we have a release in the work (once some major PR are merged) but at the moment sou should use the git version be cause the current release do not have the fix yet

I updated POT using pip install -U https://github.com/PythonOT/POT/archive/master.zip and installed version 0.8.3.dev0. But I am still getting errors.

I'm sorry but on master (the same version), when editing the loss in the example file as such:

def get_loss(w):
 a = torch.mv(H2, w) # distribution reweighting
 #return ot.emd2(a, b, M2) # squared Wasserstein 2
 return ot.sinkhorn2(a, b, M2, 0.1) # squared Wasserstein 2

It just works...
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Interestingly, when I pass in ot.sinkhorn2(a, b, M2, 0.1) it works, but the following parameters strip the gradients ot.sinkhorn2(a, b, M2, 0.0005, numItermax=10000000). I assume a low entropic regularization term causes gradients to disappear?

for such a small value sinkhorn is not numerically stable dnas the gradient can be bad, you should at least use method='sinkhorn_log' in order to ensure that the iterations do not diverge. But for such a small epsilon emd2 will be faster on small datasets.