Implicit Hypergraph Neural Networks: A Stable Framework for Higher-Order Relational Learning with Provable Guarantees

• URL: http://arxiv.org/abs/2508.09427v1
• Date: Wed, 13 Aug 2025 02:06:29 GMT
• Title: Implicit Hypergraph Neural Networks: A Stable Framework for Higher-Order Relational Learning with Provable Guarantees
• Authors: Xiaoyu Li, Guangyu Tang, Jiaojiao Jiang,
• Abstract summary: We introduce Implicit Hypergraph Neural Networks (IHGNN), which computes representations as the solution to a nonlinear fixed-point equation.<n>IHGNN consistently outperforms strong traditional graph/hypergraph neural network baselines in both accuracy and robustness.
• Score: 8.5183483099116
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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