The Expressive Power of a Class of Normalizing Flow Models

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Zhifeng Kong, Kamalika Chaudhuri ;
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:3599-3609, 2020.

Abstract

Normalizing flows have received a great deal of recent attention as they allow flexible generative modeling as well as easy likelihood computation. While a wide variety of flow models have been proposed, there is little formal understanding of the representation power of these models. In this work, we study some basic normalizing flows and rigorously establish bounds on their expressive power. Our results indicate that while these flows are highly expressive in one dimension, in higher dimensions their representation power may be limited, especially when the flows have moderate depth.

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