Use stricter numerical tolerance in rewrites and allow casting in PatternNodeRewriter (#1526)

* Implemented allow_cast in PatternNodeRewriter
to allow rewrites that would otherwise fail when the new and old dtype differ.
Example:
`np.array(1., "float64") - sigmoid(x)` cannot be rewritten as
`sigmoid(-x)` (where x is an fmatrix) because the type would change.
This commit allows an automatic cast to be added so the expression
is rewritten as `cast(sigmoid(-x), "float64")`.
Relevant tests added.

* Added test cases for which issue #1497 fails

* Changed PatternNodeRewriter::transform to allow types that do not contain dtype
like MyType in the tests

* Address #1497 by changing instances of np.isclose to a function isclose, which uses 10 ULPs by default

* Addressed failed tests (with older python/numpy versions)

* Addressed feedback by ricardoV94

* Test PatternNodeRewriter doesn't support multi-output nodes in pattern

But it's fine if they're just root inputs

---------

Co-authored-by: Luca Citi <lciti@ieee.org>
Co-authored-by: Ricardo Vieira <ricardo.vieira1994@gmail.com>

Author: 3 people

pytensor/graph/rewriting/basic.py

@@ -1550,6 +1550,7 @@ def __init__(
         tracks=(),
         get_nodes=None,
         values_eq_approx=None,
+        allow_cast=True,
     ):
         """
 
@@ -1572,6 +1573,10 @@ def __init__(
             If you provide `tracks`, you must provide this parameter. It must be a
             function that takes the tracked node and returns a list of nodes on
             which we will try this rewrite.
+        values_eq_approx
+            TODO
+        allow_cast
+            Automatically cast the output of the rewrite whenever new and old types differ
 
         Notes
         -----
@@ -1586,6 +1591,7 @@ def __init__(
         self.in_pattern = convert_strs_to_vars(in_pattern, var_map=var_map)
         self.out_pattern = convert_strs_to_vars(out_pattern, var_map=var_map)
         self.values_eq_approx = values_eq_approx
+        self.allow_cast = allow_cast
         if isinstance(in_pattern, list | tuple):
             self.op = self.in_pattern[0]
         elif isinstance(in_pattern, dict):
@@ -1630,6 +1636,10 @@ def transform(self, fgraph, node, get_nodes=True):
         if node.op != self.op:
             return False
 
+        if len(node.outputs) != 1:
+            # PatternNodeRewriter doesn't support replacing multi-output nodes
+            return False
+
         s = unify(self.in_pattern, node.out)
 
         if s is False:
@@ -1652,19 +1662,20 @@ def transform(self, fgraph, node, get_nodes=True):
             ):
                 return False
 
-        if ret.owner:
+        [old_out] = node.outputs
+        if not old_out.type.is_super(ret.type):
+            # Type doesn't match
             if not (
-                len(node.outputs) == len(ret.owner.outputs)
-                and all(
-                    o.type.is_super(new_o.type)
-                    for o, new_o in zip(node.outputs, ret.owner.outputs, strict=True)
-                )
+                self.allow_cast
+                and isinstance(old_out.type, pytensor.tensor.TensorType)
+                and isinstance(ret.type, pytensor.tensor.TensorType)
             ):
                 return False
-        else:
-            # ret is just an input variable
-            assert len(node.outputs) == 1
-            if not node.outputs[0].type.is_super(ret.type):
+
+            # Try to cast tensors
+            ret = ret.astype(old_out.type.dtype)
+            if not old_out.type.is_super(ret.type):
+                # Still doesn't match
                 return False
 
         return [ret]

pytensor/tensor/rewriting/math.py

@@ -2440,7 +2440,7 @@ def local_log1p(fgraph, node):
             log_arg.owner.inputs, only_process_constants=True
         )
         # scalar_inputs are potentially dimshuffled and fill'd scalars
-        if scalars and np.allclose(np.sum(scalars), 1):
+        if scalars and isclose(np.sum(scalars), 1):
             if nonconsts:
                 ninp = variadic_add(*nonconsts)
                 if ninp.dtype != log_arg.type.dtype:
@@ -3045,6 +3045,21 @@ def check_input(inputs):
     return [ret]
 
 
+def isclose(x, ref, rtol=0, atol=0, num_ulps=10):
+    """
+
+    Returns
+    -------
+    bool
+        True iff x is a constant close to ref (by default 10 ULPs).
+
+    """
+    x = np.asarray(x)
+    if np.issubdtype(x.dtype, np.floating):
+        atol = atol + num_ulps * np.abs(np.spacing(x.dtype.type(ref)))
+    return np.allclose(x, ref, rtol=rtol, atol=atol)
+
+
 def _skip_mul_1(r):
     if r.owner and r.owner.op == mul:
         not_is_1 = [i for i in r.owner.inputs if not _is_1(i)]
@@ -3063,7 +3078,7 @@ def _is_1(expr):
     """
     try:
         v = get_underlying_scalar_constant_value(expr)
-        return np.isclose(v, 1)
+        return isclose(v, 1)
     except NotScalarConstantError:
         return False
 
@@ -3124,7 +3139,7 @@ def is_1pexp(t, only_process_constants=True):
                     scal_sum = scalars[0]
                     for s in scalars[1:]:
                         scal_sum = scal_sum + s
-                    if np.allclose(scal_sum, 1):
+                    if isclose(scal_sum, 1):
                         return False, maybe_exp.owner.inputs[0]
     return None
 
@@ -3224,7 +3239,7 @@ def is_neg(var):
         for idx, mul_input in enumerate(var_node.inputs):
             try:
                 constant = get_underlying_scalar_constant_value(mul_input)
-                is_minus_1 = np.isclose(constant, -1)
+                is_minus_1 = isclose(constant, -1)
             except NotScalarConstantError:
                 is_minus_1 = False
             if is_minus_1:
@@ -3632,7 +3647,7 @@ def local_reciprocal_1_plus_exp(fgraph, node):
         # scalar_inputs are potentially dimshuffled and fill'd scalars
         if len(nonconsts) == 1:
             if nonconsts[0].owner and nonconsts[0].owner.op == exp:
-                if scalars_ and np.allclose(np.sum(scalars_), 1):
+                if scalars_ and isclose(np.sum(scalars_), 1):
                     out = [
                         alloc_like(
                             sigmoid(neg(nonconsts[0].owner.inputs[0])),

tests/graph/rewriting/test_basic.py

@@ -41,6 +41,7 @@
     op_y,
     op_z,
 )
+from tests.unittest_tools import assert_equal_computations
 
 
 class AssertNoChanges(Feature):
@@ -725,22 +726,35 @@ def test_patternsub_invalid_dtype(out_pattern):
     assert e.type.is_super(fg.outputs[0].type)
 
 
-def test_patternsub_different_output_lengths():
-    # Test that PatternNodeRewriter won't replace nodes with different numbers of outputs
-    ps = PatternNodeRewriter(
-        (op1, "x"),
-        ("x"),
+def test_patternsub_multi_output_nodes():
+    # Test that PatternNodeRewriter won't attempt to replace multi-output nodes
+    multiple_op_ps = PatternNodeRewriter(
+        (op_multiple_outputs, "x"),
+        "x",
         name="ps",
     )
-    rewriter = in2out(ps)
+
+    single_op_ps = PatternNodeRewriter(
+        (op_y, "x"),
+        "x",
+        name="ps",
+    )
+
+    rewriter = in2out(multiple_op_ps, single_op_ps)
 
     x = MyVariable("x")
     e1, e2 = op_multiple_outputs(x)
-    o = op1(e1)
+    o1, o2 = op_y(e1), op_y(e2)
+
+    fgraph = FunctionGraph(inputs=[x], outputs=[e2, e1], copy_inputs=False)
+    rewriter.rewrite(fgraph)
+    # This shouldn't rewrite because PatternNodeRewriter has no way of specifying which output(s) are being matched
+    assert_equal_computations(fgraph.outputs, [e2, e1])
 
-    fgraph = FunctionGraph(inputs=[x], outputs=[o])
+    fgraph = FunctionGraph(inputs=[x], outputs=[o2, o1], copy_inputs=False)
     rewriter.rewrite(fgraph)
-    assert fgraph.outputs[0].owner.op == op1
+    # Having a variable that comes out of a multi-output node should be fine
+    assert_equal_computations(fgraph.outputs, [e2, e1])
 
 
 class TestSequentialNodeRewriter:

tests/graph/utils.py

@@ -107,6 +107,9 @@ def make_node(self, *inputs):
 
 
 class MyOpMultipleOutputs(MyOp):
+    def __init__(self, name, dmap=None, x=None):
+        super().__init__(name=name, dmap=dmap, x=x, n_outs=2)
+
     def make_node(self, input):
         outputs = [input.type(), input.type()]
         return Apply(self, [input], outputs)

tests/tensor/rewriting/test_math.py

@@ -50,6 +50,7 @@
     bitwise_and,
     bitwise_or,
     bitwise_xor,
+    cast,
     conj,
     cosh,
     deg2rad,
@@ -124,6 +125,7 @@
     dvector,
     fmatrices,
     fmatrix,
+    fscalar,
     ftensor4,
     fvector,
     imatrices,
@@ -4069,25 +4071,36 @@ def test_exp_over_1_plus_exp(self):
 
     def test_local_1msigmoid(self):
         m = self.get_mode(excluding=["fusion", "inplace"])
-        x = fmatrix()
+        x = fscalar()
+        xd = dscalar()
 
         # Test `exp_over_1_plus_exp`
         f = pytensor.function([x], 1 - exp(x) / (1 + exp(x)), mode=m)
         # FIXME: PatternNodeRewriter does not copy stack trace
         #  (see https://github.com/Theano/Theano/issues/4581)
         # assert check_stack_trace(f, ops_to_check=[neg, sigmoid])
-        assert [node.op for node in f.maker.fgraph.toposort()] == [neg, sigmoid]
+        assert equal_computations(f.maker.fgraph.outputs, [sigmoid(-x)])
 
         # Test `inv_1_plus_exp`
         f = pytensor.function([x], 1 - pt.fill(x, 1.0) / (1 + exp(-x)), mode=m)
         # assert check_stack_trace(f, ops_to_check=[neg, sigmoid])
-        assert [node.op for node in f.maker.fgraph.toposort()] == [neg, sigmoid]
+        assert equal_computations(f.maker.fgraph.outputs, [sigmoid(-x)])
 
         # Test float constant
-        f = pytensor.function(
-            [x], np.array(1.000001, dtype="float32") - sigmoid(x), mode=m
-        )
-        assert [node.op for node in f.maker.fgraph.toposort()] == [neg, sigmoid]
+        for out, expected in [
+            (np.array(1.0, "float32") - sigmoid(x), sigmoid(-x)),
+            (np.array(1.0, "float64") - pt.sigmoid(x), cast(sigmoid(-x), "float64")),
+            (np.array(1.0, "float32") - sigmoid(xd), sigmoid(-xd)),
+            (np.array(1.0, "float64") - sigmoid(xd), sigmoid(-xd)),
+            (np.sum(1 / np.array([2, 3, 6], "float32")) - sigmoid(x), sigmoid(-x)),
+            (np.sum(1 / np.array([2, 3, 6], "float64")) - sigmoid(xd), sigmoid(-xd)),
+            (np.float32(1 - 9e-6) - sigmoid(x), np.float32(1 - 9e-6) - sigmoid(x)),
+            (np.float64(1 - 1e-9) - sigmoid(xd), np.float64(1 - 1e-9) - sigmoid(xd)),
+        ]:
+            rewritten = rewrite_graph(
+                out, include=["canonicalize", "specialize", "stabilize"]
+            )
+            utt.assert_equal_computations([rewritten], [expected], original=out)
 
     def test_local_sigm_times_exp(self):
         """
@@ -4235,7 +4248,8 @@ def test_log1msigm_to_softplus(self):
         f(np.random.random((54, 11)).astype(config.floatX))
 
         # Test close to 1
-        out = log(1.000001 - sigmoid(x))
+        x_dtype = np.dtype(x.dtype).type
+        out = log(np.nextafter(x_dtype(1), x_dtype(2)) - sigmoid(x))
         f = pytensor.function([x], out, mode=self.m)
         topo = f.maker.fgraph.toposort()
         assert len(topo) == 2

tests/unittest_tools.py

@@ -11,6 +11,7 @@
 from pytensor.compile.debugmode import str_diagnostic
 from pytensor.configdefaults import config
 from pytensor.gradient import verify_grad as orig_verify_grad
+from pytensor.graph.basic import equal_computations
 from pytensor.tensor.basic import as_tensor_variable
 from pytensor.tensor.math import _allclose
 from pytensor.tensor.math import add as pt_add
@@ -279,6 +280,41 @@ def assert_allclose(expected, value, rtol=None, atol=None):
         raise WrongValue(expected, value, rtol, atol)
 
 
+def assert_equal_computations(rewritten, expected, *args, original=None, **kwargs):
+    """
+    Assert that `rewritten` computes the same as `expected`.
+
+    Parameters
+    ----------
+    rewritten
+        The expression after the rewrite pass.
+    expected
+        The reference expression to compare against.
+    *args, **kwargs
+        Extra arguments forwarded to equal_computations.
+    original : optional
+        If given, will be printed in the error message.
+    """
+    __tracebackhide__ = True  # Hide traceback for py.test
+
+    ok = equal_computations(rewritten, expected, *args, **kwargs)
+
+    if not ok:
+        parts = []
+
+        def _dprint(expr):
+            return pytensor.dprint(expr, print_type=True, file="str")
+
+        if original is not None:
+            parts.append(f"\nOriginal:\n{_dprint(original)}")
+        parts.append(f"\nRewritten:\n{_dprint(rewritten)}")
+        parts.append(f"\nExpected:\n{_dprint(expected)}")
+
+        raise AssertionError("equal_computations failed\n" + "".join(parts))
+
+    return True
+
+
 class AttemptManyTimes:
     """Decorator for unit tests that forces a unit test to be attempted
     multiple times. The test needs to pass a certain number of times for it to