differentiable histogram

[jakubMitura14]

Hello I am just starting my exploration of optimal transport - still, it seems to me that it provides many differentiable approximations of nondifferentiable algorithms.
My problem requires calculating histogram from a vector and also later compare histograms derived from different vectors as a measure of their similarity ;
I had seen that your library provides some histograms based on sinkhorn barycenters. Which algorithm if any is differentiable? By differentiable I mean it can be put in a jax model as a part of loss function calculation .

Thanks for help

[marcocuturi]

hi Jakub! thanks for your interest in OTT-JAX and apologies for the delay in our response.

In principle, we do aim for full differentiability of our results. But we only test here and there in our tests, and there might be some outputs that will break differentiability. In particular, I haven't tried differentiating barycenters in ott. This is the idea behind these references:
https://hal.science/hal-01303148
https://arxiv.org/abs/1708.01955
if you do try it and see some bugs please do let us know!

[jakubMitura14]

Thanks!!