pymc-devs / pymc-devs/pytensor

Equivalent dots not merged

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graph rewriting linalg performance
Dominant language
Python
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Forks
208
Avg merge
2d 14h
Merged PRs (30d)
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Description

Description

In the example below we end up computing 4 dots, whereas only 3 are needed

import pytensor
import pytensor.tensor as pt
from pytensor.compile.mode import get_default_mode

A = pt.dmatrix('A')
x = pt.col('x')
f = (x.T @ A @ x), A @ x, A.T @ x

fn = pytensor.function([A, x], f, mode=get_default_mode().excluding("BlasOpt"))
fn.dprint()
# dot [id A] 2
#  ├─ dot [id B] 1
#  │  ├─ Transpose{axes=[1, 0]} [id C] 'x.T' 0
#  │  │  └─ x [id D]
#  │  └─ A [id E]
#  └─ x [id D]
# dot [id F] 3
#  ├─ A [id E]
#  └─ x [id D]
# dot [id G] 5
#  ├─ Transpose{axes=[1, 0]} [id H] 'A.T' 4
#  │  └─ A [id E]
#  └─ x [id D]

We could use associativity to write (x.T @ A) @ x -> as x.T @ (A @ x), where the inner dot is equivalent to the second output, so they could be merged

Alternatively, we could use the transpose rule to write the third output A.T @ x -> (x.T @ A).T which is the innermost dot in the first output, so they could be merged (with an extra transpose which is just a cheap view anyway).

With associativity we may want to be careful as order can impact a lot on performance. If we know the static shapes we can optimize like einsum does (see also #https://github.com/pymc-devs/pytensor/issues/961), but if we are already computing it anyway then we can't possible be doing worse.

The example above can easily show up in the gradient of a quadratic form graph.

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Research direction

Start with the supplied PyTensor graph example and inspect the optimizer passes that handle dot operations. Reproduce the graph with the shown function and compare its dprint output before and after optimization. Done means equivalent dot expressions are merged without introducing a worse multiplication order, with coverage for the quadratic-form case.

Written by the indexing model from the issue text.

Assessment

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

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