A Mechanistic Model for Collective Motion from Sensorimotor Regularities

Emergent coordinated behaviors of AI agents are starting to present critical safety risks. A key phenomenon driving these behaviors is the rapid formation and spread of beliefs about the world, and mechanistic understanding is crucial for collective alignment. To this end, we introduce the Flag Game, a toy model for studying the mechanisms of collective belief formation. Concretely, a hidden country flag defines the ground truth, and each bounded agent directly observes only a private crop but can exchange beliefs and weigh social evidence from peers. Despite its simplicity, the Flag Game reproduces rich collective phenomenology: non-monotonic scaling of performance with population size, accuracy gains from social-awareness prompting and team diversity, and strong effects of organizational structure. In particular, we identify that collective belief collapse at small population sizes turns into collective belief polarization as the population grows. This polarization causes the performance decline at large population sizes, but creates diversity in collective beliefs. Finally, we dissect the mechanisms underlying collective belief collapse and polarization with two complementary approaches. We first introduce social circuit attribution, a technique to predict which agent, and what view, matters most to collective dynamics, and verify its predictions by causal interventions on agents, tracing how agent patching changes collective outcomes. However, the efficacy of causal interventions on agents decreases as the population grows. We therefore develop a statistical mechanical theory for larger populations and verify that it matches the empirical phase diagram. Together, these results take a first step toward mechanistic swarm interpretability, a science of how the properties of individual agents and their communication give rise to emergent collective behavior.

Existing AI systems for modeling human behavior operate at the level of individuals or detect events after they occur. As a result, they systematically fail to capture the collective dynamics that determine whether a group remains stable or transitions into escalation or breakdown. We propose a different foundation: a group of interacting humans constitutes a complex dynamical system in the precise mathematical sense, exhibiting emergence, nonlinearity, feedback loops, sensitivity near critical points, and phase transitions between qualitatively distinct regimes. The state of such a system is not located within any single participant; it is distributed across mutual influence loops and observable through the micro-dynamics of the body. We introduce BEHAVE (Behavioral Engine for Human Activity Vector Estimation), a formal framework that models collective dynamics as continuous behavioral fields defined over an interaction space derived from observable physical signals. Kinematic micro-signals (position, velocity, body orientation, gestural activity) are structured into a directed interaction graph and aggregated into a basis of behavioral fields capturing distinct, non-redundant axes of collective state. The framework rests on one theorem and two structural propositions characterizing the tension field, the field basis, and the criticality index. Perception and forecasting layers are implemented using neural models, enabling data-driven learning and approximation of system dynamics. BEHAVE is formulated as a computational system for learning, representing, and forecasting collective dynamics from data. A working pipeline is demonstrated on a 7-agent negotiation snapshot. The same fields, recalibrated, apply to crowd safety, crisis-team dynamics, education, and clinical contexts.

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.