Riemannian Convex Potential Maps

International Conference on Machine Learning (ICML)


Modeling distributions on Riemannian manifolds is a crucial component in understanding nonEuclidean 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 normalizing flows that uses convex potentials from Riemannian optimal transport. These flows 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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