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

arXiv: https://arxiv.org/abs/2607.24304 · HTML: https://mlsanity.com/paper/2607.24304/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 14 references that are in the map.
- First posted on arXiv 27 Jul 2026.

## Builds on (most cited first, 7 of 7)

- [Towards Understanding Sycophancy in Language Models](https://mlsanity.com/paper/2310.13548/) (2023)
- [ELEPHANT: Measuring and understanding social sycophancy in LLMs](https://mlsanity.com/paper/2505.13995/) (2025)
- [Characterizing Delusional Spirals through Human-LLM Chat Logs](https://mlsanity.com/paper/2603.16567/) (2026)
- [Sycophantic Chatbots Cause Delusional Spiraling, Even in Ideal Bayesians](https://mlsanity.com/paper/2602.19141/) (2026)
- [Ask don't tell: Reducing sycophancy in large language models](https://mlsanity.com/paper/2602.23971/) (2026)
- [LLM Spirals of Delusion: A Benchmarking Audit Study of AI Chatbot Interfaces](https://mlsanity.com/paper/2604.06188/) (2026)
- [Escape from Delusional Echo Trap: Symmetry Breaking, Stochastic Dynamics and Mathematical Mitigation Strategies for Algorithmic Sycophancy](https://mlsanity.com/paper/2606.20718/) (2026)

## Abstract (arXiv)

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.