Lipschitz Generative Adversarial Nets

TL;DR

This paper introduces Lipschitz GANs (LGANs), a new family of generative adversarial networks that enforce Lipschitz constraints to ensure informative gradients, leading to more stable training and higher quality samples.

Contribution

The paper proposes LGANs, establishing their theoretical properties and demonstrating improved stability and sample quality over WGANs through empirical analysis.

Findings

LGANs guarantee unique optimal discriminative functions.

LGANs eliminate gradient uninformativeness issues.

LGANs produce higher quality samples than WGAN.

Abstract

In this paper, we study the convergence of generative adversarial networks (GANs) from the perspective of the informativeness of the gradient of the optimal discriminative function. We show that GANs without restriction on the discriminative function space commonly suffer from the problem that the gradient produced by the discriminator is uninformative to guide the generator. By contrast, Wasserstein GAN (WGAN), where the discriminative function is restricted to 1-Lipschitz, does not suffer from such a gradient uninformativeness problem. We further show in the paper that the model with a compact dual form of Wasserstein distance, where the Lipschitz condition is relaxed, may also theoretically suffer from this issue. This implies the importance of Lipschitz condition and motivates us to study the general formulation of GANs with Lipschitz constraint, which leads to a new family of GANs that we call Lipschitz GANs (LGANs). We show that LGANs guarantee the existence and uniqueness of the optimal discriminative function as well as the existence of a unique Nash equilibrium. We prove that LGANs are generally capable of eliminating the gradient uninformativeness problem. According to our empirical analysis, LGANs are more stable and generate consistently higher quality samples compared with WGAN.