[2510.04727] Directional Sheaf Hypergraph Networks: Unifying Learning on Directed and Undirected Hypergraphs

Computer Science > Machine Learning arXiv:2510.04727 (cs) [Submitted on 6 Oct 2025 (v1), last revised 1 Mar 2026 (this version, v2)] Title:Directional Sheaf Hypergraph Networks: Unifying Learning on Directed and Undirected Hypergraphs Authors:Emanuele Mule, Stefano Fiorini, Antonio Purificato, Federico Siciliano, Stefano Coniglio, Fabrizio Silvestri View a PDF of the paper titled Directional Sheaf Hypergraph Networks: Unifying Learning on Directed and Undirected Hypergraphs, by Emanuele Mule and 5 other authors View PDF HTML (experimental) Abstract: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...