# Sheaf Hypergraph Networks

arXiv: https://arxiv.org/abs/2309.17116 · HTML: https://mlsanity.com/paper/2309.17116/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 63 references that are in the map.
- First posted on arXiv 29 Sep 2023.

## Builds on (most cited first, 30 of 36)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [Videos as Space-Time Region Graphs](https://mlsanity.com/paper/1806.01810/) (2018)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [Contextual Stochastic Block Models](https://mlsanity.com/paper/1807.09596/) (2018)
- [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)
- [Fake News Detection on Social Media using Geometric Deep Learning](https://mlsanity.com/paper/1902.06673/) (2019)
- [HNHN: Hypergraph Networks with Hyperedge Neurons](https://mlsanity.com/paper/2006.12278/) (2020)
- [Sheaf Neural Networks](https://mlsanity.com/paper/2012.06333/) (2020)
- [Sheaf Neural Networks with Connection Laplacians](https://mlsanity.com/paper/2206.08702/) (2022)
- [Learning Multi-Granular Hypergraphs for Video-Based Person Re-Identification](https://mlsanity.com/paper/2104.14913/) (2021)
- [HyperSAGE: Generalizing Inductive Representation Learning on Hypergraphs](https://mlsanity.com/paper/2010.04558/) (2020)
- [Generative hypergraph clustering: from blockmodels to modularity](https://mlsanity.com/paper/2101.09611/) (2021)
- [A Non-Asymptotic Analysis of Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2212.10701/) (2022)
- [Equivariant Hypergraph Diffusion Neural Operators](https://mlsanity.com/paper/2207.06680/) (2022)
- [SkipGNN: Predicting Molecular Interactions with Skip-Graph Networks](https://mlsanity.com/paper/2004.14949/) (2020)
- [The Total Variation on Hypergraphs - Learning on Hypergraphs Revisited](https://mlsanity.com/paper/1312.5179/) (2013)
- [Evolutionary dynamics of higher-order interactions in social networks](https://mlsanity.com/paper/2001.10313/) (2020)
- [High-Order Pooling for Graph Neural Networks with Tensor Decomposition](https://mlsanity.com/paper/2205.11691/) (2022)

## Built on by (most cited first, 30 of 34)

- [Copresheaf Topological Neural Networks: A Generalized Deep Learning Framework](https://mlsanity.com/paper/2505.21251/) (2025)
- [Cooperative Sheaf Neural Networks](https://mlsanity.com/paper/2507.00647/) (2025)
- [Multimodal Cancer Survival Analysis via Hypergraph Learning with Cross-Modality Rebalance](https://mlsanity.com/paper/2505.11997/) (2025)
- [Heterogeneous Sheaf Neural Networks](https://mlsanity.com/paper/2409.08036/) (2024)
- [Polynomial Neural Sheaf Diffusion: A Spectral Filtering Approach on Cellular Sheaves](https://mlsanity.com/paper/2512.00242/) (2025)
- [Training-Free Message Passing for Learning on Hypergraphs](https://mlsanity.com/paper/2402.05569/) (2024)
- [Sheaf HyperNetworks for Personalized Federated Learning](https://mlsanity.com/paper/2405.20882/) (2024)
- [Bayesian Sheaf Neural Networks](https://mlsanity.com/paper/2410.09590/) (2024)
- [DHG-Bench: A Comprehensive Benchmark for Deep Hypergraph Learning](https://mlsanity.com/paper/2508.12244/) (2025)
- [DeepSN: A Sheaf Neural Framework for Influence Maximization](https://mlsanity.com/paper/2412.12416/) (2024)
- [Sheaves Reloaded: A Directional Awakening](https://mlsanity.com/paper/2506.02842/) (2025)
- [Directional Sheaf Hypergraph Networks: Unifying Learning on Directed and Undirected Hypergraphs](https://mlsanity.com/paper/2510.04727/) (2025)
- [SPHINX: Structural Prediction using Hypergraph Inference Network](https://mlsanity.com/paper/2410.03208/) (2024)
- [HGFormer: Topology-Aware Vision Transformer with HyperGraph Learning](https://mlsanity.com/paper/2504.02440/) (2025)
- [Hypergraph Neural Sheaf Diffusion: A Symmetric Simplicial Set Framework for Higher-Order Learning](https://mlsanity.com/paper/2505.05702/) (2025)
- [Hypergraph Neural Diffusion: A PDE-Inspired Framework for Hypergraph Message Passing](https://mlsanity.com/paper/2604.10955/) (2026)
- [Sheaf Graph Neural Networks via PAC-Bayes Spectral Optimization](https://mlsanity.com/paper/2508.00357/) (2025)
- [BHyGNN+: Unsupervised Representation Learning for Heterophilic Hypergraphs](https://mlsanity.com/paper/2602.14919/) (2026)
- [Heterophily-Agnostic Hypergraph Neural Networks with Riemannian Local Exchanger](https://mlsanity.com/paper/2603.00599/) (2026)
- [Dirac-Equation Signal Processing: Physics Boosts Topological Machine Learning](https://mlsanity.com/paper/2412.05132/) (2024)
- [On the Sheafification of Higher-Order Message Passing](https://mlsanity.com/paper/2509.23020/) (2025)
- [Dynamic Sheaf Diffusion Networks with Adaptive Local Structure for Heterogeneous Spatio-Temporal Graph Learning](https://mlsanity.com/paper/2604.11275/) (2026)
- [HyperKAN: Hypergraph Representation Learning with Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2503.12365/) (2025)
- [How Particle System Theory Enhances Hypergraph Message Passing](https://mlsanity.com/paper/2505.18505/) (2025)
- [Disentangling Hyperedges through the Lens of Category Theory](https://mlsanity.com/paper/2510.16289/) (2025)
- [The WidthWall: A Strict Expressivity Hierarchy for Hypergraph Neural Networks](https://mlsanity.com/paper/2605.13690/) (2026)
- [Hypergraph Pattern Machine: Compositional Tokenization for Higher-Order Interactions](https://mlsanity.com/paper/2605.16527/) (2026)
- [Gaussian Sheaf Neural Networks](https://mlsanity.com/paper/2605.21435/) (2026)
- [SheafStain: Sheaf-Theoretic Schr"odinger Bridge for Spatially and Biologically Coherent Virtual Staining](https://mlsanity.com/paper/2606.11846/) (2026)
- [From Diffusion to Reaction-Diffusion: A Dynamical-Systems View of Oversmoothing in Hypergraph Neural Networks](https://mlsanity.com/paper/2607.15773/) (2026)

## Abstract (arXiv)

Higher-order relations are widespread in nature, with numerous phenomena involving complex interactions that extend beyond simple pairwise connections. As a result, advancements in higher-order processing can accelerate the growth of various fields requiring structured data. Current approaches typically represent these interactions using hypergraphs. We enhance this representation by introducing cellular sheaves for hypergraphs, a mathematical construction that adds extra structure to the conventional hypergraph while maintaining their local, higherorder connectivity. Drawing inspiration from existing Laplacians in the literature, we develop two unique formulations of sheaf hypergraph Laplacians: linear and non-linear. Our theoretical analysis demonstrates that incorporating sheaves into the hypergraph Laplacian provides a more expressive inductive bias than standard hypergraph diffusion, creating a powerful instrument for effectively modelling complex data structures. We employ these sheaf hypergraph Laplacians to design two categories of models: Sheaf Hypergraph Neural Networks and Sheaf Hypergraph Convolutional Networks. These models generalize classical Hypergraph Networks often found in the literature. Through extensive experimentation, we show that this generalization significantly improves performance, achieving top results on multiple benchmark datasets for hypergraph node classification.