arXiv：cs.LG· Jan-Willem Van Looy, Alessandro Trenta, Alessio Gravina, Alessio Borgi, Ferdinando Zanchetta, Pietro Li\`o, Davide Bacciu, Rita Fioresi·· 4 小时前AI 评分34
ONDA：基于层（sheaf）的振荡神经动力学实现图神经网络长程传播
Oscillatory Neural Dynamics over Sheaves
AI 导读
研究者提出 ONDA，一个基于算子值信息波的长程图学习框架，stalks 表示通过由学习到的 sheaf 传输算子驱动的二阶动力学演化，将波状传播与局部几何表达结合。stalk 级敏感性分析显示其交叉影响永不消失，在长程传播、严重图瓶颈、图迁移和异配基准上，ONDA 持续优于标量波传播、扩散式 sheaf 基线及 SOTA 模型。
正文
Abstract: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.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.10018 [cs.LG] |
| (or arXiv:2610.10018v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.10018 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Alessio Gravina [view email]
[v1]
Wed, 7 Oct 2026 13:08:17 UTC (288 KB)
来源：arXiv：cs.LG · arxiv.org