Local Stability and Performance of Simple Gradient Penalty mu-Wasserstein GAN

TL;DR

This paper proves the local stability of a simple gradient penalty variant of Wasserstein GAN under certain conditions, highlighting the importance of penalizing data or sample manifolds for regularization, supported by experimental validation.

Contribution

The study provides a theoretical proof of local stability for simple gradient penalty WGANs and introduces measure valued differentiation for handling complex measures.

Findings

Proves local stability of SGP μ-WGAN under specific assumptions.

Shows penalizing data or sample manifolds effectively regularizes WGAN.

Experimental results support the theoretical claims.

Abstract

Wasserstein GAN(WGAN) is a model that minimizes the Wasserstein distance between a data distribution and sample distribution. Recent studies have proposed stabilizing the training process for the WGAN and implementing the Lipschitz constraint. In this study, we prove the local stability of optimizing the simple gradient penalty $\mu$-WGAN(SGP $\mu$-WGAN) under suitable assumptions regarding the equilibrium and penalty measure $\mu$. The measure valued differentiation concept is employed to deal with the derivative of the penalty terms, which is helpful for handling abstract singular measures with lower dimensional support. Based on this analysis, we claim that penalizing the data manifold or sample manifold is the key to regularizing the original WGAN with a gradient penalty. Experimental results obtained with unintuitive penalty measures that satisfy our assumptions are also provided to support our theoretical results.