Banach Wasserstein GAN

TL;DR

This paper extends Wasserstein GANs to Banach spaces, enabling feature emphasis through different norms, especially Sobolev norms, which improves image generation performance on CIFAR-10 and CelebA datasets.

Contribution

It generalizes WGAN theory to Banach spaces, allowing for feature selection via different norms, and demonstrates performance improvements with Sobolev norms.

Findings

Performance boost on CIFAR-10 with Sobolev norms

Theoretical extension of WGAN to Banach spaces

Enhanced feature emphasis in image generation

Abstract

Wasserstein Generative Adversarial Networks (WGANs) can be used to generate realistic samples from complicated image distributions. The Wasserstein metric used in WGANs is based on a notion of distance between individual images, which induces a notion of distance between probability distributions of images. So far the community has considered $\ell^2$ as the underlying distance. We generalize the theory of WGAN with gradient penalty to Banach spaces, allowing practitioners to select the features to emphasize in the generator. We further discuss the effect of some particular choices of underlying norms, focusing on Sobolev norms. Finally, we demonstrate a boost in performance for an appropriate choice of norm on CIFAR-10 and CelebA.