标题： 用符号化强化学习推进网络弹性理论 显示英文标题

标题： Advancing network resilience theories with symbolized reinforcement learning

摘要： 许多复杂网络在外部扰动、内部故障和环境变化下表现出显著的弹性，但在移除几个关键节点后，它们可以迅速恶化为功能失调。 发现衡量网络弹性的理论有可能防止灾难性崩溃——从物种灭绝到金融危机——这对现实世界系统有深远的意义。 当前的弹性理论从拓扑学的一个角度来解决这个问题，忽视了系统动态的重要作用，这是由于拓扑学与动态学之间的耦合内在复杂性超出了人类分析方法的能力。 在这里，我们报告了一种自动发现弹性理论的方法，该方法学习人工智能如何解决复杂的网络拆解问题，并将其网络攻击策略符号化为理论公式。 该提出的自归纳方法发现了第一个同时考虑拓扑学和动态学的弹性理论，强调了节点度与状态之间的相关性如何塑造整体网络弹性，并为设计系统性崩溃的早期预警信号提供了见解。 此外，我们的方法发现了改进现有广泛认可的弹性理论的公式，准确率提高了超过37.5%，显著推进了人工智能下人类对复杂网络的理解。 显示英文摘要

摘要： 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.