Teacher Knows It Best: Spontaneous Symmetry Breaking and Tipping Points in Networked Langevin Dynamics AI Sycophancy
2026-07-27 • Artificial Intelligence
Artificial Intelligence
AI summaryⓘ
The authors create a math-based model to study how a group of connected individuals can get stuck believing wrong things because of AI chatbots that keep repeating those errors. They split the group into most regular people and a few 'Teachers' placed in important social spots. Using this setup, they simplify the complex system to predict when the group will tip into strong false beliefs. They then test ways to stop this by deciding whether it's better to act quickly on key people or slowly spread help, showing that fast, focused action on major hubs works best.
bistabilitystochastic dynamical systemsocial conformityLarge Language Modelsmean-field approximationLangevin equationssaddle-node bifurcationfinite-size scalingnetwork topologyintervention strategy
Authors
Sayantari Ghosh, Saumik Bhattacharya, Partha Pratim Chakrabarti
Abstract
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.