# Advancing network resilience theories with symbolized reinforcement learning

arXiv: https://arxiv.org/abs/2507.08827 · HTML: https://mlsanity.com/paper/2507.08827/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 8 of its 39 references that are in the map.
- First posted on arXiv 4 Jul 2025.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 8 of 8)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [Symbolic Regression is NP-hard](https://mlsanity.com/paper/2207.01018/) (2022)
- [Influence maximization in complex networks through optimal percolation](https://mlsanity.com/paper/1506.08326/) (2015)
- [Machine learning dismantling and early-warning signals of disintegration in complex systems](https://mlsanity.com/paper/2101.02453/) (2021)
- [Generalized Network Dismantling](https://mlsanity.com/paper/1801.01357/) (2018)
- [Immunization and targeted destruction of networks using explosive percolation](https://mlsanity.com/paper/1604.00073/) (2016)
- [Fast and simple decycling and dismantling of networks](https://mlsanity.com/paper/1607.03276/) (2016)

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

- [AutoSND: From Execution Evidence to Structural Policies for Automated Network Dismantling Heuristic Discovery](https://mlsanity.com/paper/2608.03653/) (2026)

## Abstract (arXiv)

Many complex networks display remarkable resilience under external perturbations, internal failures and environmental changes, yet they can swiftly deteriorate into dysfunction upon the removal of a few keystone nodes. Discovering theories that measure network resilience offers the potential to prevent catastrophic collapses--from species extinctions to financial crise--with profound implications for real-world systems. Current resilience theories address the problem from a single perspective of topology, neglecting the crucial role of system dynamics, due to the intrinsic complexity of the coupling between topology and dynamics which exceeds the capabilities of human analytical methods. Here, we report an automatic method for resilience theory discovery, which learns from how AI solves a complicated network dismantling problem and symbolizes its network attack strategies into theoretical formulas. This proposed self-inductive approach discovers the first resilience theory that accounts for both topology and dynamics, highlighting how the correlation between node degree and state shapes overall network resilience, and offering insights for designing early warning signals of systematic collapses. Additionally, our approach discovers formulas that refine existing well-established resilience theories with over 37.5% improvement in accuracy, significantly advancing human understanding of complex networks with AI.