Abstract
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.
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Apr 28, 2026cs.CL
There is growing concern that AI chatbots might fuel delusional beliefs in users. Some have suggested that humans and chatbots mutually reinforce false beliefs over time, but quantitative evidence is lacking. Using a unique dataset of chat logs from individuals who exhibited delusional thinking, we developed a latent state model that captures accumulating and decaying influences between humans and chatbots. We find that a bidirectional influence model substantially outperforms a unidirectional alternative where humans are the primary driver of delusion. We find that humans exert strong but short-lived influence on chatbots, whereas chatbots exert longer-lasting influence on humans. Moreover, chatbots exert strong, stable self-influence over their own future outputs that tends to perpetuate delusions over long stretches of conversation. In fact, this chatbot self-influence constituted the dominant pathway when considering accumulated influence over time. Overall, these results indicate that humans tend to drive sharp, immediate increases in delusion, whereas chatbots sustain and propagate these effects over longer timescales. Together, these findings provide the first quantitative evidence that human-chatbot interactions can form feedback loops of delusion, decomposable into distinct pathways with dissociable temporal dynamics. By doing so, they can inform the development of safer AI systems.
Ashish Mehta, Jared Moore, Jacy Reese Anthis +6
Jul 27, 2026physics.soc-ph
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.
Sayantari Ghosh, Saumik Bhattacharya, Partha Pratim Chakrabarti
Jul 28, 2026cs.AI
AI chatbots can be "sycophantic," or overly agreeable and flattering toward users. Sycophantic AI has been shown to entrench attitudes, yet users frequently fail to recognize it (a phenomenon we call "sycophancy blindness"). We tested whether increasing users' awareness of sycophancy protects them from its harmful effects in two preregistered experiments (n = 1,590). In the first, participants received a brief written warning about sycophancy before conversing with a sycophantic chatbot. In the second, participants watched a video of a sycophantic AI validating several other users, including users on opposite sides of the same conflict, before interacting with it themselves. Both interventions changed how participants evaluated the AI. The warning reduced the AI's perceived objectivity, and the video reduced enjoyment of the AI --- an effect mediated by the reduced belief that its validation was uniquely earned. We then pooled our experiments with two prior studies of sycophancy awareness interventions (six interventions total, n = 3,982). The pattern across experiments was consistent: while the interventions made the sycophantic AI appear less objective and trustworthy, none reduced its persuasiveness. These results suggest that individual-level interventions, such as warning labels or AI literacy, may not be enough to protect users from AI harms.
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