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

arXiv: https://arxiv.org/abs/2512.22014 · HTML: https://mlsanity.com/paper/2512.22014/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 40 references that are in the map.
- First posted on arXiv 26 Dec 2025.

## Builds on (most cited first, 13 of 13)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020)
- [UniGNN: a Unified Framework for Graph and Hypergraph Neural Networks](https://mlsanity.com/paper/2105.00956/) (2021)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [Machine learning dismantling and early-warning signals of disintegration in complex systems](https://mlsanity.com/paper/2101.02453/) (2021)
- [Graph Vulnerability and Robustness: A Survey](https://mlsanity.com/paper/2105.00419/) (2021)
- [Hypergraph Isomorphism Computation](https://mlsanity.com/paper/2307.14394/) (2023)
- [A Learning Convolutional Neural Network Approach for Network Robustness Prediction](https://mlsanity.com/paper/2203.10552/) (2022)
- [Structural Robustness of Complex Networks: A Survey of A Posteriori Measures](https://mlsanity.com/paper/2302.03745/) (2023)
- [SPP-CNN: An Efficient Framework for Network Robustness Prediction](https://mlsanity.com/paper/2305.07872/) (2023)
- [A Graph Transformer-Driven Approach for Network Robustness Learning](https://mlsanity.com/paper/2306.06913/) (2023)

## Abstract (arXiv)

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.