Normalizing Flows on Tori and Spheres
Danilo Jimenez Rezende,u00a0George Papamakarios,u00a0Sebastien Racaniere,u00a0Michael Albergo,u00a0Gurtej Kanwar,u00a0Phiala Shanahan,u00a0Kyle Cranmer
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.
