Riemannian Convex Potential Maps with python
rcpm
This repository is by Brandon Amos, Samuel Cohen and Yaron Lipman and contains the JAX source code to reproduce the experiments in our ICML 2021 paper on Riemannian Convex Potential Maps.
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.
