教师最了解：网络朗之万动力学人工智能谄媚中的自发对称性破缺和临界点

中文摘要 AI 辅助

我们构建了一个统计物理框架，以对由加性噪声和社会从众性驱动的具有双稳态的网络随机动力系统进行建模。我们将此模型用于理解和缓解人工智能导致的妄想螺旋，即大语言模型的算法谄媚在社交互动社会中不断强化不准确信念的现象。通过将网络划分为大多数常规主体和少数位于拓扑中心的“有识”节点（教师），我们使用度加权平均场近似将高维耦合朗之万方程简化为单个宏观漂移方程。我们通过鞍结分岔为确定性临界翻转时间提供了封闭形式的解析推导。我们使用有限尺寸标度验证了这个解析边界，并展示了跨不同网络拓扑的通用数据塌缩。最后，我们在严格的预算约束下优化了一种干预策略，该策略平衡了拓扑足迹与驱动速度。我们通过数学证明，在某些条件下，针对大量中心的高度集中、快速干预在拯救网络方面严格优于分布式、缓慢的方法。

英文摘要

We formulate a statistical physics framework to model a networked stochastic dynamical system exhibiting bistability, driven by additive noise and social conformity. We apply this model to understand and mitigate AI-induced delusional spiraling-a phenomenon where algorithmic sycophancy from Large Language Models continuously reinforces inaccurate beliefs within a socially interacting society. By partitioning the network into a majority of regular agents and a minority of "aware" nodes (Teachers) placed at topological hubs, we use a degree-weighted mean-field approximation to reduce high-dimensional coupled Langevin equations into a single macroscopic drift equation. We provide a closed-form analytical derivation for the deterministic critical tipping time through a saddle-node bifurcation. We validate this analytical boundary using finite-size scaling and demonstrate a universal data collapse across diverse network topologies. Finally, we optimize an intervention strategy under a strict budget constraint that balances the topological footprint against driving velocity. We prove mathematically that under certain conditions, a highly concentrated, rapid intervention targeting massive hubs strictly outperforms a distributed, slow approach to rescue the network.

发表机构

• National Institute of Technology Durgapur（印度杜尔加普尔国家理工学院）
• Indian Institute of Technology Kharagpur（印度克勒格布尔印度理工学院）

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