A simple method to evaluate support size and non-uniformity of a decoder-based generative model

Abstract

Theoretical analysis in [1] suggested that adversarially trained generative models are naturally inclined to learn distribution with low support. In particular, this effect is caused by the limited capacity of the discriminator network. To verify this claim, [2] proposed a statistical test based on the birthday paradox that partially confirmed the analysis. In this paper, we continue this line of work and develop a parameter-free and straightforward method to estimate the support size of an arbitrary decoder-based generative model. Our approach considers the decoder network from a geometric viewpoint and evaluates the support size as the volume of the manifold containing the generative model samples. Additionally, we propose a method to measure non-uniformity of a generative model that can provide additional insight into the model’s behavior. We then apply these tools to perform a quantitative comparison of common generative models.