arXiv:2606.07926v1 Announce Type: cross 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 to be the best determinist
Source: arXiv cs.LG — read the full report at the original publisher.