I was reviewing the gumbel_softmax implementation [1] and realized that the Gumbel distribution was being sampled via gumbels = -torch.empty_like(logits, memory_format=torch.legacy_contiguous_format).exponential_().log()  # ~Gumbel(0,1). I couldn’t see how this would generate gumbel = -log(eps - log(uniform(0,1) + eps) so I empirically validated the distributions which checks out.
My question is the following: what is the distribution of torch.empty so that these formula generate the same distribution?
[1] https://pytorch.org/docs/stable/_modules/torch/nn/functional.html#gumbel_softmax 5