arXiv:2512.22014cs.LG2025-12

提出强于传统方法的超图同构网络,高效预测复杂系统鲁棒性。

HWL-HIN: A Hypergraph-Level Hypergraph Isomorphism Network as Powerful as the Hypergraph Weisfeiler-Lehman Test with Application to Higher-Order Network Robustness

  • 基于超图层级设计新网络架构,提升拓扑表达能力。
  • 在鲁棒性预测任务中超越现有图模型与超图神经网络。
  • 适合需要精准建模高阶关系的复杂系统分析场景。

复杂系统的鲁棒性具有重要的工程与经济意义。然而,传统的基于攻击的事后评估方法计算开销巨大。近年来,卷积神经网络(CNN)和图神经网络(GNN)等深度学习方法被广泛用作快速鲁棒性预测的代理模型。但这些方法忽视了真实系统中普遍存在的复杂高阶关联,而这类关系天然可由超图建模。尽管超图神经网络(HGNNs)已广泛应用于超图学习,其拓扑表达能力尚未达到理论上限。受图同构网络启发,本文提出一种超图层级的超图同构网络框架。理论上证明该方法的表达能力严格等价于超图Weisfeiler-Lehman测试,并用于预测超图鲁棒性。实验表明,该方法在保持训练与预测高效的同时,不仅优于现有基于图的模型,更显著超越传统HGNNs,在强调拓扑结构表示的任务中表现突出。

原文摘要 · Abstract (English)

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.

超图神经网络系统鲁棒性拓扑表达

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