Exploring Intrinsic Structures of Hyperedges as Point Clouds

Lige Zhang, Dongmian Zou

Keywords: Hypergraph, Kernel points, Kernel Attention Message Passing

Abstract: Hypergraph neural networks (HNNs) provide a powerful framework for modeling high-order relationships in complex data. However, existing approaches often overlook the intrinsic patterns carried by hyperedges. Some methods simplify a hyperedge as a fully connected subgraph or treat it as an intermediate node-like entity, which limits the expressivity of the resulting models and neglects the potentially rich information of hyperedges. In this work, we offer a new perspective for hypergraph modeling by modeling a hyperedge as a point cloud with learnable features. Building on this view, we present a novel Hypergraph Kernel Network (HypKN) framework for hypergraph representation learning, which fully exploits the intrinsic hypergraph structure. The core component in HypKN is a Kernel Attention Message Passing (KAMP) module, which mimics the classical convolution operation defined for non-Euclidean data structures and enjoys provable stability results. We evaluate HypKN on ten real-world and synthetic hypergraph datasets for node classification, where it consistently outperforms classical HNN baselines and achieves state-of-the-art performance on several benchmarks.

Submission Type: Extended abstract (max 4 main pages).

Submission Number: 64