High-Pass Matters: Theoretical Insights and Sheaflet-Based Design for Hypergraph Neural Networks

Hypergraph neural networks (HGNNs) have shown great potential in modeling higher-order relationships among multiple entities. However, most existing HGNNs primarily emphasize low-pass filtering while neglecting the role of high-frequency information. In this work, we present a theoretical investigation into the spectral behavior of HGNNs and prove that combining both low-pass and high-pass components leads to more expressive and effective models. Notably, our analysis highlights that high-pass signals play a crucial role in capturing local discriminative structures within hypergraphs. Guided by these insights, we propose a novel sheaflet-based HNNs that integrates cellular sheaf theory and framelet transforms to preserve higher-order dependencies while enabling multi-scale spectral decomposition. This framework explicitly emphasizes high-pass components, aligning with our theoretical findings. Extensive experiments on benchmark datasets demonstrate the superiority of our approach over existing methods, validating the importance of high-frequency information in hypergraph learning.

Authors

• Ming Li
• Yujie Fang School of Computer Science and Technology, Zhejiang Normal University Zhejiang Key Laboratory of Intelligent Education Technology and Application, Zhejiang Normal University
• Dongrui Shen Department of Mathematics, City University of Hong Kong
• Han Feng Department of Mathematics, City University of Hong Kong
• Xiaosheng Zhuang Department of Mathematics, City University of Hong Kong
• Kelin Xia School of Physical & Mathematical Sciences, Nanyang Technological University
• Pietro Lio

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