Normalizing Flows on Tori and Spheres
This work addresses a domain-specific problem in machine learning for tasks involving complex geometries, representing an incremental advancement by extending normalizing flows to new spaces.
The paper tackles the problem of building expressive distributions on non-Euclidean spaces like tori and spheres, which are relevant for applications involving angles, by proposing and comparing flows that are expressive and numerically stable, with results including recursive construction from simpler spaces.
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.