Directional Sheaf Hypergraph Networks: Unifying Learning on Directed and Undirected Hypergraphs
This work addresses a gap in hypergraph learning for applications requiring directionality, offering a novel framework that improves performance in heterophilic settings.
The paper tackles the problem of learning on directed hypergraphs, which are under-explored but relevant for modeling oriented group interactions, by introducing Directional Sheaf Hypergraph Networks (DSHN) that unify and generalize existing Laplacian matrices, achieving relative accuracy gains from 2% to 20% across 7 real-world datasets against 13 baselines.
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.