Coulomb GANs: Provably Optimal Nash Equilibria via Potential Fields

TL;DR

Coulomb GANs introduce a potential field approach to GAN training, ensuring convergence to a unique, optimal Nash equilibrium that accurately models the entire target distribution, thereby overcoming mode collapse.

Contribution

This paper presents Coulomb GANs, a novel formulation that guarantees convergence to a unique Nash equilibrium and improves sample diversity in image generation.

Findings

Achieved state-of-the-art results on LSUN and celebA datasets.

Generated a diverse variety of samples surpassing previous methods.

Proved the existence of a single, optimal Nash equilibrium in Coulomb GANs.

Abstract

Generative adversarial networks (GANs) evolved into one of the most successful unsupervised techniques for generating realistic images. Even though it has recently been shown that GAN training converges, GAN models often end up in local Nash equilibria that are associated with mode collapse or otherwise fail to model the target distribution. We introduce Coulomb GANs, which pose the GAN learning problem as a potential field of charged particles, where generated samples are attracted to training set samples but repel each other. The discriminator learns a potential field while the generator decreases the energy by moving its samples along the vector (force) field determined by the gradient of the potential field. Through decreasing the energy, the GAN model learns to generate samples according to the whole target distribution and does not only cover some of its modes. We prove that Coulomb GANs possess only one Nash equilibrium which is optimal in the sense that the model distribution equals the target distribution. We show the efficacy of Coulomb GANs on a variety of image datasets. On LSUN and celebA, Coulomb GANs set a new state of the art and produce a previously unseen variety of different samples.