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
6d ago

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 Machine Learning
Aug 19

Network Denoising Revisited: A Ricci-Flow-Inspired Graph Diffusion Method

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