Local Stability of Wasserstein GANs With Abstract Gradient Penalty

The convergence of generative adversarial networks (GANs) has been studied substantially in various aspects to achieve successful generative tasks. Ever since it is first proposed, the idea has achieved many theoretical improvements by injecting an instance noise, choosing different divergences, penalizing the discriminator, and so on. In essence, these efforts are to approximate a real-world measure with an idle measure through a learning procedure. In this article, we provide an analysis of GANs in the most general setting to reveal what, in essence, should be satisfied to achieve successful convergence. This work is not trivial since handling a converging sequence of an abstract measure requires a lot more sophisticated concepts. In doing so, we find an interesting fact that the discriminator can be penalized in a more general setting than what has been implemented. Furthermore, our experiment results substantiate our theoretical argument on various generative tasks.