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

2026-06-08

AI Summary

This work addresses the absence of effective U-Net architectures for hypergraph deep learning, a gap primarily caused by the difficulty in defining structure-preserving pooling and unpooling operations. The authors propose the first hypergraph-specific U-Net framework, introducing a parallel hierarchical clustering mechanism to construct globally consistent pooling (PHPool) and unpooling (PHUnpool) operators. These operators effectively retain structural information from the original hypergraph across multiscale representations, thereby avoiding local structural degradation and significantly enhancing representation fidelity. Experimental results demonstrate that the proposed model consistently outperforms existing graph and hypergraph neural network approaches across multiple tasks, including hypergraph reconstruction, classification, and node-level anomaly detection.

Abstract

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.

Problem

• hypergraph
• U-Net
• pooling
• unpooling
• structural information

Innovation

• Hypergraph U-Net
• Parallel Hierarchical Pooling
• PHUnpool
• Higher-order Structure
• Hypergraph Neural Networks