  Studied here are Wasserstein generative adversarial networks (WGANs) with
GroupSort neural networks as their discriminators. It is shown that the error
bound of the approximation for the target distribution depends on the width and
depth (capacity) of the generators and discriminators and the number of samples
in training. A quantified generalization bound is established for the
Wasserstein distance between the generated and target distributions. According
to the theoretical results, WGANs have a higher requirement for the capacity of
discriminators than that of generators, which is consistent with some existing
results. More importantly, the results with overly deep and wide
(high-capacity) generators may be worse than those with low-capacity generators
if discriminators are insufficiently strong. Numerical results obtained using
Swiss roll and MNIST datasets confirm the theoretical results.
