arXiv Machine Learning By Xiang Gu, Huichun Zhang, Jian Sun

A Residual-Shell-Based Lower Bound for Ollivier-Ricci Curvature

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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.

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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 27

Optimal Time Complexity Algorithms for Computing General Random Walk Graph Kernels on Sparse Graphs

The paper introduces linear‑time randomized algorithms for unbiased approximation of general random walk kernels (RWKs) on sparse graphs, covering both labelled and unlabelled cases. By sampling dependent random walks and constructing novel graph embeddings in ρ^d, the method avoids building the direct product graph, enabling scaling to massive datasets that cannot fit on a single machine. The authors provide exponential concentration bounds for the estimator’s sharpness and demonstrate up to 27× speed‑ups and 128× larger graph handling compared to previous cubic‑time approaches.

By Krzysztof Choromanski, Isaac Reid, Arijit Sehanobish, Avinava Dubey