We propose a novel theoretical framework of analysis for Generative Adversarial Networks (GANs). We start by pointing out a fundamental flaw in previous theoretical analyses that leads to ill-defined gradients for the discriminator. 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 provide a characterization of the trained discriminator for a wide range of losses and establish general differentiability properties of the network. Moreover, we derive new insights about the generated distribution's flow during training, advancing our understanding of GAN dynamics. We empirically corroborate these results via a publicly released analysis toolkit based on our framework, unveiling intuitions that are consistent with current GAN practice.

翻译：我们为创世反逆网络(GANs)提出了一个新的理论分析框架。我们首先指出以前理论分析中的一个根本缺陷,它导致歧视者的梯度定义不明确。我们克服了这个问题,这个问题妨碍了对GAN培训进行有原则的研究,通过考虑歧视者的结构来解决该问题。为此,我们利用无限宽线神经网络理论,通过其神经洞穴为歧视者服务。我们为广泛的损失提供了训练有素的歧视者的特点,并建立了该网络的一般差异性特征。此外,我们从培训过程中产生的分配流动中获得了新的洞察力,增进了我们对GAN动态的了解。我们根据我们的框架,通过公开发布的分析工具包,通过展示符合当前GAN实践的直觉,来以经验方式证实这些结果。