Barycentric Projections of Optimal Transport Plans on Riemannian Manifolds
arXiv:2606.07926v1 Announce Type: new Abstract: Optimal transport couplings are probabilistic objects, while many learning pipelines require deterministic maps. In Euclidean space, barycentric projection converts a coupling into a map by taking conditional expectations, but on a Riemannian manifold curvature and cut loci make this operation nontrivial. We develop a framework for barycentric projections of transport couplings on Riemannian manifolds. The intrinsic projection maps each source point to the conditional Fr’echet mean of its destination law and is shown […]