HWL-HIN: 一种超图级别的超图同构网络：其表达能力与超图Weisfeiler-Lehman测试相当，应用于更高阶网络鲁棒性
HWL-HIN: A Hypergraph-Level Hypergraph Isomorphism Network as Powerful as the Hypergraph Weisfeiler-Lehman Test with Application to Higher-Order Network Robustness
AI总结：
本文提出了一种超图级别的超图同构网络，其表达能力与超图Weisfeiler-Lehman测试相当，用于预测更高阶网络的鲁棒性。
摘要：
复杂系统中的鲁棒性在工程和经济上具有重要意义。然而，传统的基于攻击的后验鲁棒性评估会造成极大的计算开销。最近，深度学习方法，如卷积神经网络（CNN）和图神经网络（GNN），已被广泛用于快速鲁棒性预测的替代方案。然而，这些方法忽略了现实系统中普遍存在的复杂高阶相关性，这些相关性自然地被建模为超图。尽管超图神经网络（HGNNs）已被广泛用于超图学习，但其拓扑表达能力尚未达到理论上限。为了解决这一限制，受图同构网络的启发，本文提出了一种超图级别的超图同构网络框架。理论上，该方法被证明具有与超图Weisfeiler-Lehman测试严格等同的表达能力，并应用于预测超图鲁棒性。实验结果表明，尽管在训练和预测中保持了优越的效率，所提出的方法不仅在现有图基模型上表现更优，而且在优先考虑拓扑结构表示的任务中显著超越了传统HGNNs。
英文摘要：
Robustness in complex systems is of significant engineering and economic importance. However, conventional attack-based a posteriori robustness assessments incur prohibitive computational overhead. Recently, deep learning methods, such as Convolutional Neural Networks (CNNs) and Graph Neural Networks (GNNs), have been widely employed as surrogates for rapid robustness prediction. Nevertheless, these methods neglect the complex higher-order correlations prevalent in real-world systems, which are naturally modeled as hypergraphs. Although Hypergraph Neural Networks (HGNNs) have been widely adopted for hypergraph learning, their topological expressive power has not yet reached the theoretical upper bound. To address this limitation, inspired by Graph Isomorphism Networks, this paper proposes a hypergraph-level Hypergraph Isomorphism Network framework. Theoretically, this approach is proven to possess an expressive power strictly equivalent to the Hypergraph Weisfeiler-Lehman test and is applied to predict hypergraph robustness. Experimental results demonstrate that while maintaining superior efficiency in training and prediction, the proposed method not only outperforms existing graph-based models but also significantly surpasses conventional HGNNs in tasks that prioritize topological structure representation.
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