发表机构
LIX, École Polytechnique IP Paris（巴黎综合理工学院LIX）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究通过引入熵曲率解决图神经网络中信息长距离传播问题，定义弱熵曲率代理并推导相关不等式和界，转化为实用机制，经基准测试验证了该方法在解决过平滑和过挤压等问题上的有效性。
AI 中文摘要
图上的曲率概念，特别是奥利维耶-里奇曲率和福尔曼曲率，已成为解决图神经网络（GNNs）中诸如过平滑和过挤压等基本问题的有力工具，但几乎完全依赖于局部边级比较，因此无法证明信息如何在长距离上实际传播。我们引入了熵曲率，这是一种基于传输的全局曲率，通过沿瓦瑟斯坦测地线的熵的位移凸性将洛特-斯特姆-维拉尼框架扩展到图而获得。我们定义了一个易于处理的弱熵曲率代理，它为全局熵曲率提供下界，并由此推导出（i）一个控制过平滑的庞加莱型不等式，（ii）一个传输-熵泛化界以及（iii）一个扩展悖论证明在大图中稀疏性、强谱扩展和正熵曲率不能共存，将过平滑和过挤压统一为单个曲率谱的相反两端。我们将该理论转化为三种实用机制，即E-Gate聚合器、ENT结构编码和中点完成重新布线（MCR），并在六个节点分类基准和图分类上针对SDRF、FoSR、BORF、LCP和图里奇流对它们进行基准测试。
英文摘要
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.
