detach inverse in the VAMPE score

[DanielWicz]

In the original paper, it is stated:

"Another advantage of the VAMP-E based validation score is that it does not involve any inverse
operation of matrices and can be stably computed."

It seems in general, that the sym_inverse should be detached from the graph, otherwise it is involved in the computational graph and gradient is calculated through the inverse. In fact, from my point of view, both inverses and koopman should be detached from the graph, and only the torch.trace part should be contributing to the optimization.

[codecov]

Codecov Report

Patch coverage: 100.00% and no project coverage change.

Comparison is base (9a53285) 92.15% compared to head (0bb3215) 92.16%.

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #274   +/-   ##
=======================================
  Coverage   92.15%   92.16%           
=======================================
  Files         142      142           
  Lines       11652    11652           
=======================================
+ Hits        10738    10739    +1     
+ Misses        914      913    -1     

Impacted Files	Coverage Δ
deeptime/decomposition/deep/_vampnet.py	94.73% <100.00%> (ø)

... and 1 file with indirect coverage changes

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[clonker]

Hi! Thank you very much for your contributions :) please correct me if I'm wrong but I think we'd still need the gradient flow through these components - while the score doesn't directly involve any inverses, we still have to transform our data into whitened space (C^{-1/2}). Have you tried/compared training with your modification to the reference?

Thanks!

[DanielWicz]

At the moment I have tested in my own implementation in Tensorflow 2. I have noticed that it lead to faster training and faster reduction of the loss. Therefore I have decided to open this Pull request. I will try to make more controlled tests with deeptime.

Do you use some particular dataset for comparison, for example like WLALL pentapeptide from PYEMMA ?

[clonker]

Super cool! Pentapeptide would be amazing, otherwise you could also test it out on ala2: https://deeptime-ml.github.io/latest/notebooks/examples/ala2-example.html