# Escape from Delusional Echo Trap: Symmetry Breaking, Stochastic Dynamics and Mathematical Mitigation Strategies for Algorithmic Sycophancy

arXiv: https://arxiv.org/abs/2606.20718 · HTML: https://mlsanity.com/paper/2606.20718/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 18 references that are in the map.
- First posted on arXiv 16 Jun 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)
- [When Truth Is Overridden: Uncovering the Internal Origins of Sycophancy in Large Language Models](https://mlsanity.com/paper/2508.02087/) (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)
- [The Dynamics of Delusion: Modeling Bidirectional False Belief Amplification in Human-Chatbot Dialogue](https://mlsanity.com/paper/2604.25096/) (2026)

## Built on by (most cited first, 1 of 1)

- [Teacher Knows It Best: Spontaneous Symmetry Breaking and Tipping Points in Networked Langevin Dynamics AI Sycophancy](https://mlsanity.com/paper/2607.24304/) (2026)

## Abstract (arXiv)

We propose a rigorous and systematic mathematical framework for tracking the cognitive trajectories of a user, in the context of algorithmic sycophancy and AI-driven delusional spiraling. Using tools from dynamical systems theory and stochastic differential equations, we explore how individuals perceive, interpret, and update their beliefs as they interact with AI chatbots that possess hidden traits of sycophancy. We treat the evolving conviction as a continuous log-odds state variable, coupled into a stochastic differential equation, navigating a multi-valley potential energy landscape. Our analysis reveals several critical observations governing the stability and rigidity of belief dynamics. We demonstrate that the baseline prior perception of the individual is systematically enhanced by sycophantic feedback beyond a critical threshold. Here, the perceptual potential landscape undergoes a structural phase transition that severely deepens any incremental initial tilt present in the baseline state, transforming the landscape and giving rise to deep, highly resilient attractor basins that trap the individual in unshakeable, self-reinforcing, delusional convictions. Finally, we demonstrate that genuine external information can successfully challenge these rigid states. If this incoming evidence is strong and authentic enough to overcome the internal feedback barrier, it can correct the structural asymmetry caused by sycophancy, inducing a perception reversal that successfully restores the objective belief state.