Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature
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Computer Science > Machine Learning
Title:Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature
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. We introduce Entropic Curvature, a global, transport-based curvature obtained by extending the Lott-Sturm-Villani framework to graphs through the displacement convexity of entropy along Wasserstein geodesics. We define a tractable Weak Entropic Curvature proxy that lower-bounds the global entropic curvature, and from it derive (i) a Poincare-type inequality controlling oversmoothing, (ii) a transport-entropy generalization bound, and (iii) an expansion paradox proving that sparsity, strong spectral expansion, and positive entropic curvature cannot coexist in large graphs, unifying oversmoothing and oversquashing as opposite ends of a single curvature spectrum. We translate the theory into three practical mechanisms, the E-Gate aggregator, the ENT structural encoding, and Midpoint-Completion Rewiring (MCR), and benchmark them against SDRF, FoSR, BORF, LCP, and Graph Ricci Flow on six node-classification benchmarks, and graph-classification.
| Subjects: | Machine Learning (cs.LG); Social and Information Networks (cs.SI); Machine Learning (stat.ML) |
| Cite as: | arXiv:2607.22381 [cs.LG] |
| (or arXiv:2607.22381v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2607.22381
arXiv-issued DOI via DataCite (pending registration)
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Submission history
From: Yassine Abbahaddou [view email][v1] Fri, 24 Jul 2026 15:07:37 UTC (577 KB)
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