发表机构
University of Bologna; University of Pisa; Sapienza University of Rome; University of Cambridge（博洛尼亚大学; 比萨大学; 罗马第一大学; 剑桥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对图神经网络长距离传播难题，提出ONDA框架，利用算子值信息波和二阶动力学，通过茎向敏感性分析证明交叉影响不消失，在多个基准上优于现有方法。
AI 中文摘要
有效的长距离传播仍然是图神经网络中的一个核心挑战，因为增加模型的传播深度并不能保证远处节点之间能有效相互影响。层化神经网络通过茎之间的矩阵值传输来丰富图传播；然而，这种表达能力本身并不自动意味着有效的长距离通信。我们提出了ONDA，一个基于算子值信息波的长距离图学习框架。茎值表示通过由学习到的层化传输算子控制的二阶动力学演化，将波状传播与表达性局部几何相结合。我们通过茎向敏感性分析来刻画长距离影响，并表明交叉影响永不消失。在长距离传播、严重图瓶颈、图迁移和异质性基准测试中，ONDA持续优于标量波传播、扩散层化基线和最先进的模型，证明了将波动力学与矩阵值传输耦合的益处。
英文摘要
Effective long-range propagation remains a central challenge in graph neural networks, as increasing a model's propagation depth does not guarantee that distant nodes effectively influence each other. Sheaf neural networks enrich graph propagation through matrix-valued transport between stalks; still, this expressivity alone does not automatically imply effective long-range communication. We introduce ONDA, a long-range graph learning framework based on operator-valued information waves. Stalk-valued representations evolve through second-order dynamics governed by learned sheaf transport operators, combining wave-like propagation with expressive local geometry. We characterize long-range influence through a stalk-wise sensitivity analysis and show that the cross-influence never vanishes. Across long-range propagation, severe graph bottlenecks, graph transfer, and heterophilic benchmarks, ONDA consistently improves over scalar wave propagation, diffusive sheaf baselines, and state-of-the-art models, demonstrating the benefit of coupling wave dynamics with matrix-valued transport.
