CORE MACHINE LEARNING

Riemannian Convex Potential Maps

July 18, 2021

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.

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AUTHORS

Written by

Samuel Cohen

Brandon Amos

Yaron Lipman

Publisher

ICML 2021

Research Topics

Core Machine Learning

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