A Greedy Approach to Max-Sliced Wasserstein GANs
Authors: András Horváth
Keywords: GEnerative Adversarial Networks, GANs, Wasserstein distances, Sliced Wasserstein Distance, Max-sliced Wasserstein distance
TL;DR: We apply a greedy assignment on the projected samples instead of sorting to approximate Wasserstein distance
Abstract: Generative Adversarial Networks have made data generation possible in various use cases, but in case of complex, high-dimensional distributions it can be difficult to train them, because of convergence problems and the appearance of mode collapse.
Sliced Wasserstein GANs and especially the application of the Max-Sliced Wasserstein distance made it possible to approximate Wasserstein distance during training in an efficient and stable way and helped ease convergence problems of these architectures.

This method transforms sample assignment and distance calculation into sorting the one-dimensional projection of the samples, which results a sufficient approximation of the high-dimensional Wasserstein distance. 

In this paper we will demonstrate that the approximation of the Wasserstein distance by sorting the samples is not always the optimal approach and the greedy assignment of the real and fake samples can result faster convergence and better approximation of the original distribution.