Universal Approximation of Residual Flows in Maximum Mean Discrepancy

Zhifeng Kong, Kamalika Chaudhuri

Keywords: Residual flows, normalizing flows, Maximum Mean Discrepancy, universal approximation, expressiveness

TL;DR: We prove universal approximation of residual flows in maximum mean discrepancy under certain conditions.

Abstract: Normalizing flows are a class of flexible deep generative models that offer easy likelihood computation. Despite their empirical success, there is little theoretical understanding of their expressiveness. In this work, we study residual flows, a class of normalizing flows composed of Lipschitz residual blocks. We prove residual flows are universal approximators in maximum mean discrepancy. We provide upper bounds on the number of residual blocks to achieve approximation under different assumptions.