A Neural Tangent Kernel Perspective of GANs
This work addresses a fundamental theoretical bottleneck for researchers studying GANs, offering a more principled analysis framework.
The paper tackles the problem of flawed theoretical analyses of GANs by proposing a novel framework using Neural Tangent Kernel theory to model the discriminator's architecture, overcoming ill-defined gradients and deriving new insights into convergence and training dynamics, with empirical validation.
We propose a novel theoretical framework of analysis for Generative Adversarial Networks (GANs). We reveal a fundamental flaw of previous analyses which, by incorrectly modeling GANs' training scheme, are subject to ill-defined discriminator gradients. We overcome this issue which impedes a principled study of GAN training, solving it within our framework by taking into account the discriminator's architecture. To this end, we leverage the theory of infinite-width neural networks for the discriminator via its Neural Tangent Kernel. We characterize the trained discriminator for a wide range of losses and establish general differentiability properties of the network. From this, we derive new insights about the convergence of the generated distribution, advancing our understanding of GANs' training dynamics. We empirically corroborate these results via an analysis toolkit based on our framework, unveiling intuitions that are consistent with GAN practice.