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

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.

One-shot emergency psychiatric triage across 15 frontier AI chatbots

AI chatbots are increasingly used for health advice, but their performance in psychiatric triage remains undercharacterized. Psychiatric triage is particularly challenging because urgency must often be inferred from thoughts, behavior, and context rather than from objective findings. We evaluated the performance of 15 frontier AI chatbots on psychiatric triage from realistic single-message disclosures using 112 clinical vignettes, each paired with 1 of 4 original benchmark triage labels: A, routine; B, assessment within 1 week; C, assessment within 24 to 48 hours; and D, emergency care now. Vignettes covered 9 psychiatric presentation clusters and 9 focal risk dimensions, organized into 28 presentation-by-risk groups. Each group contributed 4 distinct vignettes, with 1 vignette at each triage level. Each vignette was rendered as a realistic human-authored conversational query, and the AI chatbots were tasked with assigning a triage label from that disclosure. Emergency under-triage occurred in 23 of 410 level D trials (5.6%), and all under-triaged emergencies were reassigned to level C urgency. Across target models, average accuracy ranged from 42.0% to 71.8%. Accuracy was highest for level D vignettes (94.3%) and lowest for level B vignettes (19.7%). Mean signed ordinal error was positive (+0.47 triage levels), indicating net over-triage. Dispersion was highest around the middle triage levels. All results were confirmed relative to clinician consensus labels from 50 medical doctors. When presented with user messages containing sufficient clinical information, frontier AI chatbots thus recognized psychiatric emergencies as requiring urgent medical assessment with near-zero error rates, yet showed marked over-triage for low and intermediate risk presentations.