  Generative adversarial networks (GANs) have attracted intense interest in the
field of generative models. However, few investigations focusing either on the
theoretical analysis or on algorithm design for the approximation ability of
the generator of GANs have been reported. This paper will first theoretically
analyze GANs' approximation property. Similar to the universal approximation
property of the fully connected neural networks with one hidden layer, we prove
that the generator with the input latent variable in GANs can universally
approximate the potential data distribution given the increasing hidden
neurons. Furthermore, we propose an approach named stochastic data generation
(SDG) to enhance GANs'approximation ability. Our approach is based on the
simple idea of imposing randomness through data generation in GANs by a prior
distribution on the conditional probability between the layers. SDG approach
can be easily implemented by using the reparameterization trick. The
experimental results on synthetic dataset verify the improved approximation
ability obtained by this SDG approach. In the practical dataset, four GANs
using SDG can also outperform the corresponding traditional GANs when the model
architectures are smaller.
