Do not try to save initial values buffer size in Scan

pytensor/scan/rewriting.py

@@ -1420,9 +1420,18 @@ def scan_save_mem(fgraph, node):
                     store_steps[i] = 0
                     break
 
-                if isinstance(this_slice[0], slice) and this_slice[0].start is None:
-                    store_steps[i] = 0
-                    break
+                if isinstance(this_slice[0], slice):
+                    start = this_slice[0].start
+                    if isinstance(start, Constant):
+                        start = start.data
+                    # Don't do anything if the subtensor is starting from the beginning of the buffer
+                    # Or just skipping the initial values (default output returned to the user).
+                    # Trimming the initial values would require a roll to align the buffer once scan is done
+                    # As it always starts writing at position [0+max(taps)], and ends up at position [:max(taps)]
+                    # It's cheaper to just keep the initial values in the buffer and slice them away (default output)
+                    if start in (0, None, init_l[i]):
+                        store_steps[i] = 0
+                        break
 
                 # Special case for recurrent outputs where only the last result
                 # is requested. This is needed for this rewrite to apply to

tests/link/numba/test_scan.py

@@ -474,7 +474,7 @@ class TestScanSITSOTBuffer:
             expected_buffer_size = 3
         elif buffer_size == "whole":
             xs_kept = xs  # What users think is the whole buffer
-            expected_buffer_size = n_steps - 1
+            expected_buffer_size = n_steps
         elif buffer_size == "whole+init":
             xs_kept = xs.owner.inputs[0]  # Whole buffer actually used by Scan
             expected_buffer_size = n_steps

tests/scan/test_printing.py

@@ -643,35 +643,37 @@ def test_debugprint_compiled_fn():
     # (i.e. from `Scan._fn`)
     out = pytensor.function([M], out, updates=updates, mode="FAST_RUN")
 
-    expected_output = """Scan{scan_fn, while_loop=False, inplace=all} [id A] 2 (outer_out_sit_sot-0)
-     ├─ 20000 [id B] (n_steps)
-     ├─ [    0 ... 998 19999] [id C] (outer_in_seqs-0)
-     ├─ SetSubtensor{:stop} [id D] 1 (outer_in_sit_sot-0)
-     │  ├─ AllocEmpty{dtype='int64'} [id E] 0
-     │  │  └─ 20000 [id B]
-     │  ├─ [0] [id F]
-     │  └─ 1 [id G]
-     └─ <Tensor3(float64, shape=(20000, 2, 2))> [id H] (outer_in_non_seqs-0)
-
-    Inner graphs:
-
-    Scan{scan_fn, while_loop=False, inplace=all} [id A]
-     ← Composite{switch(lt(0, i0), 1, 0)} [id I] (inner_out_sit_sot-0)
-        └─ Subtensor{i, j, k} [id J]
-           ├─ *2-<Tensor3(float64, shape=(20000, 2, 2))> [id K] -> [id H] (inner_in_non_seqs-0)
-           ├─ ScalarFromTensor [id L]
-           │  └─ *0-<Scalar(int64, shape=())> [id M] -> [id C] (inner_in_seqs-0)
-           ├─ ScalarFromTensor [id N]
-           │  └─ *1-<Scalar(int64, shape=())> [id O] -> [id D] (inner_in_sit_sot-0)
-           └─ 0 [id P]
-
-    Composite{switch(lt(0, i0), 1, 0)} [id I]
-     ← Switch [id Q] 'o0'
-        ├─ LT [id R]
-        │  ├─ 0 [id S]
-        │  └─ i0 [id T]
-        ├─ 1 [id U]
-        └─ 0 [id S]
+    expected_output = """Subtensor{start:} [id A] 3
+ ├─ Scan{scan_fn, while_loop=False, inplace=all} [id B] 2 (outer_out_sit_sot-0)
+ │  ├─ 20000 [id C] (n_steps)
+ │  ├─ [    0 ... 998 19999] [id D] (outer_in_seqs-0)
+ │  ├─ SetSubtensor{:stop} [id E] 1 (outer_in_sit_sot-0)
+ │  │  ├─ AllocEmpty{dtype='int64'} [id F] 0
+ │  │  │  └─ 20001 [id G]
+ │  │  ├─ [0] [id H]
+ │  │  └─ 1 [id I]
+ │  └─ <Tensor3(float64, shape=(20000, 2, 2))> [id J] (outer_in_non_seqs-0)
+ └─ 1 [id I]
+
+Inner graphs:
+
+Scan{scan_fn, while_loop=False, inplace=all} [id B]
+ ← Composite{switch(lt(0, i0), 1, 0)} [id K] (inner_out_sit_sot-0)
+    └─ Subtensor{i, j, k} [id L]
+       ├─ *2-<Tensor3(float64, shape=(20000, 2, 2))> [id M] -> [id J] (inner_in_non_seqs-0)
+       ├─ ScalarFromTensor [id N]
+       │  └─ *0-<Scalar(int64, shape=())> [id O] -> [id D] (inner_in_seqs-0)
+       ├─ ScalarFromTensor [id P]
+       │  └─ *1-<Scalar(int64, shape=())> [id Q] -> [id E] (inner_in_sit_sot-0)
+       └─ 0 [id R]
+
+Composite{switch(lt(0, i0), 1, 0)} [id K]
+ ← Switch [id S] 'o0'
+    ├─ LT [id T]
+    │  ├─ 0 [id U]
+    │  └─ i0 [id V]
+    ├─ 1 [id W]
+    └─ 0 [id U]
     """
 
     output_str = debugprint(out, file="str", print_op_info=True)