Cumulant GAN

TL;DR

This paper introduces Cumulant GAN, a new loss function based on cumulant generating functions that unifies various GAN loss types, improves training stability, and enhances image generation quality.

Contribution

It proposes a novel cumulant-based loss function for GANs, providing a unified theoretical framework and demonstrating improved stability and performance.

Findings

Proves linear convergence of Cumulant GAN for specific cases

Shows improved robustness and quality in image generation

Unifies multiple divergence measures within a single framework

Abstract

In this paper, we propose a novel loss function for training Generative Adversarial Networks (GANs) aiming towards deeper theoretical understanding as well as improved stability and performance for the underlying optimization problem. The new loss function is based on cumulant generating functions giving rise to \emph{Cumulant GAN}. Relying on a recently-derived variational formula, we show that the corresponding optimization problem is equivalent to R{\'e}nyi divergence minimization, thus offering a (partially) unified perspective of GAN losses: the R{\'e}nyi family encompasses Kullback-Leibler divergence (KLD), reverse KLD, Hellinger distance and $\chi^2$-divergence. Wasserstein GAN is also a member of cumulant GAN. In terms of stability, we rigorously prove the linear convergence of cumulant GAN to the Nash equilibrium for a linear discriminator, Gaussian distributions and the standard gradient descent ascent algorithm. Finally, we experimentally demonstrate that image generation is more robust relative to Wasserstein GAN and it is substantially improved in terms of both inception score and Fr\'echet inception distance when both weaker and stronger discriminators are considered.