From local to global: Hypergraph neural networks with holistic message passing

Most existing hypergraph neural networks (HNNs) follow a local message-passing paradigm, which inherently limits their receptive field and hampers their ability to capture long-range dependencies. This constraint is particularly severe in heterophilic scenarios, where we empirically observe that informative signals often reside in distant neighborhoods rather than immediate ones. To bridge this gap, we propose HyperHMP, a novel framework that shifts the focus from local aggregation to holistic message passing. By leveraging a structure-aware self-attention mechanism, HyperHMP enables direct, one-hop global information propagation across nodes and hyperedges. Specifically, we first integrate learnable positional encodings via an augmented incidence matrix to inject multi-level topological awareness. To facilitate efficient global fusion, we employ a virtual-node-assisted attention mechanism that simultaneously models node-node, node-hyperedge, and hyperedge-hyperedge interactions, effectively circumventing the information dilution typically caused by deep layer stacking. Furthermore, a hypergraph structural regularization scheme is introduced to ground the global attention within the intrinsic topology. Extensive experiments on both homophilic and heterophilic benchmarks demonstrate that HyperHMP consistently achieves state-of-the-art performance. For example, HyperHMP attains classification accuracies of 80.75% on Cora, 74.74% on Citeseer, 68.17% on Senate, and 75.17% on House, outperforming strong baselines such as HyperGT and ED-HNN by noticeable margins. These results confirm that capturing holistic structural relationships is essential for robust hypergraph representation learning. © 2026 Elsevier B.V.