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.
By Rachid Caich, Yassine Abbahaddou
arXiv:2603.13535v5 Announce Type: cross
Abstract: Evaluating Ollivier-Ricci (OR) curvature on large-scale graphs is computationally prohibitive due to the necessity of solving an optimal transport pr...
By Giorgio Micaletto, Tebe Nigrelli
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.
By Xiang Gu, Huichun Zhang, Jian Sun
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.
By James Hyun, Fran\c{c}ois G. Meyer
arXiv:2606. 17185v1 Announce Type: new Abstract: Graph neural network architectures based on the graph Laplacian approximate the Laplace-Beltrami operator, thus limiting their application to isotropic operators.
By T. Mitchell Roddenberry, Richard G. Baraniuk
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.
By Chaoqun Fei, Guoxuan Li, Tinglve Zhou, Chuanqing Wang, Yangyang Li
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...
By James Hyun, Fran\c{c}ois G. Meyer
arXiv:2203. 04711v2 Announce Type: replace Abstract: We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem.
By Dai Hai Nguyen, Koji Tsuda
The paper introduces Ricci-Diffusion, a graph denoising technique that uses curvature-guided diffusion inspired by Ricci flow. Unlike traditional similarity-driven methods, it modulates local transport in the diffusion kernel based on edge-level curvature, steering edge-weight updates toward a more regular graph geometry. The authors provide theoretical analysis showing curvature’s ability to distinguish graph structures and induce first-order corrections, and demonstrate that the method converges to a stable denoised network, improving structure recovery and downstream performance on real-world and synthetic graphs.
By Ye Fang, Chuan-Xian Ren
arXiv:2607. 19305v1 Announce Type: cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations.
By Chen Ziheng
arXiv:2607. 19305v2 Announce Type: replace-cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations.
By Chen Ziheng
arXiv:2609.37649v1 Announce Type: cross
Abstract: Many datasets carry an intrinsic directionality: citations point backward in time, cells differentiate along lineages, and traffic follows preferred...
By Gwendal Debaussart-Joniec (CB, ENS Paris Saclay), Th\'eau Blanchard (HeKA | U1346, GE Healthcare), Argyris Kalogeratos (CB, ENS Paris Saclay)