pinv: forward/backward AD which is Frechet-defined in a rank-preserving neighborhood. by nikitaved · Pull Request #66092 · pytorch/pytorch

nikitaved · 2021-10-04T20:51:38Z

Fixes #65911. Also enables complex support/tests for linalg_pinv in OpInfo.

cc @ezyang @albanD @zou3519 @gqchen @pearu @nikitaved @soulitzer @lezcano @Varal7 @jianyuh @mruberry @walterddr @IvanYashchuk @xwang233

rank-preserving neighborhood.

pytorch-probot · 2021-10-04T20:51:41Z

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nikitaved · 2021-10-04T20:58:29Z

+           # Only large tensors show issues with implicit backward used prior to
+           # explicit backward implementation.


a note: large tensors of low rank. In my environment I had to create a 1-rank 30x30 matrix to see issues with repeated "zeros" in the backward of SVD.

ezyang · 2021-10-04T23:17:04Z

not sure appropriate FB reviewer has been tagged yet

facebook-github-bot · 2021-10-05T01:59:01Z

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💊 CI failures summary and remediations

As of commit 2b5431e (more details on the Dr. CI page):

1/1 failures introduced in this PR

🕵️ 1 new failure recognized by patterns

The following CI failures do not appear to be due to upstream breakages:

pytorch_xla_linux_bionic_py3_6_clang9_test (1/1)

Step: "Test" (full log | diagnosis details | 🔁 rerun)

Oct 08 11:26:22 RuntimeError: tensorflow/compil...'rendezvous_test.0': Connection reset by peer (14)

Oct 08 11:26:22 Exception in device=CPU:1: tensorflow/compiler/xla/xla_client/mesh_service.cc:364 : Failed to meet rendezvous 'rendezvous_test.0': Connection reset by peer (14)
Oct 08 11:26:22 Traceback (most recent call last):
Oct 08 11:26:22   File "/opt/conda/lib/python3.6/site-packages/torch_xla-1.10-py3.6-linux-x86_64.egg/torch_xla/distributed/xla_multiprocessing.py", line 329, in _mp_start_fn
Oct 08 11:26:22     _start_fn(index, pf_cfg, fn, args)
Oct 08 11:26:22   File "/opt/conda/lib/python3.6/site-packages/torch_xla-1.10-py3.6-linux-x86_64.egg/torch_xla/distributed/xla_multiprocessing.py", line 323, in _start_fn
Oct 08 11:26:22     fn(gindex, *args)
Oct 08 11:26:22   File "/var/lib/jenkins/workspace/xla/test/test_mp_rendezvous.py", line 22, in _mp_fn
Oct 08 11:26:22     replicas=replicas)
Oct 08 11:26:22   File "/opt/conda/lib/python3.6/site-packages/torch_xla-1.10-py3.6-linux-x86_64.egg/torch_xla/core/xla_model.py", line 875, in rendezvous
Oct 08 11:26:22     return torch_xla._XLAC._xla_rendezvous(get_ordinal(), tag, payload, replicas)
Oct 08 11:26:22 RuntimeError: tensorflow/compiler/xla/xla_client/mesh_service.cc:364 : Failed to meet rendezvous 'rendezvous_test.0': Connection reset by peer (14)
Oct 08 11:26:23 Traceback (most recent call last):
Oct 08 11:26:23   File "/var/lib/jenkins/workspace/xla/test/test_mp_rendezvous.py", line 35, in <module>
Oct 08 11:26:23     xmp.spawn(_mp_fn, args=())
Oct 08 11:26:23   File "/opt/conda/lib/python3.6/site-packages/torch_xla-1.10-py3.6-linux-x86_64.egg/torch_xla/distributed/xla_multiprocessing.py", line 394, in spawn
Oct 08 11:26:23     start_method=start_method)
Oct 08 11:26:23   File "/opt/conda/lib/python3.6/site-packages/torch/multiprocessing/spawn.py", line 188, in start_processes
Oct 08 11:26:23     while not context.join():
Oct 08 11:26:23   File "/opt/conda/lib/python3.6/site-packages/torch/multiprocessing/spawn.py", line 144, in join
Oct 08 11:26:23     exit_code=exitcode
Oct 08 11:26:23 torch.multiprocessing.spawn.ProcessExitedException: process 3 terminated with exit code 17

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…taved/pinv_backward

lezcano

Nice! Thanks both for finding the slick formula for this backward and the rather compact implementation!

lezcano · 2021-10-05T09:22:53Z

+                # Note that by making the columns of `a` and `b` orthonormal we make sure
+                # that the product matrix `a @ b.t()` has condition number 1.


Nice! This saves us a lot of pain in future debugging.

Now, this note is slightly incorrect. The resulting matrix will have singular values 0 and 1, so the condition number will be infinite! Perhaps you mean that it has condition number 1 when restricted to its image?

Yes, exactly in the image, correct, so that pinv is stable.

albanD · 2021-10-05T16:52:02Z

+           sample_inputs_func=sample_inputs_linalg_pinv_singular,
+           # Only large tensors show issues with implicit backward used prior to
+           # explicit backward implementation.
+           decorators=[slowTest, skipCUDAIfNoMagmaAndNoCusolver, skipCUDAIfRocm, skipCPUIfNoLapack],


Is the slowTest decorator working as expected here?

@albanD It will apply the slowTest decorator to EVERY test generated by this OpInfo

mruberry · 2021-10-06T21:16:03Z

Cool! Do you have before/after perf numbers for the autograd, @nikitaved?

…taved/pinv_backward

nikitaved · 2021-10-07T19:46:38Z

@mruberry, I did run some benchmarks and surprisingly this PR also improves performance.

This PR, cpu float32:

shape: (10, 10), device: cpu, dtype: torch.float32                                                                                                                                                                 
29.8 µs ± 167 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)                                                                                                                                           
                                                                                                                                                                                                                   
shape: (1000, 10, 10), device: cpu, dtype: torch.float32                                                                                                                                                           
797 µs ± 7.44 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)                                                                                                                                            
                                                                                                                                                                                                                   
shape: (100, 100), device: cpu, dtype: torch.float32                                                                                                                                                               
273 µs ± 3.76 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)                                                                                                                                            
                                                                                                                                                                                                                   
shape: (1000, 100, 100), device: cpu, dtype: torch.float32                                                                                                                                                         
56.4 ms ± 1.6 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)                                                                                                                                              
                                                                                                                                                                                                                   
shape: (1000, 1000), device: cpu, dtype: torch.float32                                                                                                                                                             
11.7 ms ± 96.8 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)                                                                                                                                            
                                                                                                                                                                                                                   
shape: (10, 1000, 1000), device: cpu, dtype: torch.float32                                                                                                                                                         
159 ms ± 1.26 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)

Master, cpu float32:

shape: (10, 10), device: cpu, dtype: torch.float32                                                                                                                                                                 
86.3 µs ± 3.55 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)                                                                                                                                          
                                                                                                                                                                                                                   
shape: (1000, 10, 10), device: cpu, dtype: torch.float32                                                                                                                                                           
2.23 ms ± 398 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)                                                                                                                                             
                                                                                                                                                                                                                   
shape: (100, 100), device: cpu, dtype: torch.float32                                                                                                                                                               
535 µs ± 33.9 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)                                                                                                                                            
                                                                                                                                                                                                                   
shape: (1000, 100, 100), device: cpu, dtype: torch.float32                                                                                                                                                         
174 ms ± 6.25 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)                                                                                                                                              
                                                                                                                                                                                                                   
shape: (1000, 1000), device: cpu, dtype: torch.float32                                                                                                                                                             
26.9 ms ± 1.58 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)                                                                                                                                             
                                                                                                                                                                                                                   
shape: (10, 1000, 1000), device: cpu, dtype: torch.float32                                                                                                                                                         
392 ms ± 30.2 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

This PR, cuda float32:

shape: (10, 10), device: cuda, dtype: torch.float32
111 µs ± 3.58 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)

shape: (1000, 10, 10), device: cuda, dtype: torch.float32
332 µs ± 998 ns per loop (mean ± std. dev. of 7 runs, 1000 loops each)

shape: (100, 100), device: cuda, dtype: torch.float32
111 µs ± 772 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)

shape: (1000, 100, 100), device: cuda, dtype: torch.float32
7.25 ms ± 11.5 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

shape: (1000, 1000), device: cuda, dtype: torch.float32
3.21 ms ± 2.74 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

shape: (10, 1000, 1000), device: cuda, dtype: torch.float32
29.8 ms ± 21.2 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

Master, cuda float32:

shape: (10, 10), device: cuda, dtype: torch.float32
282 µs ± 15 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

shape: (1000, 10, 10), device: cuda, dtype: torch.float32
565 µs ± 3.39 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

shape: (100, 100), device: cuda, dtype: torch.float32
312 µs ± 32.1 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

shape: (1000, 100, 100), device: cuda, dtype: torch.float32
11.8 ms ± 41.1 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

shape: (1000, 1000), device: cuda, dtype: torch.float32
4.72 ms ± 32.4 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

shape: (10, 1000, 1000), device: cuda, dtype: torch.float32
42.4 ms ± 26.8 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

…taved/pinv_backward

lezcano · 2021-10-08T08:29:30Z

Faster and correct! There's no better combination than that :)

albanD

Looks good. Can you fix the last lint (EDIT: Ho it looks like the job itself failed...)and I'll merge this.

facebook-github-bot · 2021-10-08T13:23:44Z

@albanD has imported this pull request. If you are a Facebook employee, you can view this diff on Phabricator.

…ng neighborhood. (pytorch#66092) Summary: Fixes pytorch#65911. Also enables complex support/tests for `linalg_pinv` in OpInfo. cc ezyang albanD zou3519 gqchen pearu nikitaved soulitzer Lezcano Varal7 jianyuh mruberry walterddr IvanYashchuk xwang233 Pull Request resolved: pytorch#66092 Reviewed By: ejguan Differential Revision: D31503072 Pulled By: albanD fbshipit-source-id: 52018e826826ae62beaad76becb5edf880be253f

pinv: forward/backward AD which is Frechet differentiable in a

d4ddef8

rank-preserving neighborhood.

nikitaved added module: autograd Related to torch.autograd, and the autograd engine in general module: linear algebra Issues related to specialized linear algebra operations in PyTorch; includes matrix multiply matmul complex_autograd ci/slow-gradcheck labels Oct 4, 2021

nikitaved requested review from albanD, ezyang and soulitzer as code owners October 4, 2021 20:51

pytorch-probot Bot added the ciflow/default label Oct 4, 2021

nikitaved commented Oct 4, 2021

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ezyang removed their request for review October 4, 2021 23:16

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nikitaved added 2 commits October 5, 2021 08:11

add forward AD to the tests of pinverse in OpInfo

1ad418e

Merge branch 'master' of https://github.com/pytorch/pytorch into niki…

4775c45

…taved/pinv_backward

nikitaved changed the title ~~pinv: forward/backward AD which is Frechet-differentiable in a rank-preserving neighborhood.~~ pinv: forward/backward AD which is Frechet-defined in a rank-preserving neighborhood. Oct 5, 2021

nikitaved requested review from IvanYashchuk, anjali411, lezcano and mruberry October 5, 2021 08:14

minor optimization

346113f

lezcano approved these changes Oct 5, 2021

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albanD reviewed Oct 5, 2021

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nikitaved added 3 commits October 7, 2021 14:18

Merge branch 'master' of https://github.com/pytorch/pytorch into niki…

23c6ccf

…taved/pinv_backward

minor test update

b154a16

Merge branch 'master' of https://github.com/pytorch/pytorch into niki…

3743c7d

…taved/pinv_backward

albanD mentioned this pull request Oct 7, 2021

[bootcamp task] Add forward AD support for specific ops #66266

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nikitaved added 2 commits October 7, 2021 21:01

add derivations

2dbbecb

Merge branch 'master' of https://github.com/pytorch/pytorch into niki…

443ccc1

…taved/pinv_backward

nikitaved added 3 commits October 8, 2021 09:20

minor

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resolve merge conflict

0ec1de8

fix flake8

2b5431e

albanD approved these changes Oct 8, 2021

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facebook-github-bot closed this in 1b40daa Oct 11, 2021

This was referenced Oct 14, 2021

Add relative and absolute tolerances for matrix_rank, pinv #63102

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Derivative for aten::linalg_pinv is not implemented #66618

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crcrpar mentioned this pull request Nov 6, 2021

TestCommonCUDA.test_noncontiguous_samples_linalg_pinv_hermitian_cuda_float32 fails when TF32 is enabled #67947

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github-actions Bot deleted the nikitaved/pinv_backward branch February 13, 2024 01:58

		# Only large tensors show issues with implicit backward used prior to
		# explicit backward implementation.

		# Note that by making the columns of `a` and `b` orthonormal we make sure
		# that the product matrix `a @ b.t()` has condition number 1.

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