{"ID":2882582,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.09427","arxiv_id":"2508.09427","title":"Implicit Hypergraph Neural Networks: A Stable Framework for Higher-Order Relational Learning with Provable Guarantees","abstract":"Many real-world interactions are group-based rather than pairwise such as papers with multiple co-authors and users jointly engaging with items. Hypergraph neural networks have shown great promise at modeling higher-order relations, but their reliance on a fixed number of explicit message-passing layers limits long-range dependency capture and can destabilize training as depth grows. In this work, we introduce Implicit Hypergraph Neural Networks (IHGNN), which bring the implicit equilibrium formulation to hypergraphs: instead of stacking layers, IHGNN computes representations as the solution to a nonlinear fixed-point equation, enabling stable and efficient global propagation across hyperedges without deep architectures. We develop a well-posed training scheme with provable convergence, analyze the oversmoothing conditions and expressivity of the model, and derive a transductive generalization bound on hypergraphs. We further present an implicit-gradient training procedure coupled with a projection-based stabilization strategy. Extensive experiments on citation benchmarks show that IHGNN consistently outperforms strong traditional graph/hypergraph neural network baselines in both accuracy and robustness. Empirically, IHGNN is resilient to random initialization and hyperparameter variation, highlighting its strong generalization and practical value for higher-order relational learning.","short_abstract":"Many real-world interactions are group-based rather than pairwise such as papers with multiple co-authors and users jointly engaging with items. Hypergraph neural networks have shown great promise at modeling higher-order relations, but their reliance on a fixed number of explicit message-passing layers limits long-ran...","url_abs":"https://arxiv.org/abs/2508.09427","url_pdf":"https://arxiv.org/pdf/2508.09427v1","authors":"[\"Xiaoyu Li\",\"Guangyu Tang\",\"Jiaojiao Jiang\"]","published":"2025-08-13T02:06:29Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\"]","methods":"[\"Graph Neural Network\"]","has_code":false}