When AI agents talk, agreement is only half the story. A group can average to zero because everyone is unsure—or because two camps are absolutely convinced.

Physics of Agents / An interactive reading

When AI agents talk, agreement is only half the story. A group can average to zero because everyone is unsure—or because two camps are absolutely convinced. [1]

Based on El and colleagues · arXiv preprint · September 2026

One average. Two different worlds.

The paper tracks both net opinion , the average stance, and conviction , the average squared opinion. Squaring keeps strength while removing direction. Strong views on opposite sides cancel in the first measure, but add in the second. [1]

Compare these two constructed groups. In both, half lean toward − and half toward +. What changes is how strongly they lean.

Four opinions at −0.2 and four at +0.2: a weakly opinionated group. Squaring each opinion gives 0.04.

Constructed examples, not recorded communities. In the experiment, each opinion averages five sampled binary votes, giving values −1, −0.6, −0.2, +0.2, +0.6, +1. [2]

Turn the social knobs.

The authors model opinion updates using social influence and an agent’s own leaning. Here, explore a simplified community with two camps of eight agents. Can you make conviction rise while the group average stays close to zero? [3]

Build a toy community

Both camps respond to their own members.

Negative values favor opposing the other camp.

Scales this model’s response; not an LLM sampling setting. [5]

Adds +g to camp A and −g to camp B.

Try Pull apart , then raise temperature. Does conviction survive?

Your community

16 dials · two camps

The opinion–conviction map

Dial direction shows stance; needle length shows strength. On the map: open dot = start, yellow dot = now.

All trajectories above are generated by this toy model, not measured results or reproductions of the paper’s predictions. Changing a parameter recomputes the path from the same starting opinions (+0.25, −0.15). Steps are numerical updates, not the paper’s eight message rounds. No answer is designated “correct.”

Each camp has eight identical agents. We track a smooth expected opinion m between −1 and +1, not a sampled binary vote. Every agent in a camp shares that camp’s value. This deliberately reduces the system to two numbers.

a is within-camp influence, b is between-camp influence, g sets opposing personal leanings, and T is model temperature. Both camps update together. The factor 2 uses the identity 2σ(h/T) − 1 = tanh(h/(2T)); the fixed relaxation fraction 0.35 is chosen for this demonstration.

This is inspired by the paper’s mean-field approximation and temperature scaling. Our camp means replace individual neighbors; the couplings are normalized aggregate weights, not fitted coefficients. There are no language messages, learned fields, stochastic samples, or agent-to-agent differences within a camp. [3] [5]

Our conviction proxy uses squared expected opinions. The paper’s empirical conviction uses squared averages of five sampled votes, which includes sampling variability. The quantities are related in motivation but are not interchangeable. [1] [2]

Pattern labels are teaching aids: c < 0.25 is “Weak views”; otherwise |n| > 0.6 is “Aligned”, |n| < 0.2 is “Opposed camps”, and the rest is “Mixed”. The paper instead selects thresholds separately for each model and task using pooled quantiles. The map’s shaded feasible area follows n² ≤ c ≤ 1, an algebraic consequence of the definitions. [1]

A local pull becomes a collective pattern.

In the fitted model, a neighbor contributes to an agent’s next-opinion probability. Personal leanings add another push. The logistic response turns their combined influence into a probability, so a strong pull makes an opinion more likely without making it certain. [3]

A subtle result: a nominally unfriendly tie need not repel. Its effective weight is β₀ − β₋, while a friendly tie has weight β₊ + β₀. The fitted friendly influence dominates across the main model–task settings. [4]

What the paper actually found.

The authors fitted their statistical model to recorded opinion transitions, then tested it on held-out questions and graphs. These results come from the paper, separately from the workbench. [6]

Interactions carried predictive information.

The three-coupling rule led Table 1 across its reported model and task settings. Here is one slice: GPT-4o-mini, objective questions, previously unseen random test graphs. [6]

The paper’s metric averages four transition categories equally: flip to +, flip to −, stay +, stay −. These percentages measure opinion prediction, not correctness on the math questions. “Mean-field baseline” here is a fitted global-average predictor, distinct from our two-camp demonstration. [6]

More conviction can lead in different directions.

Conviction increased as the studied groups interacted. On objective math questions, incorrect-to-correct majority switches were more common than the reverse for all four models. On political statements, three of four models drifted rightward under the authors’ coding of the statements. [1] [7]

The temperature analysis varied the fitted statistical model. Its operating point lay below the reported critical temperature in every model–task cell, supporting the authors’ account of conviction buildup. This was not a sweep of the language models’ sampling temperature. [5]

Agreement alone does not certify truth. The toy workbench has no ground truth, and subjective political statements in the study have no unique correct answer. [2]

Leave room for the missing words.

The fitted model uses opinion states and connections while discarding the content of the natural-language messages. The main study also assumes a shared binary question, fixed symmetric ties, and updates based on the current inbox rather than full conversational history. [8]

The questions were filtered for high response entropy, so initially uncertain cases were selected deliberately. These are not arbitrary questions or a representative sample of human communities. [2] [8]

Even with the same setup, repeated episodes can end differently. Matching the distribution of group outcomes does not mean predicting the fate of every individual group. [8]

Reading trail

Go back to the source.

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

Batu El, Jinhee Paeng, Fatih Dinc, Shiye Su, Mete Erdogan, Aneesh Pappu, Haotian Ye, Wanjia Zhao, Surya Ganguli & James Zou.

Read in full: arXiv:2608.16578v2, 9 September 2026 · 52 PDF pages, including appendices. This is an educational interpretation of a preprint; scientific review remains required.

Canonical paper ↗ Full-text PDF ↗

[1] Agreement and conviction. §3.2, pp. 8–9, Fig. 4; Appendix C.3, p. 40, Table S3. Definitions of n and c and dataset-relative regime thresholds.

[2] Experimental setup. §2, pp. 4–5; Appendices B.1–B.3, pp. 31–33; E.6, p. 52. Personas, binary questions, five-vote averages, filtering, models, and larger-group extension.

[3] Opinion update model. §4, pp. 10–11; Appendices D.1–D.2, pp. 41–44. Local fields, logistic probabilities, and a mean-field relaxation approximation.

[4] Attraction and repulsion. §5.4, pp. 15–16, Table 3. Effective coupling combinations and the interpretation of fitted interaction strengths.

[5] Model temperature. §5.3, pp. 14–15, Fig. 7; Appendix E.3, pp. 49–50. Temperature scales the statistical model’s logit; finite-size critical temperature from a fluctuation peak.

[6] Predictive performance. §5.1, pp. 12–13, Table 1; Appendices D.3, pp. 44–45, and D.5–D.6, p. 46. Fitting, test splits, balanced accuracy, and deterministic rollouts.

[7] Accuracy and political drift. §3.3, pp. 9–10, Fig. 5; Appendix C.1, pp. 37–38, Fig. S6. Findings are specific to these models, questions, and procedures.

[8] Scope and uncertainty. §5.2, pp. 13–14; §7, pp. 18–19; Appendix E.4, p. 50. Outcome distributions, repeat-run variability, missing message content, and limits of extrapolation.