# Beyond Convolution: Advancing Hypergraph Neural Networks with Hypergraph U-Nets

arXiv: https://arxiv.org/abs/2606.09051 · HTML: https://mlsanity.com/paper/2606.09051/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 42 of its 68 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Builds on (most cited first, 30 of 42)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Enhancing Graph Neural Network-based Fraud Detectors against Camouflaged Fraudsters](https://mlsanity.com/paper/2008.08692/) (2020)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations](https://mlsanity.com/paper/1911.07979/) (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)
- [Community detection in networks: A user guide](https://mlsanity.com/paper/1608.00163/) (2016)
- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Self-Supervised Hypergraph Convolutional Networks for Session-based Recommendation](https://mlsanity.com/paper/2012.06852/) (2020)
- [Structural Entropy Guided Graph Hierarchical Pooling](https://mlsanity.com/paper/2206.13510/) (2022)
- [Generative hypergraph clustering: from blockmodels to modularity](https://mlsanity.com/paper/2101.09611/) (2021)
- [Reinforced Neighborhood Selection Guided Multi-Relational Graph Neural Networks](https://mlsanity.com/paper/2104.07886/) (2021)
- [The expressive power of pooling in Graph Neural Networks](https://mlsanity.com/paper/2304.01575/) (2023)
- [Second-Order Pooling for Graph Neural Networks](https://mlsanity.com/paper/2007.10467/) (2020)
- [Inhomogeneous Hypergraph Clustering with Applications](https://mlsanity.com/paper/1709.01249/) (2017)

## Abstract (arXiv)

Convolutions have successfully transitioned from image processing to the complex realm of non-Euclidean higher-order domains, particularly in hypergraphs. Despite the success in convolution, the exploration of a popular architecture named U-Net remains largely unexplored for hypergraph data due to the lack of well-defined pooling and unpooling operations. This work pioneers the study of U-Net architectures for hypergraph data, addressing the critical challenge of designing effective pooling and unpooling operations that retain maximal structural information from the input hypergraph. Motivated by hierarchical clustering, we propose to construct the pooling and unpooling operators all at once by cutting the clustering dendrogram at different granularities, named the Parallel Hierarchical Pooling (PHPool) and Unpooling (PHUnpool) operators. Unlike existing pooling methods that risk local structural damage through a sequential learning procedure, our PHPool operators are designed in a global and parallel manner to ensure fidelity to the original hypergraph structure with efficient computation while the PHUnpool operators are tailored to perform inverse operations of the PHPools for hypergraph reconstruction. We validate our model through hypergraph reconstruction simulation, hypergraph classification, and node-level anomaly detection, where it demonstrates superior performance over existing state-of-the-art graph and hypergraph deep learning methods.