Poisson Variational AutoEncoder

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• Introduce an algorithm for differentiating through Poisson sampling.

• Derive generative modeling theory for a variational autoencoder with Poisson approximate posterior.

• Unify neuroscience theories of rate coding, predictive coding, efficient coding, sparse coding, neural sampling, etc.

• Implement PVAE and demonstrate that it has superior latent representations that are sparse, positive integer, and are more informative for tasks like classification.