arXiv AI By Eleanor P Wiesler

Ollivier-Ricci Curvature of Riemannian Manifolds and Directed Graphs with Applications to Graph Neural Networks

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arXiv Machine Learning
Jul 27

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature

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 Machine Learning
Aug 31

Optimal Transport for Network Comparison: A Review with Machine Learning Applications

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 AI
Sep 15

Geometric Flow enhanced Graph Coarsening

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