TLDR: Another flock-of-birds moment for physicists! In a controlled binary-opinion setting, a small statistical-mechanics model predicts how communities of language-model agents evolve and connects the emergence of conviction and consensus, as well as truth-seeking on objective questions, to a few fitted interaction parameters.

Language-model agents exchange messages over a social network while a fitted dynamical model predicts their collective opinion trajectories
Figure 1. We study communities of language-model agents answering objective mathematics questions or responding to subjective political statements. Agents exchange messages over a signed communication network and update their opinions for eight rounds; the fitted dynamical model rolls the trajectories forward from the initial opinions using the signed graph and learned intrinsic fields.

How to read Figure 1: panel A follows eight agents as their opinions change; panel B shows examples of the messages associated with those changes; panel C shows two communication networks; and panel D compares observed opinion trajectories with trajectories predicted by the model.

When the system is more than one agent

To a researcher familiar with many-body interactions in physics, it is no surprise that a group can behave differently from any one of its parts. This is often called emergence, a loaded term in today's AI landscape (yes, I know).

In recent work, we studied more than 10,000 communities and asked whether the same idea applies to groups of language-model agents. Across the main experiments, agents built conviction, tended toward consensus or polarization, and sometimes overturned their initial majority. On objective mathematics questions, incorrect majorities switched to the correct answer more often than the reverse. On a label-balanced set of political statements, however, interaction shifted group opinions rightward for three of the four language models.

Why should interaction create anything new? Once agents exchange messages, one agent's opinion becomes part of another agent's input, and the other agent's response then feeds back into the group. We are no longer studying one input-output map, but a feedback system. Depending on how the agents are connected and where the conversation begins, the same population can converge, remain split, oscillate, or reverse its majority.

To study this feedback systematically, we built communities of 32 agents. Each community discussed one binary question, which was either an objective mathematics problem, with agents assigned different expertise, or a subjective political statement, with agents assigned different personas. The agents exchanged short justifications for eight rounds over a fixed communication network. Positive connections instructed agents to treat one another as friendly; negative connections instructed them to interact as unfriendly counterparts. Our primary hypothesis was that a statistical-mechanics model of social pressure could describe the resulting multi-agent dynamics.

Method: Social pressure as a cost function

We reduce each agent's current answer to a binary state, si(t) ∈ {−1,+1}. The vector s(t) contains the opinions of the full community, while J records who communicates and whether each relationship is positive (+1), negative (−1), or absent (0).

The central assumption is that an opinion update balances two pressures. An agent responds to the current opinions of its neighbors, but it also brings an intrinsic leaning modeled as depending on its persona and the question. The simplest version of these two terms defines an energy,

E(s) = −½∑i,jJijsisj − ∑igisi

where gi describes agent i's intrinsic leaning. For a positive connection, the first term favors matching opinions; for a negative connection, it favors opposing opinions. The second term favors agreement with the agent's own predisposition.

This is the energy of an Ising model. Statistical mechanics has used the same general idea, simple local interactions producing collective order, to describe systems ranging from magnets to flocks of birds. The question in our paper is whether this analogy is only descriptive, or whether it can actually predict the agents. Of course, the physicist in me is tempted to call this universality and claim not to be surprised. The fitted interaction strengths and detailed behaviors did vary across models and tasks, however (see the paper).

The fitted rule extends the simplest expression above with distinct terms for being connected and for whether a connection is positive or negative. The cost defines a stochastic local update in which the opinion favored by an agent's local field is more likely. We fit the interaction strengths and the persona- and question-dependent intrinsic field from observed one-step opinion changes. At test time, a rollout starts from the initial opinions and never receives the later observed states. The model does not generate or represent the natural-language messages themselves; it predicts only the evolving pattern of binary opinions.

A brief overview of results: Does the simple law actually predict the agents?

The paper contains the full model-by-model comparisons. The main picture is:

  • It predicts held-out opinion changes. Across four language models and both question types, the fitted rule outperformed the baselines for both one-step predictions and rollouts. For GPT-4o-mini, the same rule also transferred from random graphs to unseen low-rank and lattice networks. In other words, who talks to whom helps predict what happens, whereas the population average is not enough.
  • Interaction builds conviction. On questions selected to have varied initial responses, early rounds were dominated by lower-conviction communities, and conviction increased across every model and question-type setting. In the fitted model, the operating point lies below an inferred finite-size critical social temperature in every model and question-type condition. In this regime, low-conviction states are unstable, providing the model's account of the observed buildup of conviction.
  • Social pressure favors consensus. Consensus became more common as the agents interacted. In every fit, the effective influence of friendly connections was stronger than that of unfriendly connections. The fitted social term therefore favors consensus over a stable two-camp split, although sufficiently strong and opposed intrinsic preferences can still sustain polarization.
  • On mathematics, communities move toward the correct answer. Incorrect-to-correct majority switches were more frequent than correct-to-incorrect switches for all four language models. A separate fit that uses the known answer labels found that correct neighbors pull harder through friendly connections, while incorrect neighbors push harder through unfriendly connections. Both asymmetries point updates toward the correct answer and provide a statistical account of the truth-seeking tendency.

The theory here also has clear explanatory and predictive limits. It does not explain why every fit assigned stronger effective influence to friendly connections than to unfriendly ones. On held-out questions using in-distribution random graphs, its rollouts approximately recover the proportions of group outcomes, not the outcome of each individual community. Repeated runs with the same agents, question, and graph can still end differently.

Why this matters

Why bother with a dynamical model instead of running more agent simulations? Multi-agent systems are increasingly designed by searching over prompts, roles, and communication graphs, which can require many expensive rollouts. If a compact theoretical rule can forecast collective dynamics, we can ask how changing the graph, the population, or the interaction strengths changes the predicted outcome. We could ask which structures preserve useful disagreement, which produce brittle consensus, and which amplify a shared error. In other words, we could, in principle, design interactions to optimize for a chosen outcome. The present work does not yet optimize these choices, but it gives us a model in which to study them.

Notably, the setting here is rather limited compared to real-life networks. Our agents answer one binary question at a time; the communication graph is fixed and symmetric; each update uses only the newest messages; and the fitted state discards the natural-language content that mediates influence. In this controlled setting, however, the answer to the title question is yes. Multi-agent interactions can be represented by a state, an interaction graph, and an update law. Instead of treating the system only as a collection of transcripts, we can ask which collective behaviors are predictable and which interaction parameters account for them.

See the paper and project page for the full results, code, data, and online appendix.

Read the paper Code, data, and online appendix Back to research notes