S2-HGNN: Scale-Aware Hypergraph Node Classification with Spectral Inductive Bias

Existing methods for hypergraph node classification usually rely on local message passing and use a unified strategy for topological modeling across hyperedges of different sizes. However, they have two limitations in semi-supervised settings. First, representation learning mainly depends on local neighborhoods, making it difficult to incorporate global topological information. Second, a unified structural modeling strategy cannot effectively handle both small and large hyperedges. Small hyperedges require modeling fine-grained local relations, while large hyperedges need sparse group-level structure. To address these issues, we propose S2-HGNN, a scale-aware hypergraph node classification framework with spectral inductive bias for semi-supervised learning. S2-HGNN first injects global topological information into the input features using complementary hypergraph spectral operators. It then constructs different auxiliary topologies based on hyperedge size. For small hyperedges, it uses Top-k constrained clique expansion to preserve representative local relations. For large hyperedges, it uses star expansion to reduce redundant connections while preserving sparse group-level structure. Finally, node representations are jointly learned from the original hypergraph backbone and the two auxiliary branches, and final predictions are obtained through node-level adaptive fusion. Experiments on multiple public datasets show that the proposed method consistently outperforms strong baselines and exhibits superior robustness under feature perturbations.