Only do reshapes in `tensordot` when needed

pytensor/tensor/math.py

@@ -2158,13 +2158,11 @@ def tensordot(
     a = as_tensor_variable(a)
     b = as_tensor_variable(b)
     runtime_shape_a = a.shape
-    bcast_a = a.broadcastable
     static_shape_a = a.type.shape
-    ndim_a = a.ndim
+    ndim_a = a.type.ndim
     runtime_shape_b = b.shape
-    bcast_b = b.broadcastable
     static_shape_b = b.type.shape
-    ndim_b = b.ndim
+    ndim_b = b.type.ndim
     if na != nb:
         raise ValueError(
             "The number of axes supplied for tensordot must be equal for each tensor. "
@@ -2172,48 +2170,67 @@ def tensordot(
         )
     axes_a = list(normalize_axis_tuple(axes_a, ndim_a))
     axes_b = list(normalize_axis_tuple(axes_b, ndim_b))
+
+    # The operation is only valid if the original dimensions match in length
+    # The ravelling of the dimensions to coerce the operation into a single dot
+    # could mask such errors, so we add an Assert if needed.
     must_assert_runtime = False
-    for k in range(na):
-        ax_a = axes_a[k]
-        ax_b = axes_b[k]
-        if (bcast_a[ax_a] != bcast_b[ax_b]) or (
+    for ax_a, ax_b in zip(axes_a, axes_b, strict=True):
+        if (
             static_shape_a[ax_a] is not None
             and static_shape_b[ax_b] is not None
             and static_shape_a[ax_a] != static_shape_b[ax_b]
         ):
             raise ValueError(
-                "Input arrays have inconsistent broadcastable pattern or type shape along the axes "
+                "Input arrays have inconsistent type shape along the axes "
                 "that are to be reduced with tensordot."
             )
         elif static_shape_a[ax_a] is None or static_shape_b[ax_b] is None:
             if must_assert_runtime:
                 a = Assert(
                     "Input array shape along reduced axes of tensordot are not equal"
-                )(a, eq(a.shape[ax_a], b.shape[ax_b]))
+                )(a, eq(runtime_shape_a[ax_a], runtime_shape_b[ax_b]))
             must_assert_runtime = True
 
-    # Move the axes to sum over to the end of "a"
-    # and to the front of "b"
-    notin = [k for k in range(ndim_a) if k not in axes_a]
-    newaxes_a = notin + axes_a
-    N2 = 1
-    for axis in axes_a:
-        N2 *= runtime_shape_a[axis]
-    newshape_a = (-1, N2)
-    olda = [runtime_shape_a[axis] for axis in notin]
-
-    notin = [k for k in range(ndim_b) if k not in axes_b]
-    newaxes_b = axes_b + notin
-    N2 = 1
-    for axis in axes_b:
-        N2 *= runtime_shape_b[axis]
-    newshape_b = (N2, -1)
-    oldb = [runtime_shape_b[axis] for axis in notin]
-
-    at = a.transpose(newaxes_a).reshape(newshape_a)
-    bt = b.transpose(newaxes_b).reshape(newshape_b)
-    res = _dot(at, bt)
-    return res.reshape(olda + oldb)
+    # Convert tensordot into a stacked dot product.
+    # We stack the summed axes and the non-summed axes of each tensor separately,
+    # and place the summed axes at the end of a and the beginning of b
+    non_summed_axes_a = [k for k in range(ndim_a) if k not in axes_a]
+    non_summed_dims_a = [runtime_shape_a[axis] for axis in non_summed_axes_a]
+    transpose_axes_a = non_summed_axes_a + axes_a
+    # We only need a reshape when we need to combine summed or non-summed dims
+    # or introduce a new dimension (expand_dims) when doing a non-scalar outer product (len(axes) = 0)
+    a_needs_reshape = (ndim_a != 0) and (
+        (len(non_summed_axes_a) > 1) or (len(axes_a) != 1)
+    )
+
+    non_summed_axes_b = [k for k in range(ndim_b) if k not in axes_b]
+    non_summed_dims_b = [runtime_shape_b[axis] for axis in non_summed_axes_b]
+    transpose_axes_b = axes_b + non_summed_axes_b
+    b_needs_reshape = (ndim_b != 0) and (
+        (len(non_summed_axes_b) > 1) or (len(axes_b) != 1)
+    )
+
+    # summed_size_a and summed_size_b must be the same,
+    # but to facilitate reasoning about useless reshapes we compute both from their shapes
+    at = a.transpose(transpose_axes_a)
+    if a_needs_reshape:
+        non_summed_size_a = variadic_mul(*non_summed_dims_a)
+        summed_size_a = variadic_mul(*[runtime_shape_a[axis] for axis in axes_a])
+        at = at.reshape((non_summed_size_a, summed_size_a))
+
+    bt = b.transpose(transpose_axes_b)
+    if b_needs_reshape:
+        non_summed_size_b = variadic_mul(*non_summed_dims_b)
+        summed_size_b = variadic_mul(*[runtime_shape_b[axis] for axis in axes_b])
+        bt = bt.reshape((summed_size_b, non_summed_size_b))
+
+    res = dot(at, bt)
+
+    if a_needs_reshape or b_needs_reshape:
+        res = res.reshape(non_summed_dims_a + non_summed_dims_b)
+
+    return res
 
 
 def outer(x, y):

tests/tensor/test_math.py

@@ -19,7 +19,7 @@ from pytensor.compile.mode import get_default_mode
 from pytensor.compile.sharedvalue import shared
 from pytensor.configdefaults import config
 from pytensor.gradient import NullTypeGradError, grad, numeric_grad
-from pytensor.graph.basic import Variable, ancestors, applys_between
+from pytensor.graph.basic import Variable, ancestors, applys_between, equal_computations
 from pytensor.graph.fg import FunctionGraph
 from pytensor.graph.replace import vectorize_node
 from pytensor.link.c.basic import DualLinker
@@ -2278,7 +2278,7 @@ class TestTensordot:
 
         with pytest.raises(
             ValueError,
-            match="Input arrays have inconsistent broadcastable pattern or type shape",
+            match="Input arrays have inconsistent type shape",
         ):
             tensordot(ones(shape=(7, 4)), ones(shape=(7, 4)), axes=1)
 
@@ -2323,6 +2323,41 @@ class TestTensordot:
         else:
             assert np.allclose(np.tensordot(xv, yv, axes=axes), z.eval({x: xv, y: yv}))
 
+    def test_eager_simplification(self):
+        # Test that cases where tensordot isn't needed, it returns a simple graph
+        scl = tensor(shape=())
+        vec = tensor(shape=(None,))
+        mat = tensor(shape=(None, None))
+
+        # scalar product
+        out = tensordot(scl, scl, axes=[[], []])
+        assert equal_computations([out], [scl * scl])
+
+        # vector-vector product
+        out = tensordot(vec, vec, axes=[[-1], [-1]])
+        assert equal_computations([out], [dot(vec, vec)])
+
+        # matrix-vector product
+        out = tensordot(mat, vec, axes=[[-1], [-1]])
+        assert equal_computations([out], [dot(mat, vec)])
+
+        out = tensordot(mat, vec, axes=[[-2], [-1]])
+        assert equal_computations([out], [dot(mat.T, vec)])
+
+        # vector-matrix product
+        out = tensordot(vec, mat, axes=[[-1], [-2]])
+        assert equal_computations([out], [dot(vec, mat)])
+
+        out = tensordot(vec, mat, axes=[[-1], [-1]])
+        assert equal_computations([out], [dot(vec, mat.T)])
+
+        # matrix-matrix product
+        out = tensordot(mat, mat, axes=[[-1], [-2]])
+        assert equal_computations([out], [dot(mat, mat)])
+
+        out = tensordot(mat, mat, axes=[[-1], [-1]])
+        assert equal_computations([out], [dot(mat, mat.T)])
+
 
 def test_smallest():
     x = dvector()