Coulomb GANs: Provably Optimal Nash Equilibria via Potential Fields

Thomas Unterthiner, Bernhard Nessler, Calvin Seward, Günter Klambauer, Martin Heusel, Hubert Ramsauer, Sepp Hochreiter

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, 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 LSUN bedrooms, CelebA faces, CIFAR-10 and the Google Billion Word text generation.

TL;DR: Coulomb GANs can optimally learn a distribution by posing the distribution learning problem as optimizing a potential field

Keywords: Deep Learning, Generative Adversarial Network, GAN, Generative Model, Potential Field

Code: [ bioinf-jku/coulomb_gan](https://github.com/bioinf-jku/coulomb_gan)

Data: [CelebA](https://paperswithcode.com/dataset/celeba), [LSUN](https://paperswithcode.com/dataset/lsun)

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/arxiv:1708.08819/code)