Teacher Knows It Best: Spontaneous Symmetry Breaking and Tipping Points in Networked Langevin Dynamics AI Sycophancy

arXiv:2607.24304v1 Announce Type: cross 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.

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.

Physics and Society (physics.soc-ph); Artificial Intelligence (cs.AI); Dynamical Systems (math.DS)

arXiv:2607.24304 [physics.soc-ph]

(or arXiv:2607.24304v1 [physics.soc-ph] for this version)

https://doi.org/10.48550/arXiv.2607.24304 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Teacher Knows It Best: Spontaneous Symmetry Breaking and Tipping Points in Networked Langevin Dynamics AI Sycophancy

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