ->
+          devec = Nx.devectorize(t, keep_names: true)
+          new_axis = Nx.reshape(devec, {1, 3, 1}, names: [:x, nil, nil])
+
+          Nx.vectorize(new_axis, x: 1)
+        end)
+
+      assert grad == Nx.tensor([[1], [1], [1]]) |> Nx.vectorize(x: 3)
+    end
+
+    test "supports heterogenous vectorization combinations" do
       x = Nx.tensor([[1, 2, 3], [4, 5, 6]])
       y = Nx.tensor([10, 20])
 
       # first case: y is vectorized scalar, x is vectorized vectors, different vectorized axis names
       # expected result: equivalent to fully broadcasting one tensor onto the other
       x_vec = Nx.vectorize(x, :x)
       y_vec = Nx.vectorize(y, :y)
-      {grad_x_vec, grad_y_vec} = Nx.Defn.grad({x_vec, y_vec}, fn {a, b} -> Nx.multiply(a, b) end)
 
+      grad_fun = fn x, y ->
+        Nx.Defn.grad({x, y}, fn {a, b} -> Nx.multiply(a, b) end)
+      end
+
+      {grad_x_vec, grad_y_vec} = grad_fun.(x_vec, y_vec)
+
+      # Explicit assertion on the results
       assert grad_x_vec ==
-               Nx.tensor([[30.0, 30.0, 30.0], [30.0, 30.0, 30.0]])
-               |> Nx.vectorize(x_vec.vectorized_axes)
+               Nx.tensor([
+                 [
+                   [10.0, 10.0, 10.0],
+                   [20.0, 20.0, 20.0]
+                 ],
+                 [
+                   [10.0, 10.0, 10.0],
+                   [20.0, 20.0, 20.0]
+                 ]
+               ])
+               |> Nx.vectorize([:x, :y])
+
+      assert grad_y_vec ==
+               Nx.tensor([
+                 [6.0, 6.0],
+                 [15.0, 15.0]
+               ])
+               |> Nx.vectorize([:x, :y])
 
-      assert grad_y_vec == Nx.tensor([21.0, 21.0]) |> Nx.vectorize(y_vec.vectorized_axes)
+      # Conceptual assertion: the result should be equivalent to calling Nx.Defn.grad with
+      # each cross-entry of the combined vectors [(x0, y0), (x0, y1), (x1, y0), (x1, y1)]
+
+      {x0y0_wrt_x, x0y0_wrt_y} = grad_fun.(x[0], y[0])
+      {x0y1_wrt_x, x0y1_wrt_y} = grad_fun.(x[0], y[1])
+      {x1y0_wrt_x, x1y0_wrt_y} = grad_fun.(x[1], y[0])
+      {x1y1_wrt_x, x1y1_wrt_y} = grad_fun.(x[1], y[1])
+
+      assert grad_x_vec ==
+               [x0y0_wrt_x, x0y1_wrt_x, x1y0_wrt_x, x1y1_wrt_x]
+               |> Nx.stack()
+               |> Nx.reshape({2, 2, 3})
+               |> Nx.vectorize([:x, :y])
+
+      assert grad_y_vec ==
+               [x0y0_wrt_y, x0y1_wrt_y, x1y0_wrt_y, x1y1_wrt_y]
+               |> Nx.stack()
+               |> Nx.reshape({2, 2})
+               |> Nx.vectorize([:x, :y])
 
       # second case: y is vectorized scalar, x is vectorized vectors, same vectorized axis name
       # expected result: equivalent to "row-wise" broadcasting