Understanding the Effectiveness of Lipschitz-Continuity in Generative Adversarial Nets

Understand

In this paper, we investigate the underlying factor that leads to failure and success in the training of GANs.

• We study the property of the optimal discriminative function and show that in many GANs, the gradient from the optimal discriminative function is not reliable, which turns out to be the fundamental cause of failure in training of GANs.
• We further demonstrate that a well-defined distance metric does not necessarily guarantee the convergence of GANs.
• Finally, we prove in this paper that Lipschitz-continuity condition is a general solution to make the gradient of the optimal discriminative function reliable, and characterized the necessary condition where Lipschitz-continuity ensures the convergence, which leads to a broad family of valid GAN objectives under Lipschitz-continuity condition, where Wasserstein distance is one special case.