Banach Wasserstein GAN
This work addresses image generation for AI practitioners by offering a flexible framework, though it is incremental as it builds on existing WGAN methods.
The authors tackled the problem of generating realistic images by generalizing Wasserstein GANs to Banach spaces, allowing control over emphasized features, and demonstrated improved performance on CIFAR-10 and CelebA datasets.
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.