A Uniform Generalization Error Bound for Generative Adversarial Networks

Hao Chen, Zhanfeng Mo, Qingyi Gao, Zhouwang Yang, Xiao Wang

Keywords: GANs, Uniform Generalization Bound, Deep Learning, Weight normalization

TL;DR: This theoretical issue establishes a uniform generalization error bound on GANs.

Abstract: This paper focuses on the theoretical investigation of unsupervised generalization theory of generative adversarial networks (GANs). We first formulate a more reasonable definition of general error and generalization bounds for GANs. On top of that, we establish a bound for generalization error with a fixed generator in a general weight normalization context. Then, we obtain a width-independent bound by applying $\ell_{p,q}$ and spectral norm weight normalization. To better understand the unsupervised model, GANs, we establish the generalization bound, which uniformly holds with respect to the choice of generators. Hence, we can explain how the complexity of discriminators and generators contribute to generalization error. For $\ell_{p,q}$ and spectral weight normalization, we provide explicit guidance on how to design parameters to train robust generators. Our numerical simulations also verify that our generalization bound is reasonable.