  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.
