Physics of Agents: Statistical Mechanics Predicts Collective Behavior of AI Agents

AI agents increasingly operate as part of interacting systems rather than in isolation. As agents exchange information and jointly make decisions, their interactions can improve collective reasoning but may also produce herding, polarization, or amplify shared biases. Understanding and predicting these collective dynamics is therefore important for designing effective and aligned multi-agent systems. Here, we study over 10,000 communities of language-model agents that repeatedly exchange messages and revise their opinions across objective mathematics questions and subjective political statements. Despite substantial diversity in possible behavior, the individual and group dynamics can be represented by three characteristic regimes: indifference, polarization, and consensus. AI agents start indifferent and build conviction as they interact. On objective questions, communication improves collective accuracy, while on subjective questions it often drifts group opinions toward the right in the political spectrum. We explain these observations with a statistical-mechanics formalism in which agents stochastically favor lower social pressure. Given only initial opinions, our model predicts individual trajectories, outperforms all standard baselines, generalizes to unseen community graphs, and reproduces the observed group archetype distributions. Our fitted model parameters reveal the mechanics underlying our key observations: i) communities operate below the critical social temperature, which explains conviction buildup; ii) attractive ties outweigh repulsive ones, which favors consensus; and iii) agents holding the correct answer exert the strongest pull, which drives truth-seeking. Overall, our results demonstrate that collective behavior of AI agents, like that of other complex systems, follows compact and predictive dynamical laws.

A ghost mechanism: An analytical model of abrupt learning

\emph{Abrupt learning} is commonly observed in neural networks, where long plateaus in network performance are followed by rapid convergence to a desirable solution. Yet, despite its common occurrence, the complex interplay of task, network architecture, and learning rule has made it difficult to understand the underlying mechanisms. Here, we introduce a minimal dynamical system trained on a delayed-activation task and demonstrate analytically how even a one-dimensional system can exhibit abrupt learning through ghost points rather than bifurcations. Through our toy model, we show that the emergence of a ghost point destabilizes learning dynamics. We identify a critical learning rate that prevents learning through two distinct loss landscape features: a no-learning zone and an oscillatory minimum. Testing these predictions in recurrent neural networks (RNNs), we confirm that ghost points precede abrupt learning and accompany the destabilization of learning. We demonstrate two complementary remedies: lowering the model output confidence prevents the network from getting stuck in no-learning zones, while increasing trainable ranks beyond task requirements (\textit{i.e.}, adding sloppy parameters) provides more stable learning trajectories. Our model reveals a bifurcation-free mechanism for abrupt learning and illustrates the importance of both deliberate uncertainty and redundancy in stabilizing learning dynamics.