# Machine learning dismantling and early-warning signals of disintegration in complex systems

arXiv: https://arxiv.org/abs/2101.02453 · HTML: https://mlsanity.com/paper/2101.02453/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 71 references that are in the map.
- First posted on arXiv 7 Jan 2021.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Deep Object Pose Estimation for Semantic Robotic Grasping of Household Objects](https://mlsanity.com/paper/1809.10790/) (2018)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [Multilayer Networks](https://mlsanity.com/paper/1309.7233/) (2013)
- [Epidemic processes in complex networks](https://mlsanity.com/paper/1408.2701/) (2014)
- [The structure and dynamics of multilayer networks](https://mlsanity.com/paper/1407.0742/) (2014)
- [Bots increase exposure to negative and inflammatory content in online social systems](https://mlsanity.com/paper/1802.07292/) (2018)
- [Influence maximization in complex networks through optimal percolation](https://mlsanity.com/paper/1506.08326/) (2015)
- [Generalized Network Dismantling](https://mlsanity.com/paper/1801.01357/) (2018)
- [Network dismantling](https://mlsanity.com/paper/1603.08883/) (2016)
- [The Emergence of Consensus: A Primer](https://mlsanity.com/paper/1704.07767/) (2017)
- [Small vulnerable sets determine large network cascades in power grids](https://mlsanity.com/paper/1804.06432/) (2018)
- [Learning fine-grained search space pruning and heuristics for combinatorial optimization](https://mlsanity.com/paper/2001.01230/) (2020)
- [Immunization and targeted destruction of networks using explosive percolation](https://mlsanity.com/paper/1604.00073/) (2016)
- [The physics of spreading processes in multilayer networks](https://mlsanity.com/paper/1604.02021/) (2016)
- [Fast and simple decycling and dismantling of networks](https://mlsanity.com/paper/1607.03276/) (2016)
- [Collective Influence Algorithm to find influencers via optimal percolation in massively large social media](https://mlsanity.com/paper/1603.08273/) (2016)
- [New Online Ecology of Adversarial Aggregates: ISIS and beyond](https://mlsanity.com/paper/1603.09426/) (2016)
- [The dynamical structure of political corruption networks](https://mlsanity.com/paper/1801.01869/) (2018)
- [Optimal percolation on multiplex networks](https://mlsanity.com/paper/1707.01401/) (2017)
- [Effective approach to epidemic containment using link equations in complex networks](https://mlsanity.com/paper/1711.10443/) (2017)

## Built on by (most cited first, 14 of 14)

- [wsGAT: Weighted and Signed Graph Attention Networks for Link Prediction](https://mlsanity.com/paper/2109.11519/) (2021)
- [A Learning Convolutional Neural Network Approach for Network Robustness Prediction](https://mlsanity.com/paper/2203.10552/) (2022)
- [Detecting Vulnerable Nodes in Urban Infrastructure Interdependent Network](https://mlsanity.com/paper/2307.09866/) (2023)
- [Identify Critical Nodes in Complex Network with Large Language Models](https://mlsanity.com/paper/2403.03962/) (2024)
- [mGNN: Generalizing the Graph Neural Networks to the Multilayer Case](https://mlsanity.com/paper/2109.10119/) (2021)
- [SPP-CNN: An Efficient Framework for Network Robustness Prediction](https://mlsanity.com/paper/2305.07872/) (2023)
- [Advancing network resilience theories with symbolized reinforcement learning](https://mlsanity.com/paper/2507.08827/) (2025)
- [Beyond MMD: Evaluating Graph Generative Models with Geometric Deep Learning](https://mlsanity.com/paper/2512.14241/) (2025)
- [Edge Rewiring Goes Neural: Boosting Network Resilience without Rich Features](https://mlsanity.com/paper/2110.09035/) (2021)
- [CNN-based Prediction of Network Robustness With Missing Edges](https://mlsanity.com/paper/2208.11847/) (2022)
- [Mastering Percolation-like Games with Deep Learning](https://mlsanity.com/paper/2305.07687/) (2023)
- [A Quick Framework for Evaluating Worst Robustness of Complex Networks](https://mlsanity.com/paper/2403.00027/) (2024)
- [Interpretable Early Warnings using Machine Learning in an Online Game-experiment](https://mlsanity.com/paper/2502.09880/) (2025)
- [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)

From physics to engineering, biology and social science, natural and artificial systems are characterized by interconnected topologies whose features - e.g., heterogeneous connectivity, mesoscale organization, hierarchy - affect their robustness to external perturbations, such as targeted attacks to their units. Identifying the minimal set of units to attack to disintegrate a complex network, i.e. network dismantling, is a computationally challenging (NP-hard) problem which is usually attacked with heuristics. Here, we show that a machine trained to dismantle relatively small systems is able to identify higher-order topological patterns, allowing to disintegrate large-scale social, infrastructural and technological networks more efficiently than human-based heuristics. Remarkably, the machine assesses the probability that next attacks will disintegrate the system, providing a quantitative method to quantify systemic risk and detect early-warning signals of system's collapse. This demonstrates that machine-assisted analysis can be effectively used for policy and decision making to better quantify the fragility of complex systems and their response to shocks.