  In this paper, we show that the approximation for distributions by
Wasserstein GAN depends on both the width/depth (capacity) of generators and
discriminators, as well as the number of samples in training. A quantified
generalization bound is developed for Wasserstein distance between the
generated distribution and the target distribution. It implies that with
sufficient training samples, for generators and discriminators with proper
number of width and depth, the learned Wasserstein GAN can approximate
distributions well. We discover that discriminators suffer a lot from the curse
of dimensionality, meaning that GANs have higher requirement for the capacity
of discriminators than generators, which is consistent with the theory in
arXiv:1703.00573v5 [cs.LG]. More importantly, overly deep (high capacity)
generators may cause worse results (after training) than low capacity
generators if discriminators are not strong enough. Different from Wasserstein
GAN in arXiv:1701.07875v3 [stat.ML], we adopt GroupSort neural networks
arXiv:1811.05381v2 [cs.LG] in the model for their better approximation to
1-Lipschitz functions. Compared to some existing generalization (convergence)
analysis of GANs, we expect our work are more applicable.
