mlsanityData to 7 Oct 2026

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

arXiv 2607.22381 ↗First posted 24 Jul 2026cs.LG cs.SI stat.MLcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 25 of its 72 references that are in the map. First posted on arXiv 24 Jul 2026.

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25 of 72 references.

References · 25

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
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  9. 2020A Note on Over-Smoothing for Graph Neural Networkscited by 245
  10. 2019Constant Curvature Graph Convolutional Networkscited by 106
  11. 2022FoSR: First-order spectral rewiring for addressing oversquashing in GNNscited by 104
  12. 2022Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvaturecited by 96
13 more
  1. 2022How Powerful are K-hop Message Passing Graph Neural Networkscited by 90
  2. 2019Community Detection on Networks with Ricci Flowcited by 62
  3. 2023Towards Understanding the Generalization of Graph Neural Networkscited by 41
  4. 2023Mitigating Over-Smoothing and Over-Squashing using Augmentations of Forman-Ricci Curvaturecited by 39
  5. 2023Graph Positional Encoding via Random Feature Propagationcited by 30
  6. 2021Curvature Graph Neural Networkcited by 24
  7. 2021Learning Parametrised Graph Shift Operatorscited by 16
  8. 2024A Manifold Perspective on the Statistical Generalization of Graph Neural Networkscited by 16
  9. 2016Configuring Random Graph Models with Fixed Degree Sequencescited by 15
  10. 2023Curvature-based Clustering on Graphscited by 14
  11. 2023Effective Structural Encodings via Local Curvature Profilescited by 13
  12. 2024The Effectiveness of Curvature-Based Rewiring and the Role of Hyperparameters in GNNs Revisitedcited by 11
  13. 2026Which Graph Shift Operator? A Spectral Answer to an Empirical Questioncited by 1

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