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

TL;DR

This paper introduces a hypergraph-level Hypergraph Isomorphism Network that matches the theoretical expressive power of the Hypergraph Weisfeiler-Lehman test, enabling efficient and accurate robustness prediction in complex higher-order systems.

Contribution

It proposes a novel hypergraph neural network framework with proven expressive power equivalent to the Hypergraph Weisfeiler-Lehman test, advancing hypergraph learning capabilities.

Findings

Outperforms existing graph-based models in robustness prediction

Maintains high efficiency in training and prediction

Surpasses conventional HGNNs in topological structure tasks

Abstract

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.