English

Wasserstein GANs Work Because They Fail (to Approximate the Wasserstein Distance)

Machine Learning 2021-10-06 v4 Machine Learning

Abstract

Wasserstein GANs are based on the idea of minimising the Wasserstein distance between a real and a generated distribution. We provide an in-depth mathematical analysis of differences between the theoretical setup and the reality of training Wasserstein GANs. In this work, we gather both theoretical and empirical evidence that the WGAN loss is not a meaningful approximation of the Wasserstein distance. Moreover, we argue that the Wasserstein distance is not even a desirable loss function for deep generative models, and conclude that the success of Wasserstein GANs can in truth be attributed to a failure to approximate the Wasserstein distance.

Keywords

Cite

@article{arxiv.2103.01678,
  title  = {Wasserstein GANs Work Because They Fail (to Approximate the Wasserstein Distance)},
  author = {Jan Stanczuk and Christian Etmann and Lisa Maria Kreusser and Carola-Bibiane Schönlieb},
  journal= {arXiv preprint arXiv:2103.01678},
  year   = {2021}
}