2021/06/18 by Samuel N. Cohen, Brandon Amos, Cohen, Samuel +3 · 1 citation
Computer Science · #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2106.10272
openalex publication_date 2021/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Modeling distributions on Riemannian manifolds is a crucial component in understanding non-Euclidean data that arises, e.g., in physics and geology. The budding approaches in this space are limited by representational and computational tradeoffs. We propose and study a class of flows that uses convex potentials from Riemannian optimal transport. These are universal and can model distributions on any compact Riemannian manifold without requiring domain knowledge of the manifold to be integrated into the architecture. We demonstrate that these flows can model standard distributions on spheres, and tori, on synthetic and geological data. Our source code is freely available online at http://github.com/facebookresearch/rcpm