Rewrite dots as multiplication without summation

pytensor/tensor/math.py

@@ -29,7 +29,7 @@
     stack,
     switch,
 )
-from pytensor.tensor.blockwise import Blockwise, vectorize_node_fallback
+from pytensor.tensor.blockwise import Blockwise
 from pytensor.tensor.elemwise import (
     CAReduce,
     Elemwise,
@@ -2726,6 +2726,22 @@ def logsumexp(x, axis=None, keepdims=False):
     return log(sum(exp(x), axis=axis, keepdims=keepdims))
 
 
+# Predefine all batched variations of Dot
+_inner_prod = Blockwise(
+    _dot,
+    signature="(n),(n)->()",
+)
+
+_matrix_vec_prod = Blockwise(
+    _dot,
+    signature="(m,k),(k)->(m)",
+)
+
+_vec_matrix_prod = Blockwise(
+    _dot,
+    signature="(k),(k,n)->(n)",
+)
+
 _matrix_matrix_matmul = Blockwise(
     _dot,
     signature="(m,k),(k,n)->(m,n)",
@@ -2795,14 +2811,24 @@ def matmul(x1: "ArrayLike", x2: "ArrayLike", dtype: Optional["DTypeLike"] = None
 
 
 @_vectorize_node.register(Dot)
-def vectorize_node_dot_to_matmul(op, node, batched_x, batched_y):
+def vectorize_node_dot(op, node, batched_x, batched_y):
     old_x, old_y = node.inputs
-    if old_x.type.ndim == 2 and old_y.type.ndim == 2:
-        # If original input is equivalent to a matrix-matrix product,
-        # return specialized Matmul Op to avoid unnecessary new Ops.
-        return matmul(batched_x, batched_y).owner
-    else:
-        return vectorize_node_fallback(op, node, batched_x, batched_y)
+    old_x_ndim = old_x.type.ndim
+    old_y_ndim = old_y.type.ndim
+    match (old_x_ndim, old_y_ndim):
+        case (1, 1):
+            batch_op = _inner_prod
+        case (2, 1):
+            batch_op = _matrix_vec_prod
+        case (1, 2):
+            batch_op = _vec_matrix_prod
+        case (2, 2):
+            batch_op = _matrix_matrix_matmul
+        case _:
+            raise ValueError(
+                f"Core dot Op should have 1D or 2D inputs, got {old_x_ndim}D and {old_y_ndim}D."
+            )
+    return batch_op(batched_x, batched_y).owner
 
 
 def nan_to_num(x, nan=0.0, posinf=None, neginf=None):

pytensor/tensor/rewriting/math.py

@@ -44,6 +44,11 @@
     Prod,
     Sum,
     _conj,
+    _dot,
+    _inner_prod,
+    _matrix_matrix_matmul,
+    _matrix_vec_prod,
+    _vec_matrix_prod,
     add,
     digamma,
     dot,
@@ -242,6 +247,66 @@ def local_batched_matmul_to_core_matmul(fgraph, node):
     return None
 
 
+@register_canonicalize
+@register_specialize
+@node_rewriter(
+    [_dot, _inner_prod, _matrix_vec_prod, _vec_matrix_prod, _matrix_matrix_matmul]
+)
+def local_dot_to_mul(fgraph, node):
+    """Rewrite dots that correspond to multiplication without summation."""
+    a, b = node.inputs
+    a_st_shape = a.type.shape
+    b_st_shape = b.type.shape
+    if isinstance(node.op, Dot):
+        core_a_ndim = a.type.ndim
+        core_b_ndim = b.type.ndim
+    else:
+        # Blockwise variants of Dot
+        core_a_ndim = len(node.op.inputs_sig[0])
+        core_b_ndim = len(node.op.inputs_sig[1])
+
+    if core_a_ndim > 2 or core_b_ndim > 2:
+        # Shouldn't happen, but here just in case
+        return None
+
+    if core_b_ndim == 1:
+        if a_st_shape[-1] == 1 or b_st_shape[-1] == 1:
+            if core_a_ndim == 1:
+                # inner product: (..., 1) * (..., 1) -> (...)
+                # just squeeze the last dimensions of a and b
+                new_a = a.squeeze(-1)
+                new_b = b.squeeze(-1)
+            else:
+                # matrix vector product: (..., m, 1) * (..., 1) -> (..., m)
+                # the last dimension b is already aligned for the elemwise multiplication
+                # after we squeeze the last dimension of a
+                new_a = a.squeeze(-1)
+                new_b = b
+        else:
+            return None
+
+    else:
+        if a_st_shape[-1] == 1 or b_st_shape[-2] == 1:
+            if core_a_ndim == 1:
+                # vector_matrix product: (..., 1) * (..., 1, n) -> (..., n)
+                # the last dimension of a is already aligned for the elemwise multiplication
+                # after we squeeze the one to last dimension of b
+                new_a = a
+                new_b = b.squeeze(-2)
+            else:
+                # matrix matrix product: (..., m, 1) * (..., 1, n) -> (..., m, n)
+                # the dimensions of a and b are already aligned for the elemwise multiplication
+                new_a = a
+                new_b = b
+        else:
+            return None
+
+    new_a = copy_stack_trace(a, new_a)
+    new_b = copy_stack_trace(b, new_b)
+    new_out = copy_stack_trace(node.out, mul(new_a, new_b))
+    return [new_out]
+
+
 def is_inverse_pair(node_op, prev_op, inv_pair):
     """
     Given two consecutive operations, check if they are the

tests/compile/test_profiling.py

@@ -6,7 +6,7 @@
 import numpy as np
 
 import pytensor.tensor as pt
-from pytensor.compile import ProfileStats
+from pytensor.compile import ProfileStats, get_mode
 from pytensor.compile.function import function
 from pytensor.configdefaults import config
 from pytensor.ifelse import ifelse
@@ -28,7 +28,10 @@ def test_profiling(self):
             x = [fvector(f"val{i}") for i in range(3)]
 
             z = []
-            z += [pt.outer(x[i], x[i + 1]).sum(axis=1) for i in range(len(x) - 1)]
+            z += [
+                pt.dot(x[i][:, None], x[i + 1][None, :]).sum(axis=1)
+                for i in range(len(x) - 1)
+            ]
             z += [x[i] + x[i + 1] for i in range(len(x) - 1)]
 
             p = ProfileStats(False, gpu_checks=False)
@@ -38,6 +41,9 @@ def test_profiling(self):
             else:
                 m = None
 
+            # This test requires an unoptimized outer mul written as a dot
+            m = get_mode(m).excluding("local_dot_to_mul")
+
             f = function(x, z, profile=p, name="test_profiling", mode=m)
 
             inp = [np.arange(1024, dtype="float32") + 1 for i in range(len(x))]

tests/tensor/rewriting/test_math.py

@@ -16,7 +16,8 @@
 from pytensor.compile.mode import Mode, get_default_mode, get_mode
 from pytensor.compile.ops import DeepCopyOp, deep_copy_op
 from pytensor.configdefaults import config
-from pytensor.graph.basic import Apply, equal_computations
+from pytensor.graph import vectorize_graph
+from pytensor.graph.basic import Apply, ancestors, equal_computations
 from pytensor.graph.fg import FunctionGraph
 from pytensor.graph.rewriting.basic import (
     SequentialNodeRewriter,
@@ -4571,3 +4572,51 @@ def test_log_kv_stabilization():
         out.eval({x: 1000.0}, mode=mode),
         -1003.2180912984705,
     )
+
+
+@pytest.mark.parametrize(
+    "a_shape,b_shape",
+    [
+        ((1,), (1,)),
+        ((3, 1), (1,)),
+        ((1,), (1, 3)),
+        ((3, 1), (1, 3)),
+    ],
+)
+@pytest.mark.parametrize("batched", (False, True))
+def test_local_dot_to_mul(batched, a_shape, b_shape):
+    a = tensor("a", shape=a_shape)
+    b = tensor("b", shape=b_shape)
+
+    out = dot(a, b)
+    if batched:
+        batch_a = tensor("batch_a", shape=(1, 5, *a_shape))
+        batch_b = tensor("batch_b", shape=(7, 1, *b_shape))
+        out = vectorize_graph(out, {a: batch_a, b: batch_b})
+        a = batch_a
+        b = batch_b
+
+    assert (
+        sum(
+            isinstance(var.owner.op, (Blockwise | Dot))
+            for var in ancestors([out])
+            if var.owner
+        )
+        == 1
+    )
+
+    rewritten_out = rewrite_graph(out)
+    assert rewritten_out.type.shape == out.type.shape
+    assert not any(
+        isinstance(var.owner.op, (Blockwise | Dot))
+        for var in ancestors([rewritten_out])
+        if var.owner
+    )
+
+    a_test = np.random.normal(size=a.type.shape)
+    b_test = np.random.normal(size=b.type.shape)
+    test_mode = Mode(linker="py", optimizer=None)
+    np.testing.assert_allclose(
+        out.eval({a: a_test, b: b_test}, mode=test_mode),
+        rewritten_out.eval({a: a_test, b: b_test}, mode=test_mode),
+    )

tests/tensor/test_basic.py

@@ -770,9 +770,9 @@ def test_alloc_constant_folding(self):
             self.allocs,
             [
                 # IncSubtensor1
-                (some_matrix[:60], 2),
+                (some_matrix[:60], 1),
                 # AdvancedIncSubtensor1
-                (some_matrix[arange(60)], 2),
+                (some_matrix[arange(60)], 1),
                 # AdvancedIncSubtensor
                 (some_matrix[idx, idx], 1),
             ],

tests/tensor/test_blas.py

@@ -1723,7 +1723,7 @@ class TestGer(unittest_tools.OptimizationTestMixin):
 
     def setup_method(self):
         self.mode = pytensor.compile.get_default_mode().including("fast_run")
-        self.mode = self.mode.excluding("c_blas", "scipy_blas")
+        self.mode = self.mode.excluding("c_blas", "scipy_blas", "local_dot_to_mul")
         dtype = self.dtype = "float64"  # optimization isn't dtype-dependent
         self.A = tensor(dtype=dtype, shape=(None, None))
         self.a = tensor(dtype=dtype, shape=())
@@ -1795,7 +1795,11 @@ def test_b_nonconst_does_not_triggers_ger(self):
 
     def test_outer(self):
         rng = np.random.default_rng(unittest_tools.fetch_seed())
-        f = self.function([self.x, self.y], outer(self.x, self.y))
+        f = self.function(
+            [self.x, self.y],
+            # Old outer used to be written like this
+            pt.dot(self.x[:, None], self.y[None, :]),
+        )
         self.assertFunctionContains(f, self.ger_destructive)
         f(
             rng.random(5).astype(self.dtype),