# Generalization Performance of Hypergraph Neural Networks

arXiv: https://arxiv.org/abs/2501.12554 · HTML: https://mlsanity.com/paper/2501.12554/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 67 references that are in the map.
- First posted on arXiv 22 Jan 2025.

## Builds on (most cited first, 29 of 29)

- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Invariant and Equivariant Graph Networks](https://mlsanity.com/paper/1812.09902/) (2018)
- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks](https://mlsanity.com/paper/1707.09564/) (2017)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/1905.13192/) (2019)
- [What Can Neural Networks Reason About?](https://mlsanity.com/paper/1905.13211/) (2019)
- [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)
- [HNHN: Hypergraph Networks with Hyperedge Neurons](https://mlsanity.com/paper/2006.12278/) (2020)
- [Expressive Power of Invariant and Equivariant Graph Neural Networks](https://mlsanity.com/paper/2006.15646/) (2020)
- [A PAC-Bayesian Approach to Generalization Bounds for Graph Neural Networks](https://mlsanity.com/paper/2012.07690/) (2020)
- [Hyper-SAGNN: a self-attention based graph neural network for hypergraphs](https://mlsanity.com/paper/1911.02613/) (2019)
- [Reconstruction for Powerful Graph Representations](https://mlsanity.com/paper/2110.00577/) (2021)
- [Theory of Graph Neural Networks: Representation and Learning](https://mlsanity.com/paper/2204.07697/) (2022)
- [k-hop Graph Neural Networks](https://mlsanity.com/paper/1907.06051/) (2019)
- [Ordered Subgraph Aggregation Networks](https://mlsanity.com/paper/2206.11168/) (2022)
- [Learning Theory Can (Sometimes) Explain Generalisation in Graph Neural Networks](https://mlsanity.com/paper/2112.03968/) (2021)
- [Generalization in Graph Neural Networks: Improved PAC-Bayesian Bounds on Graph Diffusion](https://mlsanity.com/paper/2302.04451/) (2023)
- [Beyond Weisfeiler-Lehman: A Quantitative Framework for GNN Expressiveness](https://mlsanity.com/paper/2401.08514/) (2024)
- [The expressive power of kth-order invariant graph networks](https://mlsanity.com/paper/2007.12035/) (2020)
- [Structural Patterns and Generative Models of Real-world Hypergraphs](https://mlsanity.com/paper/2006.07060/) (2020)
- [How Do Hyperedges Overlap in Real-World Hypergraphs? -- Patterns, Measures, and Generators](https://mlsanity.com/paper/2101.07480/) (2021)
- [One Positive Label is Sufficient: Single-Positive Multi-Label Learning with Label Enhancement](https://mlsanity.com/paper/2206.00517/) (2022)
- [I'm Me, We're Us, and I'm Us: Tri-directional Contrastive Learning on Hypergraphs](https://mlsanity.com/paper/2206.04739/) (2022)
- [Learning Hypergraph-regularized Attribute Predictors](https://mlsanity.com/paper/1503.05782/) (2015)

## Built on by (most cited first, 2 of 2)

- [DHG-Bench: A Comprehensive Benchmark for Deep Hypergraph Learning](https://mlsanity.com/paper/2508.12244/) (2025)
- [Topology-Aware PAC-Bayesian Generalization Analysis for Graph Neural Networks](https://mlsanity.com/paper/2604.10553/) (2026)

## Abstract (arXiv)

Hypergraph neural networks have been promising tools for handling learning tasks involving higher-order data, with notable applications in web graphs, such as modeling multi-way hyperlink structures and complex user interactions. Yet, their generalization abilities in theory are less clear to us. In this paper, we seek to develop margin-based generalization bounds for four representative classes of hypergraph neural networks, including convolutional-based methods (UniGCN), set-based aggregation (AllDeepSets), invariant and equivariant transformations (M-IGN), and tensor-based approaches (T-MPHN). Through the PAC-Bayes framework, our results reveal the manner in which hypergraph structure and spectral norms of the learned weights can affect the generalization bounds, where the key technical challenge lies in developing new perturbation analysis for hypergraph neural networks, which offers a rigorous understanding of how variations in the model's weights and hypergraph structure impact its generalization behavior. Our empirical study examines the relationship between the practical performance and theoretical bounds of the models over synthetic and real-world datasets. One of our primary observations is the strong correlation between the theoretical bounds and empirical loss, with statistically significant consistency in most cases.