arXiv:2606. 04695v1 Announce Type: new Abstract: High-dimensional optimal transport is seldom available in closed form.
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The paper introduces a weak Gromov-Wasserstein (wGW) framework that compares source relations with relations between target conditional laws, focusing on inner-product relations and preserving conditional means. It defines the barycentric weak inner-product GW (wIGW) distance, proves existence of minimizers under finite second moments, and presents a ridge-regularized dual formulation leading to an iterative algorithm for finitely supported measures. Experiments on point clouds, graphs, and a PBMC multiome study demonstrate that mean-preserving target refinements can incur zero cost and improve atlas-based cell type transfer.
arXiv:2603. 15384v2 Announce Type: replace-cross Abstract: We improve and extend persistence spheres, introduced in~\cite{pegoraro2025persistence}.
arXiv:2606. 02047v1 Announce Type: cross Abstract: We introduce Convex Distance Operator Transport (CDOT), the first convex optimal transport framework that aligns distributions across heterogeneous domains by jointly preserving feature correspondence and intrinsic geometric structure.
arXiv:2605. 09916v2 Announce Type: replace-cross Abstract: We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal transport in large-scale, non-Euclidean datasets.
arXiv:2609. 26647v1 Announce Type: cross Abstract: We study statistical rates in entropic optimal transport in the semi-discrete regime where one measure has finite support and the other is subGaussian.
arXiv:2605. 14981v2 Announce Type: replace Abstract: Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system.