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.

翻译：本文研究了以GroupSort神经网络为判别器的Wasserstein生成对抗网络（WGANs）。研究表明，目标分布近似的误差界取决于生成器和判别器的宽度与深度（容量）以及训练样本数量。本文建立了生成分布与目标分布之间Wasserstein距离的量化泛化界。根据理论结果，WGANs对判别器容量的要求高于生成器，这与现有部分结论一致。更重要的是，若判别器强度不足，采用过深过宽（高容量）生成器的效果可能劣于低容量生成器。基于Swiss roll和MNIST数据集的数值实验结果验证了上述理论结论。