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.
We study how artificial intelligence (AI) interacts with social communication networks to shape the stability of collective knowledge. Agents exchange information through a network while receiving AI-generated content, and AI systems retrain on the aggregate social information they influence. This interaction generates two feedback forces: an AI contagion channel, through which distortions diffuse across the network, and an AI social distortion multiplier, through which retraining amplifies past errors. Despite the high dimensionality of the environment, we show that the long-run behavior of the system admits a two-dimensional representation whose spectral radius determines whether AI-mediated information systems are dynamically stable or unstable. We characterize a sharp regulatory frontier identifying the minimum filtering required for stability and show how network topology shapes systemic informational risk.
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.
As generative AI agents are deployed at scale, safety will depend not only on technical safeguards and individual model design, but also on collective equilibria that determine how agent populations process information, prioritize actions, and respond to uncertainty. Yet the same equilibria that enable agents to coordinate also create a social attack surface. The standard framework to assess this vulnerability is critical mass dynamics: the minimum fraction of adversarial agents required to overturn an equilibrium through direct competition. Here, we show that this approach risks underestimating system vulnerability by reducing the problem to the identification of singular tipping points, and ignoring indirect but potentially more efficient routes through which collective behavior can be redirected. Through experiments with populations of LLM agents and an analytic framework that captures their collective dynamics at scale, we map critical-mass thresholds that define a directed, weighted topology over the space of coordination equilibria, and treat this topology as a navigable landscape. We show that indirect tipping through intermediate stepping-stone equilibria can reduce the committed minority required to reach an alternative state, bypass majority requirements, and make possible transitions inaccessible through direct challenges. The diversity of available alternatives and timing of the attack further reshape this landscape, creating opportunities for control as well as risks of unintended destabilization. These results show that an equilibrium's resistance to committed intervention is not an intrinsic property but a structural feature of its competitive relations with alternative states. Securing populations of interacting AI agents therefore requires mapping this social landscape alongside individual agent capabilities and the technical channels through which they interact.
Ariel Flint, Luca Maria Aiello, Sara M. Constantino +2