HyperKAN: Hypergraph Representation Learning with Kolmogorov-Arnold Networks

Abstract

Hypergraph representation learning has garnered increasing attention across various domains due to its capability to model high-order relationships. Traditional methods often rely on hypergraph neural networks (HNNs) employing message passing mechanisms to aggregate vertex and hyperedge features. However, these methods are constrained by their dependence on hypergraph topology, leading to the challenge of imbalanced information aggregation, where high-degree vertices tend to aggregate redundant features, while low-degree vertices often struggle to capture sufficient structural features. To overcome the above challenges, we introduce HyperKAN, a novel framework for hypergraph representation learning that transcends the limitations of message-passing techniques. HyperKAN begins by encoding features for each vertex and then leverages Kolmogorov-Arnold Networks (KANs) to capture complex nonlinear relationships. By adjusting structural features based on similarity, our approach generates refined vertex representations that effectively addresses the challenge of imbalanced information aggregation. Experiments conducted on the real-world datasets demonstrate that HyperKAN significantly outperforms state of-the-art HNN methods, achieving nearly a 9% performance improvement on the Senate dataset.