Optimize while scans when only last state is needed

pytensor/scan/op.py

@@ -1182,7 +1182,7 @@ class Scan(Op, ScanMethodsMixin, HasInnerGraph):
         # these are states that do not feed anything back in the recurrent
         # computation, and hence they do not have an initial state. The scan
         # node however receives an input for each such argument, the input
-        # in this case is just a int saying how many steps of this output we
+        # in this case is just an int saying how many steps of this output we
         # need to store. This input does not have the same dtype, nor is it the same
         # type of tensor as the output, it is always a scalar int.
         new_inputs += [as_tensor_variable(ons) for ons in self.outer_nitsot(inputs)]

pytensor/scan/rewriting.py

@@ -28,10 +28,18 @@ from pytensor.graph.features import ReplaceValidate
 from pytensor.graph.fg import FunctionGraph
 from pytensor.graph.op import compute_test_value
 from pytensor.graph.replace import clone_replace
-from pytensor.graph.rewriting.basic import GraphRewriter, in2out, node_rewriter
+from pytensor.graph.rewriting.basic import (
+    GraphRewriter,
+    copy_stack_trace,
+    in2out,
+    node_rewriter,
+)
 from pytensor.graph.rewriting.db import EquilibriumDB, SequenceDB
+from pytensor.graph.rewriting.utils import get_clients_at_depth
 from pytensor.graph.type import HasShape
 from pytensor.graph.utils import InconsistencyError
+from pytensor.raise_op import Assert
+from pytensor.scalar import ScalarConstant
 from pytensor.scan.op import Scan, ScanInfo
 from pytensor.scan.utils import (
     ScanArgs,
@@ -1103,6 +1111,71 @@ def sanitize(x):
         return at.as_tensor_variable(x)
 
 
+@node_rewriter([Scan])
+def while_scan_merge_subtensor_last_element(fgraph, scan_node):
+    """
+    Replace while_scan_out[abs(min(tap)):][-1] by while_scan_out[-1], for
+    recurring outputs, asserting that at least one step occurs.
+    Only the first step can be ensured by the inputs alone (i.e., `n_steps > 0`),
+    as the while scan could abort earlier anytime after that. This means it is
+    not possible to replace while_scan_out[abs(min(tap)):][-i]
+    by while_scan_out[-i], for -i != -1.
+    """
+    op = scan_node.op
+
+    if not op.info.as_while:
+        return None
+
+    # Optimization is not implemented form mit-mot
+    recurrent_outputs = op.outer_mitsot_outs(scan_node.outputs) + op.outer_sitsot_outs(
+        scan_node.outputs
+    )
+    recurrent_outputs_taps_slices = (
+        op.info.mit_sot_in_slices + op.info.sit_sot_in_slices
+    )
+
+    n_steps = scan_node.inputs[0]
+    non_zero_steps_cond = n_steps > 0
+    assert_non_zero_steps_op = Assert("n_steps > 0")
+
+    subtensor_merge_replacements = {}
+
+    # Iterate over all nodes that are two computations below the while scan
+    for node2 in get_clients_at_depth(fgraph, scan_node, depth=2):
+        if not isinstance(node2.op, Subtensor):
+            continue
+
+        node1 = node2.inputs[0].owner
+        if not (node1 and isinstance(node1.op, Subtensor)):
+            continue
+
+        x = node1.inputs[0]
+        if x not in recurrent_outputs:
+            continue
+
+        slice1 = get_idx_list(node1.inputs, node1.op.idx_list)
+        slice2 = get_idx_list(node2.inputs, node2.op.idx_list)
+
+        min_tap = abs(min(recurrent_outputs_taps_slices[recurrent_outputs.index(x)]))
+
+        if (
+            len(slice1) == 1
+            and isinstance(slice1[0], slice)
+            and isinstance(slice1[0].start, aes.ScalarConstant)
+            and slice1[0].start.data == min_tap
+            and slice1[0].stop is None
+            and slice1[0].step is None
+            and len(slice2) == 1
+            and isinstance(slice2[0], aes.ScalarConstant)
+            and slice2[0].data == -1
+        ):
+            out = assert_non_zero_steps_op(x[-1], non_zero_steps_cond)
+            copy_stack_trace([node2.outputs[0], node2.inputs[0]], out)
+            subtensor_merge_replacements[node2.outputs[0]] = out
+
+    return subtensor_merge_replacements
+
+
 @node_rewriter([Scan])
 def save_mem_new_scan(fgraph, node):
     r"""Graph optimizer that reduces scan memory consumption.
@@ -1124,6 +1197,17 @@ def save_mem_new_scan(fgraph, node):
     that SITSOT output. Only the most recently computed timestep ever needs to
     be kept in memory.
 
+    There are two ways in which the Scan buffer size is controlled:
+    1. Each recurring output is saved in an input empty tensor x with the initial
+    state written at x[:abs(min(taps))]. The remaining x[abs(min(taps)):]
+    positions determine how many intermediate results should be stored.
+    This rewrite shortens x[abs(min(taps)):] to the smallest possible size.
+    2. Each non-recurrent output (nit-sot) is associated with a scalar integer
+    input that determines how many steps should be saved in the perform method.
+    This rewrite reduces this number to the smallest possible.
+
+    The scan perform implementation takes the output sizes into consideration,
+    saving the newest results over the oldest ones whenever the buffer is filled.
     """
     if not isinstance(node.op, Scan):
         return False
@@ -1172,13 +1256,16 @@ def save_mem_new_scan(fgraph, node):
     # index(step) for any output scan actually needs to compute
     # In other words n_steps should be equal to this maximal !
     # Note: if we have a shared variable that gets updated at every step
-    # of the loop, reducing the number of steps will affect the the
-    # value of the shared variable after the loop so we need not to
+    # of the loop, reducing the number of steps will affect the
+    # value of the shared variable after the loop so we cannot
     # change the number of steps in that case. To do this we set
     # global_nsteps to None which is seen as a flag that nothing needs
-    # to be done
+    # to be done.
+    # Note: For simplicity while Scans also have global_nsteps set to None.
+    #  All step optimizations require knowing the shape of the output, which
+    #  cannot be determined from the inputs alone.
     assert len(node.outputs) >= c_outs
-    if len(node.outputs) == c_outs:
+    if len(node.outputs) == c_outs and not op.info.as_while:
         global_nsteps = {"real": -1, "sym": []}
     else:
         global_nsteps = None
@@ -1257,7 +1344,7 @@ def save_mem_new_scan(fgraph, node):
                 else:
                     # there is a **gotcha** here ! Namely, scan returns an
                     # array that contains the initial state of the output
-                    # as well. Which means that if have a initial state of
+                    # as well. Which means that if y has an initial state of
                     # length 3, and you look for 5 steps you get an output
                     # y of length 8. If you only use y[:5], this does not
                     # mean that you only need to loop for 5 steps but
@@ -1285,9 +1372,9 @@ def save_mem_new_scan(fgraph, node):
 
     # 2.3. Analyze global_nsteps to figure out for how many steps scan
     # needs to iterate
-    if global_nsteps is not None:
+    if global_nsteps is None:
         nw_steps = node.inputs[0]
-
+    else:
         # there are some symbolic tensors that limit the number of
         # steps
         if len(global_nsteps["sym"]) == 0:
@@ -1303,6 +1390,7 @@ def save_mem_new_scan(fgraph, node):
             real_steps = None
         nw_steps = select_min(select_max(sym_steps, real_steps), node.inputs[0])
 
+        # FIXME: This is not correct. Scan with 0 steps seems to be supported
         # Make sure the ScanSaveMem optimization never makes the new
         # number of steps to be 0 (this could happen, for instance, if
         # the optimization detects that the outputs of the Scan go through
@@ -1310,9 +1398,6 @@ def save_mem_new_scan(fgraph, node):
         # 0 iterations are not supported. Make sure the new number of steps
         # is at least 1.
         nw_steps = select_max(nw_steps, 1)
-    else:
-        nw_steps = node.inputs[0]
-        global_nsteps = None
 
     # 2.4 Loop over the clients again now looking just to see how many
     # intermediate steps to store
@@ -1335,19 +1420,33 @@ def save_mem_new_scan(fgraph, node):
                     store_steps[i] = 0
                     break
 
-                if i > op_info.n_mit_mot:
-                    length = node.inputs[0] + init_l[i]
+                # Special case for recurrent outputs where only the last result
+                # is requested. This is needed for this rewrite to apply to
+                # do-while Scans at all. Otherwise, `get_canonical_form_slice` in
+                # the `else` branch would reintroduce a shape dependency on the
+                # original Scan which would lead this rewrite to abort in the end.
+                if (
+                    i <= op.info.n_mit_mot
+                    and isinstance(this_slice[0], ScalarConstant)
+                    and this_slice[0].value == -1
+                ):
+                    start = nw_steps - 1
                 else:
-                    try:
-                        length = shape_of[out][0]
-                    except KeyError:
-                        length = out.shape[0]
-                cf_slice = get_canonical_form_slice(this_slice[0], length)
+                    if i <= op.info.n_mit_mot:
+                        try:
+                            length = shape_of[out][0]
+                        except KeyError:
+                            length = out.shape[0]
+                    else:
+                        length = node.inputs[0] + init_l[i]
+
+                    cf_slice = get_canonical_form_slice(this_slice[0], length)
+
+                    if isinstance(cf_slice[0], slice):
+                        start = at.extract_constant(cf_slice[0].start)
+                    else:
+                        start = at.extract_constant(cf_slice[0])
 
-                if isinstance(cf_slice[0], slice):
-                    start = at.extract_constant(cf_slice[0].start)
-                else:
-                    start = at.extract_constant(cf_slice[0])
                 if start == 0 or store_steps[i] == 0:
                     store_steps[i] = 0
                 else:
@@ -1498,6 +1597,7 @@ def save_mem_new_scan(fgraph, node):
                             nw_input = expand_empty(_nw_input, nw_steps)
                             nw_inputs[in_idx] = nw_input
                         else:
+                            # FIXME: This is never used
                             nw_input = nw_inputs[in_idx][: (initl + nw_steps)]
 
                     elif (
@@ -1554,8 +1654,8 @@ def save_mem_new_scan(fgraph, node):
                         )
                     else:
                         fslice = sanitize(cnf_slice[0])
-
                     nw_slice = (fslice,) + tuple(old_slices[1:])
+
                     nw_pos = inv_compress_map[idx]
 
                     subtens = Subtensor(nw_slice)
@@ -1604,9 +1704,16 @@ def save_mem_new_scan(fgraph, node):
                         ) + tuple(old_slices[1:])
 
                     else:
-                        position = (
-                            cnf_slice[0] - nw_steps - init_l[pos] + store_steps[pos]
-                        )
+                        # Special case when only last value is requested
+                        if (
+                            isinstance(old_slices[0], ScalarConstant)
+                            and old_slices[0].value == -1
+                        ):
+                            position = old_slices[0]
+                        else:
+                            position = (
+                                cnf_slice[0] - nw_steps - init_l[pos] + store_steps[pos]
+                            )
 
                         nw_slice = (sanitize(position),) + tuple(old_slices[1:])
                     subtens = Subtensor(nw_slice)
@@ -2403,6 +2510,12 @@ scan_seqopt1.register(
     position=5,
 )
 
+scan_eqopt2.register(
+    "while_scan_merge_subtensor_last_element",
+    in2out(while_scan_merge_subtensor_last_element, ignore_newtrees=True),
+    "fast_run",
+    "scan",
+)
 
 scan_eqopt2.register(
     "constant_folding_for_scan2",

pytensor/tensor/rewriting/subtensor.py

@@ -479,6 +479,7 @@ def local_subtensor_merge(fgraph, node):
     expresses all slices in a canonical form, and then merges them together.
 
     """
+    from pytensor.scan.op import Scan
 
     if isinstance(node.op, Subtensor):
         u = node.inputs[0]
@@ -489,6 +490,16 @@ def local_subtensor_merge(fgraph, node):
             # slices of the first applied subtensor
             slices1 = get_idx_list(u.owner.inputs, u.owner.op.idx_list)
             slices2 = get_idx_list(node.inputs, node.op.idx_list)
+
+            # Don't try to do the optimization on do-while scan outputs,
+            # as it will create a dependency on the shape of the outputs
+            if (
+                x.owner is not None
+                and isinstance(x.owner.op, Scan)
+                and x.owner.op.info.as_while
+            ):
+                return None
+
             # Get the shapes of the vectors !
             try:
                 # try not to introduce new shape into the graph

tests/scan/test_rewriting.py

@@ -1395,6 +1395,98 @@ class TestSaveMem:
         rng = np.random.default_rng(utt.fetch_seed())
         my_f(rng.uniform(size=(3,)), 4, np.int64([2, 2, 3]))
 
+    def test_while_scan_taps(self):
+        n_steps = scalar("n_steps", dtype="int64")
+        x0 = vector("x0")
+
+        ys, _ = pytensor.scan(
+            # Fibonacci Sequence
+            lambda xtm2, xtm1: (xtm1 + xtm2, {}, until(xtm1 >= 34)),
+            outputs_info=[{"initial": x0, "taps": [-2, -1]}],
+            n_steps=n_steps,
+        )
+        # Save memory is triggered by choosing only last value
+        y = ys[-1]
+
+        f = pytensor.function(
+            [n_steps, x0], y, mode=get_default_mode().including("scan")
+        )
+
+        np.testing.assert_equal(f(n_steps=1000, x0=[1, 1]), 55)
+        np.testing.assert_equal(f(n_steps=1, x0=[1, 1]), 2)
+        with pytest.raises(AssertionError, match="n_steps > 0"):
+            f(n_steps=0, x0=[1, 1])
+
+        # ys_trace is an Alloc that controls the size of the inner buffer,
+        # it should have shape[0] == 3, with two entries for the taps and one
+        # entry for the intermediate output
+        [scan_node] = (n for n in f.maker.fgraph.apply_nodes if isinstance(n.op, Scan))
+        _, ys_trace = scan_node.inputs
+        debug_fn = pytensor.function(
+            [n_steps, x0], ys_trace.shape[0], accept_inplace=True
+        )
+        assert debug_fn(n_steps=1000, x0=[1, 1]) == 3
+
+    def test_while_scan_map(self):
+        xs = vector("xs")
+        ys, _ = pytensor.scan(
+            lambda x: (x + 1, {}, until(x + 1 >= 10)),
+            outputs_info=[None],
+            sequences=[xs],
+        )
+        # Save memory is triggered by choosing only last value
+        y = ys[-1]
+
+        f = pytensor.function([xs], y, mode=get_default_mode().including("scan"))
+        np.testing.assert_equal(f(xs=np.arange(100, dtype=config.floatX)), 10)
+        np.testing.assert_equal(f(xs=[0]), 1)
+        with pytest.raises(IndexError):
+            f(xs=[])
+
+        # len_ys is a numerical input that controls the shape of the inner buffer
+        # It should be 1, as only the last output is needed
+        [scan_node] = (n for n in f.maker.fgraph.apply_nodes if isinstance(n.op, Scan))
+        _, _, len_ys = scan_node.inputs
+        debug_fn = pytensor.function([xs], len_ys, accept_inplace=True)
+        assert debug_fn(xs=np.zeros((100,), dtype=config.floatX)) == 1
+
+    def test_while_scan_taps_and_map(self):
+        x0 = scalar("x0")
+        seq = vector("seq")
+        n_steps = scalar("n_steps", dtype="int64")
+
+        # while loop
+        [ys, zs], _ = pytensor.scan(
+            lambda s, xtm1: ((xtm1 + 1, xtm1 + 1 + s), {}, until(xtm1 >= 99)),
+            sequences=[seq],
+            outputs_info=[x0, None],
+            n_steps=n_steps,
+        )
+        # Save memory is triggered by choosing only last value
+        y = ys[-1]
+        z = zs[-1]
+
+        f = pytensor.function(
+            [x0, seq, n_steps], [y, z], mode=get_default_mode().including("scan")
+        )
+        test_seq = np.zeros(200, dtype=config.floatX)
+        np.testing.assert_allclose(f(x0=0, seq=test_seq, n_steps=200), 100)
+        np.testing.assert_allclose(f(x0=1, seq=test_seq, n_steps=20), 21)
+        np.testing.assert_allclose(f(x0=np.e, seq=test_seq, n_steps=1), np.e + 1)
+        with pytest.raises(AssertionError, match="n_steps > 0"):
+            f(x0=0, seq=test_seq, n_steps=0)
+
+        # Evaluate the shape of ys_trace and len_zs to confirm the rewrite worked correctly.
+        # If a MissingInputError is raised, it means the rewrite failed
+        [scan_node] = (n for n in f.maker.fgraph.apply_nodes if isinstance(n.op, Scan))
+        _, _, ys_trace, len_zs = scan_node.inputs
+        debug_fn = pytensor.function(
+            [n_steps], [ys_trace.shape[0], len_zs], accept_inplace=True
+        )
+        stored_ys_steps, stored_zs_steps = debug_fn(n_steps=200)
+        assert stored_ys_steps == 2
+        assert stored_zs_steps == 1
+
 
 def test_inner_replace_dot():
     """