# Coarse Grained Exponential Variational Autoencoders

## TL;DR

This paper introduces a semi-continuous latent space for variational autoencoders, enabling the use of complex distributions for inference and improving upon traditional Gaussian-based VAEs.

## Contribution

It proposes a novel semi-continuous latent representation that approximates continuous densities, allowing for arbitrary parametric distributions in VAEs.

## Key findings

- Consistent performance improvements over standard VAEs.
- Demonstrates the flexibility of polynomial exponential family distributions.
- Enhances the expressiveness of the inference process.

## Abstract

Variational autoencoders (VAE) often use Gaussian or category distribution to model the inference process. This puts a limit on variational learning because this simplified assumption does not match the true posterior distribution, which is usually much more sophisticated. To break this limitation and apply arbitrary parametric distribution during inference, this paper derives a \emph{semi-continuous} latent representation, which approximates a continuous density up to a prescribed precision, and is much easier to analyze than its continuous counterpart because it is fundamentally discrete. We showcase the proposition by applying polynomial exponential family distributions as the posterior, which are universal probability density function generators. Our experimental results show consistent improvements over commonly used VAE models.