# SPP-CNN: An Efficient Framework for Network Robustness Prediction

arXiv: https://arxiv.org/abs/2305.07872 · HTML: https://mlsanity.com/paper/2305.07872/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 77 references that are in the map.
- First posted on arXiv 13 May 2023.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Rich feature hierarchies for accurate object detection and semantic segmentation](https://mlsanity.com/paper/1311.2524/) (2013)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Spatial Pyramid Pooling in Deep Convolutional Networks for Visual Recognition](https://mlsanity.com/paper/1406.4729/) (2014)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (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)
- [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)
- [A Learning Convolutional Neural Network Approach for Network Robustness Prediction](https://mlsanity.com/paper/2203.10552/) (2022)
- [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)
- [Exact Controllability of Complex Networks](https://mlsanity.com/paper/1310.5806/) (2013)
- [Controllability of networked MIMO systems](https://mlsanity.com/paper/1505.01255/) (2015)
- [Structural Robustness of Complex Networks: A Survey of A Posteriori Measures](https://mlsanity.com/paper/2302.03745/) (2023)
- [Graph measures and network robustness](https://mlsanity.com/paper/1311.5064/) (2013)

## Built on by (most cited first, 1 of 1)

- [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)

This paper addresses the robustness of a network to sustain its connectivity and controllability against malicious attacks. This kind of network robustness is typically measured by the time-consuming attack simulation, which returns a sequence of values that record the remaining connectivity and controllability after a sequence of node- or edge-removal attacks. For improvement, this paper develops an efficient framework for network robustness prediction, the spatial pyramid pooling convolutional neural network (SPP-CNN). The new framework installs a spatial pyramid pooling layer between the convolutional and fully-connected layers, overcoming the common mismatch issue in the CNN-based prediction approaches and extending its generalizability. Extensive experiments are carried out by comparing SPP-CNN with three state-of-the-art robustness predictors, namely a CNN-based and two graph neural networks-based frameworks. Synthetic and real-world networks, both directed and undirected, are investigated. Experimental results demonstrate that the proposed SPP-CNN achieves better prediction performances and better generalizability to unknown datasets, with significantly lower time-consumption, than its counterparts.