AISTATS 2020poster62 citations
The Expressive Power of a Class of Normalizing Flow Models
Zhifeng Kong, Kamalika Chaudhuri
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.
BibTeX
@InProceedings{pmlr-v108-kong20a,
title = {The Expressive Power of a Class of Normalizing Flow Models},
author = {Kong, Zhifeng and Chaudhuri, Kamalika},
booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics},
pages = {3599--3609},
year = {2020},
editor = {Chiappa, Silvia and Calandra, Roberto},
volume = {108},
series = {Proceedings of Machine Learning Research},
month = {26--28 Aug},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v108/kong20a/kong20a.pdf},
url = {https://proceedings.mlr.press/v108/kong20a.html},
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. }
}