HGNN Shield: Defending Hypergraph Neural Networks Against High-Order Structure Attack

Hypergraph Neural Networks (HGNNs) are crucial in modeling complex high-order correlations in diverse domains, utilizing hyperedges that connect multiple vertices. However, their susceptibility to structural attacks and irrational connections can disrupt message propagation and degrade performance. To address these issues, we introduce the HGNN Shield, a defense framework incorporating two key modules: Hyperedge-Dependent Estimation (HDE) and High-Order Shield (HOS). The HDE module prioritizes vertex dependencies within hyperedges and adapts traditional connectivity measures to hypergraphs, facilitating precise structural modifications. This adaptation allows for a nuanced assessment of vertex relationships within hyperedges, contributing theoretically by extending classical graph-based connection dependency measures to hypergraphs. Following HDE, the HOS module, positioned before convolutional layers, consists of three submodules: Hyperpath Cut, Hyperpath Link, and Hyperpath Refine. These components collectively detect, disconnect, and refine adversarial connections, ensuring robust message propagation. The theoretical contribution of the HOS module lies in maintaining hyperpath integrity and learning trajectory under adversarial conditions, providing a certifiable defense mechanism against high-order structural attacks. Experiments on six hypergraph datasets indicate that HGNN Shield significantly enhances robustness and maintains data integrity against targeted attacks, outperforming existing methods (an average performance improvement of 9.33% over other methods). Our framework not only improves HGNN reliability but also advances security in hypergraph-based applications.