方向性sheaf超图网络：统一学习于有向和无向超图
Directional Sheaf Hypergraph Networks: Unifying Learning on Directed and Undirected Hypergraphs
AI总结：
DSHN通过结合sheaf理论与非对称关系处理，统一并泛化了现有超图学习中的拉普拉斯矩阵，提升了超图学习的性能。
摘要：
超图提供了一种自然的方式来表示多个实体之间的高阶相互作用。尽管无向超图已被广泛研究，但能够建模定向群体相互作用的有向超图，尽管在许多应用中具有相关性，仍很少被探索。最近在这一方向上的方法往往表现出对同质性的隐含偏见，这限制了它们在异质性设置中的有效性。根植于代数拓扑中的Cellular Sheaves概念，Sheaf Neural Networks（SNNs）被引入作为克服这种缺点的有效解决方案。虽然已知有超图的泛化，但仅适用于无向超图，无法处理有向情况。在本文中，我们介绍了Directional Sheaf Hypergraph Networks（DSHN），一种将sheaf理论与在超图中对非对称关系进行原则性处理相结合的框架。从中，我们构建了Directed Sheaf Hypergraph Laplacian，一个复数运算符，通过它我们统一并泛化了图和超图学习文献中提出的许多现有拉普拉斯矩阵。在7个真实世界数据集上，针对13个基线，DSHN实现了从2%到20%的相对准确率提升，展示了在超图中对方向性的原则性处理，结合sheaves的表达能力，如何显著提高性能。
英文摘要：
Hypergraphs provide a natural way to represent higher-order interactions among multiple entities. While undirected hypergraphs have been extensively studied, the case of directed hypergraphs, which can model oriented group interactions, remains largely under-explored despite its relevance for many applications. Recent approaches in this direction often exhibit an implicit bias toward homophily, which limits their effectiveness in heterophilic settings. Rooted in the algebraic topology notion of Cellular Sheaves, Sheaf Neural Networks (SNNs) were introduced as an effective solution to circumvent such a drawback. While a generalization to hypergraphs is known, it is only suitable for undirected hypergraphs, failing to tackle the directed case. In this work, we introduce Directional Sheaf Hypergraph Networks (DSHN), a framework integrating sheaf theory with a principled treatment of asymmetric relations within a hypergraph. From it, we construct the Directed Sheaf Hypergraph Laplacian, a complex-valued operator by which we unify and generalize many existing Laplacian matrices proposed in the graph- and hypergraph-learning literature. Across 7 real-world datasets and against 13 baselines, DSHN achieves relative accuracy gains from 2% up to 20%, showing how a principled treatment of directionality in hypergraphs, combined with the expressive power of sheaves, can substantially improve performance.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
