pymc-devs / pymc-devs/pytensor

Second gradient of simple Scan shows some missing simplifications

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Python
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Description

Description
import pytensor
import pytensor.tensor as pt
from pytensor.compile.mode import Mode

x0 = pt.scalar("x0")
ys, _ = pytensor.scan(
    lambda ytm1: ytm1 ** 2,
    outputs_info=[x0],
    n_steps=4,
    mode=Mode(linker="py", optimizer="fast_run").excluding("fusion"),
)
f = ys[-1]
g = pt.grad(f, x0)
h = pt.grad(g, x0)
mode = Mode(linker="py", optimizer="fast_run").excluding("scan_pushout")
fn = pytensor.function([x0], h, mode=mode)

# Issues: 
#  - Unused outer_in_seqs-1 in Scan{grad_of_grad_of_scan_fn} isn't removed
#      - Probably only becomes useless after inner graph is rewritten
#  - Repeated 2 * inner_in_mit_mot-0-0. Also equivalent add of it twice. Problem remains with fusion
#  - Nested IncSubtensor (sometimes separate by a reverse slice). This can probably be cleaned up quite a lot
#  - Unnecessary ExpandDims on value written by SetSubtensor
#  - Cryptic [3:-6:-1] slice, equivalent to [3:None:-1]
#  - Useless alloc(0, 4)[:4].inc(...)
# Useless sum on length 1 tensor at the end of graph

fn.dprint(print_shape=True, print_op_info=True)
dprint 

Sum{axes=None} [id A] shape=() 23
 └─ Subtensor{start:stop:step} [id B] shape=(?,) 22
    ├─ Scan{grad_of_scan_fn, while_loop=False, inplace=all} [id C] shape=(?,) 21 (outer_out_mit_mot-0)
    │  ├─ 4 [id D] shape=() (n_steps)
    │  ├─ Subtensor{start:stop:step} [id E] shape=(?,) 10 (outer_in_seqs-0)
    │  │  ├─ Scan{scan_fn, while_loop=False, inplace=all} [id F] shape=(?,) 8 (outer_out_sit_sot-0)
    │  │  │  ├─ 4 [id G] shape=() (n_steps)
    │  │  │  └─ SetSubtensor{:stop} [id H] shape=(5,) 6 (outer_in_sit_sot-0)
    │  │  │     ├─ AllocEmpty{dtype='float64'} [id I] shape=(5,) 2
    │  │  │     │  └─ 5 [id J] shape=()
    │  │  │     ├─ ExpandDims{axis=0} [id K] shape=(1,) 3
    │  │  │     │  └─ x0 [id L] shape=()
    │  │  │     └─ 1 [id M] shape=()
    │  │  ├─ 3 [id N] shape=()
    │  │  ├─ -6 [id O] shape=()
    │  │  └─ -1 [id P] shape=()
    │  └─ Subtensor{::step} [id Q] shape=(?,) 20 (outer_in_mit_mot-0)
    │     ├─ IncSubtensor{:stop} [id R] shape=(5,) 19
    │     │  ├─ Alloc [id S] shape=(5,) 1
    │     │  │  ├─ [0.] [id T] shape=(1,)
    │     │  │  └─ 5 [id J] shape=()
    │     │  ├─ Subtensor{::step} [id U] shape=(?,) 18
    │     │  │  ├─ IncSubtensor{:stop} [id V] shape=(4,) 17
    │     │  │  │  ├─ Alloc [id W] shape=(4,) 0
    │     │  │  │  │  ├─ [0.] [id T] shape=(1,)
    │     │  │  │  │  └─ 4 [id D] shape=()
    │     │  │  │  ├─ Subtensor{::step} [id X] shape=(?,) 16
    │     │  │  │  │  ├─ Scan{grad_of_grad_of_scan_fn, while_loop=False, inplace=all}.1 [id Y] shape=(?,) 15 (outer_out_nit_sot-0)
    │     │  │  │  │  │  ├─ 4 [id D] shape=() (outer_in_nit_sot-0)
    │     │  │  │  │  │  ├─ Subtensor{:stop} [id Z] shape=(?,) 12 (outer_in_seqs-0)
    │     │  │  │  │  │  │  ├─ Scan{scan_fn, while_loop=False, inplace=all} [id F] shape=(?,) 8 (outer_out_sit_sot-0)
    │     │  │  │  │  │  │  │  └─ ···
    │     │  │  │  │  │  │  └─ 4 [id BA] shape=()
    │     │  │  │  │  │  ├─ Subtensor{start:stop} [id BB] shape=(?,) 11 (outer_in_seqs-1)
    │     │  │  │  │  │  │  ├─ Scan{scan_fn, while_loop=False, inplace=all} [id F] shape=(?,) 8 (outer_out_sit_sot-0)
    │     │  │  │  │  │  │  │  └─ ···
    │     │  │  │  │  │  │  ├─ 1 [id M] shape=()
    │     │  │  │  │  │  │  └─ 5 [id BC] shape=()
    │     │  │  │  │  │  ├─ Subtensor{start:stop:step} [id BD] shape=(?,) 14 (outer_in_seqs-2)
    │     │  │  │  │  │  │  ├─ Scan{grad_of_scan_fn, while_loop=False, inplace=all} [id BE] shape=(?,) 13 (outer_out_mit_mot-0)
    │     │  │  │  │  │  │  │  ├─ 4 [id D] shape=() (n_steps)
    │     │  │  │  │  │  │  │  ├─ Subtensor{start:stop:step} [id E] shape=(?,) 10 (outer_in_seqs-0)
    │     │  │  │  │  │  │  │  │  └─ ···
    │     │  │  │  │  │  │  │  └─ Subtensor{::step} [id BF] shape=(?,) 9 (outer_in_mit_mot-0)
    │     │  │  │  │  │  │  │     ├─ IncSubtensor{start:} [id BG] shape=(?,) 7
    │     │  │  │  │  │  │  │     │  ├─ Alloc [id S] shape=(5,) 1
    │     │  │  │  │  │  │  │     │  │  └─ ···
    │     │  │  │  │  │  │  │     │  ├─ IncSubtensor{i} [id BH] shape=(?,) 4
    │     │  │  │  │  │  │  │     │  │  ├─ Alloc [id W] shape=(4,) 0
    │     │  │  │  │  │  │  │     │  │  │  └─ ···
    │     │  │  │  │  │  │  │     │  │  ├─ 1.0 [id BI] shape=()
    │     │  │  │  │  │  │  │     │  │  └─ -1 [id P] shape=()
    │     │  │  │  │  │  │  │     │  └─ 1 [id M] shape=()
    │     │  │  │  │  │  │  │     └─ -1 [id P] shape=()
    │     │  │  │  │  │  │  ├─ 3 [id N] shape=()
    │     │  │  │  │  │  │  ├─ -6 [id O] shape=()
    │     │  │  │  │  │  │  └─ -1 [id P] shape=()
    │     │  │  │  │  │  ├─ IncSubtensor{:stop} [id BJ] shape=(5,) 5 (outer_in_mit_mot-0)
    │     │  │  │  │  │  │  ├─ Alloc [id S] shape=(5,) 1
    │     │  │  │  │  │  │  │  └─ ···
    │     │  │  │  │  │  │  ├─ [1.] [id BK] shape=(1,)
    │     │  │  │  │  │  │  └─ 1 [id M] shape=()
    │     │  │  │  │  │  └─ 4 [id D] shape=() (outer_in_nit_sot-0)
    │     │  │  │  │  └─ -1 [id P] shape=()
    │     │  │  │  └─ 4 [id BA] shape=()
    │     │  │  └─ -1 [id P] shape=()
    │     │  └─ -1 [id P] shape=()
    │     └─ -1 [id P] shape=()
    ├─ 4 [id BA] shape=()
    ├─ 3 [id N] shape=()
    └─ -1 [id P] shape=()

Inner graphs:

Scan{grad_of_scan_fn, while_loop=False, inplace=all} [id C]
 ← Add [id BL] shape=() (inner_out_mit_mot-0-0)
    ├─ Mul [id BM] shape=()
    │  ├─ 2.0 [id BN] shape=()
    │  ├─ *1-<Scalar(float64, shape=())> [id BO] shape=() -> [id Q] (inner_in_mit_mot-0-0)
    │  └─ *0-<Scalar(float64, shape=())> [id BP] shape=() -> [id E] (inner_in_seqs-0)
    └─ *2-<Scalar(float64, shape=())> [id BQ] shape=() -> [id Q] (inner_in_mit_mot-0-1)

Scan{scan_fn, while_loop=False, inplace=all} [id F]
 ← Sqr [id BR] shape=() (inner_out_sit_sot-0)
    └─ *0-<Scalar(float64, shape=())> [id BP] shape=() -> [id H] (inner_in_sit_sot-0)

Scan{grad_of_grad_of_scan_fn, while_loop=False, inplace=all} [id Y]
 ← Add [id BS] shape=() (inner_out_mit_mot-0-0)
    ├─ Mul [id BT] shape=()
    │  ├─ 2.0 [id BU] shape=()
    │  ├─ *3-<Scalar(float64, shape=())> [id BV] shape=() -> [id BJ] (inner_in_mit_mot-0-0)
    │  └─ *0-<Scalar(float64, shape=())> [id BP] shape=() -> [id Z] (inner_in_seqs-0)
    └─ *4-<Scalar(float64, shape=())> [id BW] shape=() -> [id BJ] (inner_in_mit_mot-0-1)
 ← Add [id BX] shape=() (inner_out_mit_mot-0-1)
    ├─ *3-<Scalar(float64, shape=())> [id BV] shape=() -> [id BJ] (inner_in_mit_mot-0-0)
    └─ *3-<Scalar(float64, shape=())> [id BV] shape=() -> [id BJ] (inner_in_mit_mot-0-0)
 ← Mul [id BY] shape=() (inner_out_nit_sot-0)
    ├─ 2.0 [id BU] shape=()
    ├─ *3-<Scalar(float64, shape=())> [id BV] shape=() -> [id BJ] (inner_in_mit_mot-0-0)
    └─ *2-<Scalar(float64, shape=())> [id BQ] shape=() -> [id BD] (inner_in_seqs-2)

Scan{grad_of_scan_fn, while_loop=False, inplace=all} [id BE]
 ← Add [id BZ] shape=() (inner_out_mit_mot-0-0)
    ├─ Mul [id CA] shape=()
    │  ├─ 2.0 [id CB] shape=()
    │  ├─ *1-<Scalar(float64, shape=())> [id BO] shape=() -> [id BF] (inner_in_mit_mot-0-0)
    │  └─ *0-<Scalar(float64, shape=())> [id BP] shape=() -> [id E] (inner_in_seqs-0)
    └─ *2-<Scalar(float64, shape=())> [id BQ] shape=() -> [id BF] (inner_in_mit_mot-0-1)

Contributor guide

Open the contributing guide

First steps

  1. Read the whole issue, then the project's contributing guide.
  2. Comment on the issue to say you are picking it up — it saves two people doing the same work.
  3. Fork the repository and make your change on a branch.
  4. Open a pull request that references the issue number.

Research direction

Start by running the provided pytensor.scan, pt.grad, Mode, and dprint reproducer, then inspect the printed Scan gradient graphs and the optimizer stages excluding fusion and scan_pushout. The issue lists redundant inputs, arithmetic, subtensors, ExpandDims, alloc/incsubtensor operations, and a final length-one sum; done means the relevant simplifications are removed without changing the computed result.

Written by the indexing model from the issue text.

Assessment

Tech stack
python
Domain
compilers, performance
Issue type
Refactor
Difficulty
4/5
Estimated time
3-5 days
Activity status
Stale
Clarity
Mostly clear
Newbie friendliness
35/100

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