arXiv:2604.14211v2 Announce Type: replace-cross Abstract: This thesis is an exposition of Ollivier-Ricci Curvature of metric spaces as introduced by Yann Ollivier, which is based upon the 1-Wasserste...
arXiv:2607. 22381v1 Announce Type: new Abstract: Curvature notions on graphs, particularly Ollivier-Ricci and Forman, have emerged as powerful tools for addressing fundamental issues in Graph Neural Networks (GNNs) such as oversmoothing and oversquashing, but rely almost exclusively on local edge-level comparisons and therefore fail to certify how information actually propagates over long distances.
arXiv:2604. 12211v2 Announce Type: replace Abstract: Ollivier-Ricci curvature (ORC), defined via the Wasserstein distance that captures rich geometric information, has received growing attention in both theory and applications.
arXiv:2608.27500v3 Announce Type: replace-cross Abstract: Network comparison using optimal transport is a growing area of research in network science. Unlike standard graph metrics, optimal transport...
The paper reviews the use of optimal transport for comparing undirected, unweighted graphs, focusing on three main distances: Wasserstein, Gromov-Wasserstein, and Bures-Wasserstein. It discusses closed-form solutions for the Wasserstein distance in one dimension, how transport plans identify influential nodes after perturbations, and derives spectral bounds for the Bures-Wasserstein distance to avoid full decompositions. The authors evaluate these distances on synthetic clustering data and a real-world time‑series network for anomaly detection.
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:2606. 24987v1 Announce Type: cross Abstract: Optimal transport (OT) has become a central language for comparing probability measures, but exact balanced OT is often both too rigid for data with missing, created, or destroyed mass and subject to unfavorable high-dimensional sample complexity.
arXiv:2610.04953v2 Announce Type: replace-cross Abstract: Euclidean combinatorial optimization problems (ECOPs), such as the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (...
arXiv:2608. 28262v1 Announce Type: new Abstract: Entropic optimal transport (EOT) has been shown to offer a computationally tractable approximation to exact optimal transport.
arXiv:2607. 07232v1 Announce Type: cross Abstract: Diffusion models represent a leading paradigm for graph generation, with notable impact in domains such as molecular design.
The paper introduces RicciPool, a graph pooling method that incorporates higher‑order connectivity via Ollivier‑Ricci curvature to reweight edges before spectral clustering. Unlike traditional pooling approaches that focus only on rough topology, RicciPool leverages local connection information to improve cluster assignment. Experiments on protein and social network datasets demonstrate its effectiveness.
arXiv:2607. 06646v1 Announce Type: cross Abstract: This paper introduces Diffusion Semi-Relaxed Fused Gromov-Wasserstein (DsrFGW), a novel method for graph comparison that unifies node features and structural connectivity through optimal transport.