# Directional Sheaf Hypergraph Networks: Unifying Learning on Directed and Undirected Hypergraphs

arXiv: https://arxiv.org/abs/2510.04727 · HTML: https://mlsanity.com/paper/2510.04727/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 52 references that are in the map.
- First posted on arXiv 6 Oct 2025.

## Builds on (most cited first, 24 of 24)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (2019)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [UniGNN: a Unified Framework for Graph and Hypergraph Neural Networks](https://mlsanity.com/paper/2105.00956/) (2021)
- [You are AllSet: A Multiset Function Framework for Hypergraph Neural Networks](https://mlsanity.com/paper/2106.13264/) (2021)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [HNHN: Hypergraph Networks with Hyperedge Neurons](https://mlsanity.com/paper/2006.12278/) (2020)
- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [Simplicial Closure and higher-order link prediction](https://mlsanity.com/paper/1802.06916/) (2018)
- [Equivariant Hypergraph Diffusion Neural Operators](https://mlsanity.com/paper/2207.06680/) (2022)
- [Sheaf Hypergraph Networks](https://mlsanity.com/paper/2309.17116/) (2023)
- [Semi-supervised Hypergraph Node Classification on Hypergraph Line Expansion](https://mlsanity.com/paper/2005.04843/) (2020)
- [Nonlinear Higher-Order Label Spreading](https://mlsanity.com/paper/2006.04762/) (2020)
- [Preventing Over-Smoothing for Hypergraph Neural Networks](https://mlsanity.com/paper/2203.17159/) (2022)
- [Hypergraph Convolutional Networks via Equivalency between Hypergraphs and Undirected Graphs](https://mlsanity.com/paper/2203.16939/) (2022)
- [Hypergraph Neural Networks through the Lens of Message Passing: A Common Perspective to Homophily and Architecture Design](https://mlsanity.com/paper/2310.07684/) (2023)
- [Classification in biological networks with hypergraphlet kernels](https://mlsanity.com/paper/1703.04823/) (2017)
- [Sheaf4Rec: Sheaf Neural Networks for Graph-based Recommender Systems](https://mlsanity.com/paper/2304.09097/) (2023)
- [AI-driven Hypergraph Network of Organic Chemistry: Network Statistics and Applications in Reaction Classification](https://mlsanity.com/paper/2208.01647/) (2022)

## Built on by (most cited first, 4 of 4)

- [Polynomial Neural Sheaf Diffusion: A Spectral Filtering Approach on Cellular Sheaves](https://mlsanity.com/paper/2512.00242/) (2025)
- [ChemHyperMag: Physics-informed magnetic hypergraph learning improves molecular ADMET prediction](https://mlsanity.com/paper/2607.18332/) (2026)
- [Mitigating Over-squashing without Rewiring: A Sheaf Effective Resistance Perspective](https://mlsanity.com/paper/2610.04157/) (2026)
- [Gluing Local Contexts into Global Meaning: A Sheaf-Theoretic Decomposition of Transformer Representations](https://mlsanity.com/paper/2610.17117/) (2026)

## Abstract (arXiv)

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.