Banach Wasserstein GAN

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.

arXiv commentIn NeurIPS2018. 10 pages, 9 page appendix

References in corpus (4)

• Spectral Normalization for Generative Adversarial Networks
• SGDR: Stochastic Gradient Descent with Warm Restarts
• On the regularization of Wasserstein GANs
• First Order Generative Adversarial Networks

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