Riemannian Convex Potential Maps

• URL: http://arxiv.org/abs/2106.10272v1
• Date: Fri, 18 Jun 2021 17:59:06 GMT
• Title: Riemannian Convex Potential Maps
• Authors: Samuel Cohen, Brandon Amos, Yaron Lipman
• Abstract summary: We propose and study a class of flows that uses convex potentials from Riemannian optimal transport. We demonstrate that these flows can model standard distributions on spheres, and tori, on synthetic and geological data.
• Score: 28.39224890275125
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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

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