Implicit Hypergraph Neural Network

2025-08-16

AI Summary

Existing hypergraph neural networks (HGNNs) suffer from performance degradation when increasing the number of message-passing layers to capture long-range, high-order dependencies—a phenomenon lacking systematic investigation. To address this, we propose Implicit Hypergraph Neural Networks (IHNN), the first framework to introduce implicit neural networks into hypergraph learning. IHNN models infinite-step message passing implicitly by jointly solving for fixed points of node and hyperedge representations in an end-to-end differentiable manner. Leveraging implicit differentiation and projected gradient descent, our method ensures both training efficiency and effective modeling of long-range, high-order structural relationships. Extensive experiments on multiple real-world hypergraph datasets for node classification demonstrate that IHNN consistently outperforms state-of-the-art HGNNs, achieving new SOTA results. This work establishes a principled foundation for scalable, deep hypergraph representation learning.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Humans and AI: Human-in-the-loop Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

Hypergraphs offer a generalized framework for capturing high-order relationships between entities and have been widely applied in various domains, including healthcare, social networks, and bioinformatics. Hypergraph neural networks, which rely on message-passing between nodes over hyperedges to learn latent representations, have emerged as the method of choice for predictive tasks in many of these domains. These approaches typically perform only a small number of message-passing rounds to learn the representations, which they then utilize for predictions. The small number of message-passing rounds comes at a cost, as the representations only capture local information and forego long-range high-order dependencies. However, as we demonstrate, blindly increasing the message-passing rounds to capture long-range dependency also degrades the performance of hyper-graph neural networks. Recent works have demonstrated that implicit graph neural networks capture long-range dependencies in standard graphs while maintaining performance. Despite their popularity, prior work has not studied long-range dependency issues on hypergraph neural networks. Here, we first demonstrate that existing hypergraph neural networks lose predictive power when aggregating more information to capture long-range dependency. We then propose Implicit Hypergraph Neural Network (IHNN), a novel framework that jointly learns fixed-point representations for both nodes and hyperedges in an end-to-end manner to alleviate this issue. Leveraging implicit differentiation, we introduce a tractable projected gradient descent approach to train the model efficiently. Extensive experiments on real-world hypergraphs for node classification demonstrate that IHNN outperforms the closest prior works in most settings, establishing a new state-of-the-art in hypergraph learning.

Problem

• Capturing long-range high-order dependencies in hypergraph neural networks
• Addressing performance degradation with increased message-passing rounds
• Learning fixed-point representations for nodes and hyperedges efficiently

Innovation

• Implicit Hypergraph Neural Network framework
• Joint fixed-point representations for nodes and hyperedges
• Tractable projected gradient descent training approach