Supplementary Information SI) A Proof of for pi V

Assume that we observe data sampled from pi-VAE model defined according to equation 1, 2 with Poisson noise and parameters =( f, T,) . Assume the following holds: i) The firing rate function f in equation 1 is injective. Because the Bernoulli model is identifiable, the Poisson model is also identifiable. Then we applied two GIN blocks. GIN block, and randomly permuted the input before passing it through each GIN block.