Gaussian AutoEncoder

TL;DR

This paper introduces a deterministic AutoEncoder with a novel regularizer that directly enforces the latent space distribution to match desired properties, improving over previous stochastic methods like VAE and WAE.

Contribution

It proposes a new regularizer for AutoEncoders that directly aligns the empirical latent distribution with the target distribution, avoiding randomness and arbitrary regularizers.

Findings

Regularizer effectively enforces Gaussian distribution in latent space.

Method can be adapted to other distributions like uniform on hypercube.

Improves latent space distribution matching without stochastic sampling.

Abstract

Generative AutoEncoders require a chosen probability distribution in latent space, usually multivariate Gaussian. The original Variational AutoEncoder (VAE) uses randomness in encoder - causing problematic distortion, and overlaps in latent space for distinct inputs. It turned out unnecessary: we can instead use deterministic encoder with additional regularizer to ensure that sample distribution in latent space is close to the required. The original approach (WAE) uses Wasserstein metric, what required comparing with random sample and using an arbitrarily chosen kernel. Later CWAE finally derived a non-random analytic formula by averaging $L_2$ distance of Gaussian-smoothened sample over all 1D projections. However, these arbitrarily chosen regularizers do not lead to Gaussian distribution. This article proposes approach for regularizers directly optimizing agreement between empirical distribution function and its desired CDF for chosen properties, for example radii and distances for Gaussian distribution, or coordinate-wise, to directly attract this distribution in latent space of AutoEncoder. We can also attract different distributions with this general approach, for example latent space uniform distribution on $[0,1]^D$ hypercube or torus would allow for data compression without entropy coding, increased density near codewords would optimize for the required quantization.