RelaxedBernoulli samples not differentiable about dhod

[changhoonhahn]

When I tried replacing _hod with tfp.distributions.Normal I didn't run into any issues...

[EiffL]

Ok, sorry it took me a while to get around to this, but I confirm you are not crazy, I can't get non-zero gradients with the relaxed Bernoulli. It is very likely an issue with some underflowing. I'll try to dig out my own implementation of the Gumbel-Softmax which was working perfectly fine. Maybe that'll point us to what is wrong here

[EiffL]

hehehehehhehe:

So yeah the problem comes from underflows when the probability for Ncen drops too close to 0. I would say one simple workaround is to clip the probability to some p_min, once my brain has rebooted a little bit more might think of a cleverer solution.

I've added another demo notebook: https://github.com/DifferentiableUniverseInitiative/DHOD/blob/master/nb/dhod_centrals_gs.ipynb
This works as long as we don't sample too far away from Mmin, need to implement that clipping.

[EiffL]

Sweet, closing this issue then

[EiffL]

Before we forgetr.... @all-contributors, let's add @changhoonhahn for code