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

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.

arXiv comment21 pages, 39 figures, 2 tables

References in corpus (9)

• Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks
• GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium
• Generative Adversarial Text to Image Synthesis
• Improved Training of Wasserstein GANs
• Improved Techniques for Training GANs
• Which Training Methods for GANs do actually Converge?
• Stabilizing Training of Generative Adversarial Networks through Regularization
• Amortised MAP Inference for Image Super-resolution
• Gradient descent GAN optimization is locally stable