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.
Abstract (translated)
超图提供了一种捕捉实体之间高阶关系的通用框架，并在医疗保健、社交网络和生物信息学等各个领域得到了广泛应用。基于超边进行节点间消息传递以学习潜在表示的超图神经网络，已成为这些领域许多预测任务中的首选方法。这些方法通常只执行少量的消息传递轮次来学习表示，然后利用这些表示来进行预测。这种少量的消息传递轮次会导致表示仅捕获局部信息，并忽略长程高阶依赖关系。然而，我们证明盲目增加消息传递轮数以捕捉长程依赖同样会降低超图神经网络的性能。 近期工作表明，隐式图神经网络能够在标准图中捕获长距离依赖性的同时保持良好的性能表现，但之前的工作没有研究过超图神经网络中的远程依赖问题。在这里，我们首先证明现有的超图神经网络在聚合更多信息以捕捉长程依赖时会失去预测能力。然后，我们提出了一种新的框架——隐式超图神经网络（IHNN），该框架通过端到端的方式共同学习节点和超边的固定点表示，从而缓解这一问题。利用隐式微分，我们引入了一种可操作的投影梯度下降方法来高效训练模型。 在真实世界的超图上进行节点分类任务的广泛实验表明，在大多数情况下，IHNN超越了最近的相关工作，建立了新的最先进的技术成果。
URL
https://arxiv.org/abs/2508.14101
