A Neural Tangent Kernel Perspective of GANs

TL;DR

This paper introduces a new theoretical framework for analyzing GANs using Neural Tangent Kernel theory, addressing previous modeling flaws and providing insights into training dynamics and convergence.

Contribution

It develops a principled approach to study GAN training by incorporating discriminator architecture and NTK theory, improving understanding of convergence and training behavior.

Findings

Discriminator's architecture crucial for GAN training analysis

New insights into GAN convergence properties

Empirical validation supports theoretical predictions

Abstract

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.