# A Learning Convolutional Neural Network Approach for Network Robustness Prediction

arXiv: https://arxiv.org/abs/2203.10552 · HTML: https://mlsanity.com/paper/2203.10552/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 76 references that are in the map.
- First posted on arXiv 20 Mar 2022.

## Builds on (most cited first, 18 of 18)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Making Convolutional Networks Shift-Invariant Again](https://mlsanity.com/paper/1904.11486/) (2019)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [Graph Neural Network Encoding for Community Detection in Attribute Networks](https://mlsanity.com/paper/2006.03996/) (2020)
- [Appropriate Learning Rates of Adaptive Learning Rate Optimization Algorithms for Training Deep Neural Networks](https://mlsanity.com/paper/2002.09647/) (2020)
- [Machine learning dismantling and early-warning signals of disintegration in complex systems](https://mlsanity.com/paper/2101.02453/) (2021)
- [Predicting Network Controllability Robustness: A Convolutional Neural Network Approach](https://mlsanity.com/paper/1908.09471/) (2019)
- [Toward Stronger Robustness of Network Controllability: A Snapback Network Model](https://mlsanity.com/paper/1801.06082/) (2018)
- [Towards Optimal Robustness of Network Controllability: An Empirical Necessary Condition](https://mlsanity.com/paper/1912.12416/) (2019)
- [Knowledge-Based Prediction of Network Controllability Robustness](https://mlsanity.com/paper/2003.08563/) (2020)
- [Smart Rewiring for Network Robustness](https://mlsanity.com/paper/1303.5269/) (2013)
- [Exact Controllability of Complex Networks](https://mlsanity.com/paper/1310.5806/) (2013)
- [Controllability of networked MIMO systems](https://mlsanity.com/paper/1505.01255/) (2015)
- [Networkcontrology](https://mlsanity.com/paper/1510.08320/) (2015)
- [Multiplex congruence network of natural numbers](https://mlsanity.com/paper/1512.01615/) (2015)

## Built on by (most cited first, 6 of 6)

- [A.I. Robustness: a Human-Centered Perspective on Technological Challenges and Opportunities](https://mlsanity.com/paper/2210.08906/) (2022)
- [Fast Inference of Removal-Based Node Influence](https://mlsanity.com/paper/2403.08333/) (2024)
- [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)
- [Comprehensive Analysis of Network Robustness Evaluation Based on Convolutional Neural Networks with Spatial Pyramid Pooling](https://mlsanity.com/paper/2308.08012/) (2023)
- [HWL-HIN: A Hypergraph-Level Hypergraph Isomorphism Network as Powerful as the Hypergraph Weisfeiler-Lehman Test with Application to Higher-Order Network Robustness](https://mlsanity.com/paper/2512.22014/) (2025)

## Abstract (arXiv)

Network robustness is critical for various societal and industrial networks again malicious attacks. In particular, connectivity robustness and controllability robustness reflect how well a networked system can maintain its connectedness and controllability against destructive attacks, which can be quantified by a sequence of values that record the remaining connectivity and controllability of the network after a sequence of node- or edge-removal attacks. Traditionally, robustness is determined by attack simulations, which are computationally very time-consuming or even practically infeasible. In this paper, an improved method for network robustness prediction is developed based on learning feature representation using convolutional neural network (LFR-CNN). In this scheme, higher-dimensional network data are compressed to lower-dimensional representations, and then passed to a CNN to perform robustness prediction. Extensive experimental studies on both synthetic and real-world networks, both directed and undirected, demonstrate that 1) the proposed LFR-CNN performs better than other two state-of-the-art prediction methods, with significantly lower prediction errors; 2) LFR-CNN is insensitive to the variation of the network size, which significantly extends its applicability; 3) although LFR-CNN needs more time to perform feature learning, it can achieve accurate prediction faster than attack simulations; 4) LFR-CNN not only can accurately predict network robustness, but also provides a good indicator for connectivity robustness, better than the classical spectral measures.