#KL_divergence = nan
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Referring here https://stackoverflow.com/questions/59736801/why-do-i-get-a-nan-when-computing-the-kl-divergence-between-two-onehotcategorica - it might be because of log(0) or the 0/0 operation? Have you tried adding a small epsilon to see if you can get a different output?
the problem is that i use distrib.log_prob(y) with distrib a bernoulli
I can add a small epsilon to y but not to the distribtuion
thats where i'm stuck