Summable Reparameterizations of Wasserstein Critics in the One-Dimensional Setting

TL;DR

This paper introduces a class of function decompositions, including Taylor and Fourier series, that improve Wasserstein GAN critics in one-dimensional density estimation, with potential for extension to higher dimensions.

Contribution

It identifies a new class of critic functions suitable for Wasserstein GANs, demonstrating their effectiveness in one-dimensional problems and outlining future scaling strategies.

Findings

Decompositions like Taylor and Fourier improve critic performance.

Critics outperform standard GAN approaches in experiments.

Potential for scaling to higher-dimensional problems.

Abstract

Generative adversarial networks (GANs) are an exciting alternative to algorithms for solving density estimation problems---using data to assess how likely samples are to be drawn from the same distribution. Instead of explicitly computing these probabilities, GANs learn a generator that can match the given probabilistic source. This paper looks particularly at this matching capability in the context of problems with one-dimensional outputs. We identify a class of function decompositions with properties that make them well suited to the critic role in a leading approach to GANs known as Wasserstein GANs. We show that Taylor and Fourier series decompositions belong to our class, provide examples of these critics outperforming standard GAN approaches, and suggest how they can be scaled to higher dimensional problems in the future.