AI RESEARCH
Sobolev--Ricci Curvature
arXiv CS.LG
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ArXi:2603.12652v1 Announce Type: new Ricci curvature is a fundamental concept in differential geometry for encoding local geometric structure, and its graph-based analogues have recently gained prominence as practical tools for reweighting, pruning, and reshaping network geometry. We propose Sobole-Ricci Curvature (SRC), a graph Ricci curvature canonically induced by Sobole transport geometry, which admits efficient evaluation via a tree-metric Sobole structure on neighborhood measures.