Understanding the Effectiveness of Lipschitz-Continuity in Generative Adversarial Nets
This addresses training instability in GANs for researchers and practitioners, offering a theoretical foundation and improved methods, though it is incremental as it builds on existing Lipschitz-continuity concepts.
The paper tackled the problem of training instability in Generative Adversarial Networks (GANs) by identifying unreliable gradients from the optimal discriminative function as a fundamental cause of failure, and proved that Lipschitz-continuity ensures reliable gradients and convergence, leading to new objectives that produce more stable outputs and consistently higher-quality generated samples than Wasserstein distance.
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. We experiment with several new objectives, which are sound according to our theorems, and we found that, compared with Wasserstein distance, the outputs of the discriminator with new objectives are more stable and the final qualities of generated samples are also consistently higher than those produced by Wasserstein distance.