Generative Adversarial Network Performance in Low-Dimensional Settings

A generative adversarial network (GAN) is an artifcial neural network with a distinctive training architecture, designed to create examples that faithfully reproduce a target distribution. GANs have recently had particular success in applications involving high-dimensional distributions in areas such as image processing. Little work has been reported for low dimensions, where properties of GANs may be better identifed and understood. We studied GAN performance in simulated low-dimensional settings, allowing us to transparently assess effects of target distribution complexity and training data sample size on GAN performance in a simple experiment. This experiment revealed two important forms of GAN error, tail underflling and bridge bias, where the latter is analogous to the tunneling observed in high-dimensional GANs.