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.

翻译：超图为表示多个实体间的高阶交互提供了一种自然的方式。尽管无向超图已得到广泛研究，但有向超图——能够建模有向的群体交互——尽管在许多应用中具有重要意义，却仍未得到充分探索。该方向的最新方法通常隐含地偏向于同质性，这限制了它们在异质性场景中的有效性。基于代数拓扑中的胞腔层概念，层神经网络被提出作为规避此类缺陷的有效解决方案。虽然其向超图的推广已为人所知，但该推广仅适用于无向超图，无法处理有向情形。在本工作中，我们提出了有向层超图网络，这是一个将层理论与超图中非对称关系的原理性处理相结合的框架。基于此，我们构建了有向层超图拉普拉斯算子，这是一个复值算子，通过它我们统一并推广了图与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、与13个基线方法相比，有向层超图网络实现了从2%到20%的相对准确率提升，这表明对超图中方向性的原理性处理，结合层的表达能力，能够显著提高性能。