# High-order Knowledge Based Network Controllability Robustness Prediction: A Hypergraph Neural Network Approach

arXiv: https://arxiv.org/abs/2603.02265 · HTML: https://mlsanity.com/paper/2603.02265/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 62 references that are in the map.
- First posted on arXiv 28 Feb 2026.

## Builds on (most cited first, 15 of 15)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [You are AllSet: A Multiset Function Framework for Hypergraph Neural Networks](https://mlsanity.com/paper/2106.13264/) (2021)
- [Cross-Scale Internal Graph Neural Network for Image Super-Resolution](https://mlsanity.com/paper/2006.16673/) (2020)
- [Be More with Less: Hypergraph Attention Networks for Inductive Text Classification](https://mlsanity.com/paper/2011.00387/) (2020)
- [Predicting Network Controllability Robustness: A Convolutional Neural Network Approach](https://mlsanity.com/paper/1908.09471/) (2019)
- [Brain Graph Super-Resolution Using Adversarial Graph Neural Network with Application to Functional Brain Connectivity](https://mlsanity.com/paper/2105.00425/) (2021)
- [SHINE: SubHypergraph Inductive Neural nEtwork](https://mlsanity.com/paper/2210.07309/) (2022)
- [Simplifying Distributed Neural Network Training on Massive Graphs: Randomized Partitions Improve Model Aggregation](https://mlsanity.com/paper/2305.09887/) (2023)
- [Recent Advances in Hypergraph Neural Networks](https://mlsanity.com/paper/2503.07959/) (2025)
- [Toward Stronger Robustness of Network Controllability: A Snapback Network Model](https://mlsanity.com/paper/1801.06082/) (2018)
- [Knowledge-Based Prediction of Network Controllability Robustness](https://mlsanity.com/paper/2003.08563/) (2020)
- [Controllability of networked MIMO systems](https://mlsanity.com/paper/1505.01255/) (2015)
- [DARTS-PRIME: Regularization and Scheduling Improve Constrained Optimization in Differentiable NAS](https://mlsanity.com/paper/2106.11655/) (2021)
- [Neural Network Graph Similarity Computation Based on Graph Fusion](https://mlsanity.com/paper/2502.18291/) (2025)

## Abstract (arXiv)

In order to evaluate the invulnerability of networks against various types of attacks and provide guidance for potential performance enhancement as well as controllability maintenance, network controllability robustness (NCR) has attracted increasing attention in recent years. Traditionally, controllability robustness is determined by attack simulations, which are computationally time-consuming and only applicable to small-scale networks. Although some machine learning-based methods for predicting network controllability robustness have been proposed, they mainly focus on pairwise interactions in complex networks, and the underlying relationships between high-order structural information and controllability robustness have not been explored. In this paper, a dual hypergraph attention neural network model based on high-order knowledge (NCR-HoK) is proposed to accomplish robustness learning and controllability robustness curve prediction. Through a node feature encoder, hypergraph construction with high-order relations, and a dedicated dual hypergraph attention module, the proposed method can effectively learn three types of network information simultaneously: explicit structural information in the original graph, high-order connection information in local neighborhoods, and hidden features in the embedding space. Notably, we explore for the first time the impact of high-order knowledge on network controllability robustness. Compared with state-of-the-art methods for network robustness learning, the proposed method achieves superior performance on both synthetic and real-world networks with low computational overhead.