Normalizing Flows on Tori and Spheres

TL;DR

This paper develops and compares expressive, numerically stable normalizing flows tailored for complex geometric spaces like tori and spheres, extending flow models beyond Euclidean domains.

Contribution

It introduces recursive construction methods for normalizing flows on tori and spheres, addressing the challenge of modeling distributions on non-Euclidean geometries.

Findings

Flows on tori and spheres are effective for complex geometric data.

Recursive construction ensures stability and expressiveness.

Comparison shows advantages over Euclidean-based flows.

Abstract

Normalizing flows are a powerful tool for building expressive distributions in high dimensions. So far, most of the literature has concentrated on learning flows on Euclidean spaces. Some problems however, such as those involving angles, are defined on spaces with more complex geometries, such as tori or spheres. In this paper, we propose and compare expressive and numerically stable flows on such spaces. Our flows are built recursively on the dimension of the space, starting from flows on circles, closed intervals or spheres.