Add rewrite to lift linear algebra through certain linalg ops

Author: jessegrabowski

pytensor/compile/builders.py

@@ -7,7 +7,7 @@
 from typing import cast
 
 import pytensor.tensor as pt
-from pytensor import function
+from pytensor.compile.function import function
 from pytensor.compile.function.pfunc import rebuild_collect_shared
 from pytensor.compile.mode import optdb
 from pytensor.compile.sharedvalue import SharedVariable

pytensor/tensor/nlinalg.py

@@ -7,6 +7,7 @@
 from numpy.core.numeric import normalize_axis_tuple  # type: ignore
 
 from pytensor import scalar as ps
+from pytensor.compile.builders import OpFromGraph
 from pytensor.gradient import DisconnectedType
 from pytensor.graph.basic import Apply
 from pytensor.graph.op import Op
@@ -614,7 +615,7 @@ def svd(a, full_matrices: bool = True, compute_uv: bool = True):
 
     Returns
     -------
-    U, V,  D : matrices
+    U, V, D : matrices
 
     """
     return Blockwise(SVD(full_matrices, compute_uv))(a)
@@ -1011,6 +1012,12 @@ def tensorsolve(a, b, axes=None):
     return TensorSolve(axes)(a, b)
 
 
+class KroneckerProduct(OpFromGraph):
+    """
+    Wrapper Op for Kronecker graphs
+    """
+
+
 def kron(a, b):
     """Kronecker product.
 
@@ -1042,7 +1049,8 @@ def kron(a, b):
     out_shape = tuple(a.shape * b.shape)
     output_out_of_shape = a_reshaped * b_reshaped
     output_reshaped = output_out_of_shape.reshape(out_shape)
-    return output_reshaped
+
+    return KroneckerProduct(inputs=[a, b], outputs=[output_reshaped])(a, b)
 
 
 __all__ = [

pytensor/tensor/rewriting/linalg.py

@@ -1,22 +1,35 @@
 import logging
+from collections.abc import Callable
 from typing import cast
 
+from pytensor import Variable
+from pytensor.graph import Apply, FunctionGraph
 from pytensor.graph.rewriting.basic import copy_stack_trace, node_rewriter
 from pytensor.tensor.basic import TensorVariable, diagonal
 from pytensor.tensor.blas import Dot22
 from pytensor.tensor.blockwise import Blockwise
 from pytensor.tensor.elemwise import DimShuffle
 from pytensor.tensor.math import Dot, Prod, _matrix_matrix_matmul, log, prod
-from pytensor.tensor.nlinalg import MatrixInverse, det
+from pytensor.tensor.nlinalg import (
+    KroneckerProduct,
+    MatrixInverse,
+    MatrixPinv,
+    det,
+    inv,
+    kron,
+    pinv,
+)
 from pytensor.tensor.rewriting.basic import (
     register_canonicalize,
     register_specialize,
     register_stabilize,
 )
 from pytensor.tensor.slinalg import (
+    BlockDiagonal,
     Cholesky,
     Solve,
     SolveBase,
+    block_diag,
     cholesky,
     solve,
     solve_triangular,
@@ -305,3 +318,62 @@ def local_log_prod_sqr(fgraph, node):
 
         # TODO: have a reduction like prod and sum that simply
         # returns the sign of the prod multiplication.
+
+
+@register_specialize
+@node_rewriter([Blockwise])
+def local_lift_through_linalg(
+    fgraph: FunctionGraph, node: Apply
+) -> list[Variable] | None:
+    """
+    Rewrite compositions of linear algebra operations by lifting expensive operations (Cholesky, Inverse) through Ops
+    that join matrices (KroneckerProduct, BlockDiagonal).
+
+    This rewrite takes advantage of commutation between certain linear algebra operations to do several smaller matrix
+    operations on component matrices instead of one large one. For example, when taking the inverse of Kronecker
+    product, we can take the inverse of each component matrix and then take the Kronecker product of the inverses. This
+    reduces the cost of the inverse from O((n*m)^3) to O(n^3 + m^3) where n and m are the dimensions of the component
+    matrices.
+
+    Parameters
+    ----------
+    fgraph: FunctionGraph
+        Function graph being optimized
+    node: Apply
+        Node of the function graph to be optimized
+
+    Returns
+    -------
+    list of Variable, optional
+        List of optimized variables, or None if no optimization was performed
+    """
+
+    # TODO: Simplify this if we end up Blockwising KroneckerProduct
+    if isinstance(node.op.core_op, MatrixInverse | Cholesky | MatrixPinv):
+        y = node.inputs[0]
+        outer_op = node.op
+
+        if y.owner and (
+            isinstance(y.owner.op, Blockwise)
+            and isinstance(y.owner.op.core_op, BlockDiagonal)
+            or isinstance(y.owner.op, KroneckerProduct)
+        ):
+            input_matrices = y.owner.inputs
+
+            if isinstance(outer_op.core_op, MatrixInverse):
+                outer_f = cast(Callable, inv)
+            elif isinstance(outer_op.core_op, Cholesky):
+                outer_f = cast(Callable, cholesky)
+            elif isinstance(outer_op.core_op, MatrixPinv):
+                outer_f = cast(Callable, pinv)
+            else:
+                raise NotImplementedError  # pragma: no cover
+
+            inner_matrices = [cast(TensorVariable, outer_f(m)) for m in input_matrices]
+
+            if isinstance(y.owner.op, KroneckerProduct):
+                return [kron(*inner_matrices)]
+            elif isinstance(y.owner.op.core_op, BlockDiagonal):
+                return [block_diag(*inner_matrices)]
+            else:
+                raise NotImplementedError  # pragma: no cover

tests/tensor/rewriting/test_linalg.py

@@ -14,9 +14,16 @@
 from pytensor.tensor.blockwise import Blockwise
 from pytensor.tensor.elemwise import DimShuffle
 from pytensor.tensor.math import _allclose, dot, matmul
-from pytensor.tensor.nlinalg import Det, MatrixInverse, matrix_inverse
+from pytensor.tensor.nlinalg import (
+    Det,
+    KroneckerProduct,
+    MatrixInverse,
+    MatrixPinv,
+    matrix_inverse,
+)
 from pytensor.tensor.rewriting.linalg import inv_as_solve
 from pytensor.tensor.slinalg import (
+    BlockDiagonal,
     Cholesky,
     Solve,
     SolveBase,
@@ -333,3 +340,53 @@ def test_invalid_batched_a(self):
             ref_fn(test_a, test_b),
             rtol=1e-7 if config.floatX == "float64" else 1e-5,
         )
+
+
+@pytest.mark.parametrize(
+    "constructor", [pt.dmatrix, pt.tensor3], ids=["not_batched", "batched"]
+)
+@pytest.mark.parametrize(
+    "f_op, f",
+    [
+        (MatrixInverse, pt.linalg.inv),
+        (Cholesky, pt.linalg.cholesky),
+        (MatrixPinv, pt.linalg.pinv),
+    ],
+    ids=["inv", "cholesky", "pinv"],
+)
+@pytest.mark.parametrize(
+    "g_op, g",
+    [(BlockDiagonal, pt.linalg.block_diag), (KroneckerProduct, pt.linalg.kron)],
+    ids=["block_diag", "kron"],
+)
+def test_local_lift_through_linalg(constructor, f_op, f, g_op, g):
+    if pytensor.config.floatX.endswith("32"):
+        pytest.skip("Test is flaky at half precision")
+
+    A, B = list(map(constructor, "ab"))
+    X = f(g(A, B))
+
+    f1 = pytensor.function(
+        [A, B], X, mode=get_default_mode().including("local_lift_through_linalg")
+    )
+    f2 = pytensor.function(
+        [A, B], X, mode=get_default_mode().excluding("local_lift_through_linalg")
+    )
+
+    all_apply_nodes = f1.maker.fgraph.apply_nodes
+    f_ops = [
+        x for x in all_apply_nodes if isinstance(getattr(x.op, "core_op", x.op), f_op)
+    ]
+    g_ops = [
+        x for x in all_apply_nodes if isinstance(getattr(x.op, "core_op", x.op), g_op)
+    ]
+
+    assert len(f_ops) == 2
+    assert len(g_ops) == 1
+
+    test_vals = [
+        np.random.normal(size=(3,) * A.ndim).astype(config.floatX) for _ in range(2)
+    ]
+    test_vals = [x @ np.swapaxes(x, -1, -2) for x in test_vals]
+
+    np.testing.assert_allclose(f1(*test_vals), f2(*test_vals), atol=1e-8)

tests/tensor/test_nlinalg.py

@@ -590,6 +590,14 @@ def setup_method(self):
         self.op = kron
         super().setup_method()
 
+    def test_vec_vec_kron_raises(self):
+        x = vector()
+        y = vector()
+        with pytest.raises(
+            TypeError, match="kron: inputs dimensions must sum to 3 or more"
+        ):
+            kron(x, y)
+
     @pytest.mark.parametrize("shp0", [(2,), (2, 3), (2, 3, 4), (2, 3, 4, 5)])
     @pytest.mark.parametrize("shp1", [(6,), (6, 7), (6, 7, 8), (6, 7, 8, 9)])
     def test_perform(self, shp0, shp1):