Summary
Probine and colleagues at UT Austin run 30-agent networks of Llama-3.1-8B, Qwen3-VL-8B or Gemma-3-4B (Probine et al. 2026). Agents are assigned stances on climate change, vaccines or gun control and post to one another over random graphs. The authors score each post as an opinion and fit classical opinion-dynamics models to the trajectories. Averaging models (DeGroot) and averaging with an anchor to each agent's starting opinion (Friedkin–Johnsen) fit about equally badly. Adding one term, a pull toward a single opinion shared by all agents, cuts held-out integral mean-opinion error by 81–88% for Llama3.1 and 54–62% for Qwen3. For Gemma3 the cut is 87% on vaccines and 30% on gun control, and on climate error rises by 6%. In the fitted parameters the anchor to starting opinion never exceeds 0.04 and the bias weight runs 0.17–0.36. Once the bias term is present, homophily weighting changes held-out mean error by at most about 6%, though Qwen3 fits substantial homophily strength.
This is a collective dynamics finding. It is the concept's second account fitted to data, after the Ising fit in Physics of Agents, and the first whose dominant term is individual. On the wiki's reading of the paper's equation (4) with λ₀ near zero (it fits at 0.038 or less, not zero), the best model's dynamics settle with every agent close to the shared bias, so it predicts agreement. The authors do not derive or report this. It reaches agreement through a disposition each agent brings, not through peer coupling. For Llama3.1 the neighbour term is near zero on every topic. On the concept's open disagreement, it adds a route to agreement other than peer attraction. It also bears on the reading that polarization needs persistent heterogeneity: assigned stances, restated in every prompt, fit as near-zero anchoring, so here they do not persist.
Method
Simulation. n=30 agents per run on a directed graph drawn from Erdős–Rényi, Chung–Lu or stochastic-block models. Each agent is told it is a social media user and given one of five stances (opposed, skeptical, neutral, tends to agree, strongly believes) on a topic statement, described as its stable perspective. Before each post the agent sees up to 10 posts sampled from the agents it follows. It also sees its stance prompt again and a rolling history of its own earlier justifications. It writes a justification and then a post. Posting order and times are random.
Opinion measurement. A post's opinion is its cosine similarity to a pro reference text minus its similarity to an anti reference text, under OpenAI's text-embedding-3-small. An agent's opinion is the mean over its last five posts. Before an agent's first post its initialization prompt is scored instead. The statements and reference texts are not given.
Models fitted. DeGroot (neighbour averaging). Friedkin–Johnsen (FJ: averaging plus weight λ₀ on the agent's initial opinion). FJ+Bias, which adds weight λ_b on a uniform opinion b ∈ [−1, 1], the same for all agents. Each also has a homophily variant that down-weights neighbours by opinion distance with strength γ. Weights sum to one. RQ1 and RQ2 use an adjacency-based form, with influence fixed by the graph and only scalar weights fitted. Self-weight λ_self and neighbour weight λ_neigh are then reported separately.
Data. Per LLM–topic pair, 24 training runs and 8 test runs, each about 10 time steps. Training and test use different initial-opinion configurations: uniform, bimodal, centred and skewed for training, and consensus-pro, consensus-anti, centred-with-extremes and hollow-centred for test. 329 runs in all, by the authors' count (A.1.3). RQ3 uses one Chung–Lu graph, Gemma3 on vaccines, 29 fitting runs and 12 evaluation runs.
Key results
Bias carries the fit (Table 5). Across all nine LLM–topic pairs, FJ tracks DeGroot almost exactly, so anchoring to initial opinion buys nothing. Adding the bias term cuts integral mean-opinion error (FJ against FJ+Bias, computed from Table 5) by 81%, 83% and 88% for Llama3.1 on climate, gun control and vaccines. For Qwen3 the cuts are 61%, 54% and 62%, and for Gemma3 −6%, 30% and 87%. Wasserstein-1 falls by up to 67% on the authors' count (66% against FJ in Table 5), also on Llama3.1 vaccines. Variance error is not reduced by bias in any cell. Vaccines gains most for every model, and the authors suggest alignment training pushes models toward a consistent stance on health misinformation whatever stance they are assigned.
Fitted weights (Table 1, FJ+Homo+Bias). λ_self runs 0.53–0.70, which the authors say mainly sets convergence speed against the sampling interval. λ₀ is at most 0.04 (0.038, Llama3.1 gun control), even though every post is generated from a prompt that restates the assigned stance. λ_b runs 0.17–0.36. λ_neigh runs 0 (Llama3.1 gun control) to 0.20 (Qwen3 vaccines). The fitted b is positive in all nine cells, from 0.23 to 0.85.
How social each model is. The authors summarise this as the ratio λ_neigh / (λ_b·b). Llama3.1 stays at 0–0.13 on every topic. Qwen3 runs 0.72–1.61. Gemma3 runs from 0.05 on vaccines to 3.69 on gun control. The authors call Llama3.1 almost purely dispositional and Qwen3 the most social. They suggest, without testing it, that newer post-training teaches models to weigh the conversation over a stance fixed in training.
Homophily. In the authors' sweep over three representative LLM–topic pairs (Figure 2), γ moves the fit by about a percent at most. In Table 5, once bias is present, adding homophily changes held-out integral mean error by at most about 6% (Qwen3: 0.536→0.519 on climate, 0.601→0.620 on gun control, 0.333→0.351 on vaccines). Without bias, homophily helps more, about 13–16% in some cells (DeGroot to DeGroot+Homo, Qwen3 and Llama3.1 climate). Fitted γ is 0 in four cells. The authors note Qwen3 alone fits substantial homophily (γ 1.09, 0.97 and 23.2).
Network-specific weights do not help (Table 2). On the single RQ3 graph, a full per-edge influence matrix lowers training error (8.91 against 9.22 ×10⁻³) but raises both test errors (Wasserstein-1 0.541 against 0.534; mean error 0.249 against 0.223). The homophily variant gives identical numbers because its fitted γ collapses to zero.
Why it matters
It answers a different question from the Ising fit, and the two are not in conflict. Physics of Agents predicts whether each agent flips or stays, using peer couplings plus a per-agent intrinsic field regressed from persona and question. Its fitted couplings favour consensus because attraction outweighs repulsion. This paper predicts the trajectory of the population's opinion distribution, and its best model also points to agreement, by a different route. It has no repulsive channel, the anchor to assigned stance fits near zero, and the one remaining heterogeneity-preserving term, homophily, adds nothing to held-out fit once the bias is present. So every agent drifts toward the same b. That fixed point is the wiki's derivation from the paper's equation (4) with λ₀≈0, not a result the authors report. Both papers find agreement, then: one through social attraction, one through a shared pull that needs no neighbours.
The innate bias maps onto part of the Ising intrinsic field. The authors' b is one number per model and topic, the same for every agent and independent of its assigned stance. The Ising field gᵢ is per agent and regressed from persona and question embeddings. So b corresponds at most to the persona-independent, question-level part of gᵢ, with the persona-specific part removed, and the paper's result is that this part of the agent's own pressure dominates. Physics of Agents' interaction-free baseline (intrinsic field alone) is near chance for three of four models, which looks opposite. The metrics differ, though: balanced accuracy on rare individual flips there, mean and distributional error on the population here. A uniform b is suited to what Physics of Agents reports as population-level drift: three of four models drifting right on political statements, and, on label-balanced objective questions, Llama-3.1-8B's share of +1 answers falling from 39% to 16% with no content reason. That alignment is the wiki's reading. Neither paper compares the two terms.
Llama 3.1 8B points the same way in three designs, with a caveat. Here its neighbour weight is near zero on every topic. In Weng et al.'s scripted-majority test, Llama3.1-8B's accuracy is unchanged when six scripted peers are wrong, and the authors call the Llama 3.1 series resistant to external guidance. In Physics of Agents, Llama-3.1-8B-Instruct shows the content-free label drift. The checkpoints may not be identical (an Ollama llama3.1:8b tag here, the Instruct release there). Weng et al. also find Llama3.1-8B moving against the group: its accuracy drops under a correct majority (53.0% to 46.2%) and it changes answers often under Doubt. A non-negative neighbour weight cannot represent that, so a near-zero λ_neigh here may also be an average over pull and push. The shared reading, a model-level lean that outweighs peers, is the wiki's. Prompts, tasks and quantization differ, so this is convergence, not replication.
It is the concept's first evidence that structure can matter little. The concept's pattern is that population size, wiring and composition change the outcome with the model fixed. Here the graph enters only as a known input, per-edge weights do not improve held-out fit, and the authors read the fitted weights as a profile of the model that carries across networks. On this paper's evidence, how much the network matters is itself a property of the model, near zero for Llama3.1 and comparable to the bias for Qwen3.
interpretive tensions
Measured bias or measurement offset. Opinions at t=0 are scored from the initialization prompt and later ones from posts, all against unpublished reference texts. A constant gap between how prompts and posts sit in embedding space, or a stylistic lean in the posts, would show up as regression toward a uniform b. b is positive in every cell. The paper does not test for an offset. The authors' reading, a trained-in stance (they cite Santurkar et al.), is plausible for vaccines, but the data cannot tell it apart from the instrument.
Agreement is partly built into the model class. Apart from homophily and the λ₀ anchor, none of the fitted models can sustain a split. There is no repulsive term, and the bias is a single uniform value. That both heterogeneity-preserving terms fit near zero is informative. It still does not show that these networks cannot polarize, because the model class could not represent most ways they might. Bias also leaves variance error unchanged, so the fits capture where the mean goes better than how spread out opinions stay. Runs last about 10 steps, so no endpoint is observed. The paper reports no consensus or polarization outcome directly.
Out-of-distribution test sets favour the bias term. The test set includes consensus-pro and consensus-anti starts that training lacks. A population started at one pole that drifts toward b is exactly what a model without b cannot predict. The 88% is real out-of-sample, but it is measured on starts chosen to stress the drift.
Small and older models. All three are 4–8B open-weight models, one of them the vision-language variant of Qwen3. The authors say consistency across families points to properties common to instruction-tuned LLMs. They also suggest Llama3.1's extreme reflects its age, and that cuts against generalising from it. They also argue that because the agents are homogeneous, larger networks should show similar patterns. That is asserted in the Limitations, not tested: N is 30 throughout.
Portability is claimed on one graph. The RQ3 test is one Chung–Lu graph, one model and one topic. The RQ1/RQ2 fits pool three graph families, which partly supports transfer, but no fit is tested on a graph family it was not trained on. Physics of Agents does test that.
The social ratio divides by b. λ_neigh / (λ_b·b) grows as the fitted bias nears zero. Gemma3 gun control's 3.69 pairs λ_neigh 0.14 with the lowest λ_b (0.17) and the lowest b (0.23). The ratio mixes how much an agent listens with how far its innate opinion is from zero.
concepts
- Collective dynamics — the second account fitted to data, after the Ising fit, and the first whose dominant term is individual. In eight of nine model–topic pairs it fits a shared innate opinion that every agent regresses toward, with near-zero anchoring to assigned stance. Homophily adds nothing to held-out fit once the bias is present, though Qwen3 fits substantial homophily strength. On the wiki's reading of equation (4) with λ₀ near zero, the fitted dynamics converge on agreement without needing peer influence. The neighbour weight is itself model-dependent. The fit is partial, because the paper fixes N and reports no endpoint outcomes. Population structure here is a fitting input, not a manipulated variable.
cross-references
- Physics of Agents — the Ising fit. On the wiki's mapping, the innate bias b corresponds to the persona-independent part of its intrinsic field gᵢ. Both papers run a Llama 3.1 8B model, though not demonstrably the same checkpoint, and both point to agreement by different mechanisms (Why it matters).
- Flag game — polarization sustained by private evidence. This paper has no private evidence. On the wiki's reading of a fitted weight (λ₀ ≤ 0.04), its assigned stances do not persist. The paper shows no decay curve or endpoint. That fits the concept's reading that polarization needs persistent heterogeneity, though it does not test it.
- Piao et al. — their left skew comes from agents drifting from assigned stances toward the model's own lean, which the authors call self-inconsistency. That drift resembles what this paper's uniform bias fits, in a different setup (fixed graphs, small open models). This paper does not cite or test it. There, homophilic rewiring of the network keeps camps apart. Here, homophily is opinion-distance weighting on a fixed graph, not rewiring, and it adds nothing to held-out fit once the bias is present. That is consistent with Piao's static-network control, where one camp dominates.
- Weng et al. — Llama3.1-8B is unmoved by a scripted wrong majority, matching its near-zero neighbour weight here. Under a correct majority and under Doubt, Weng et al. find it moving against the group, which a non-negative λ_neigh cannot represent.
- Sycophancy — adjacent, not instantiating. λ_neigh is peer influence with no user and no correctness standard. The cross-model spread (Llama3.1 near zero, Qwen3 comparable to the bias) is a peer-conformity profile, not capitulation against known evidence.
- Persona selection — adjacent, not instantiating. The paper assigns a stance persona and finds it decays (λ₀ ≤ 0.04) toward a model-level opinion that the authors attribute to training. It measures no persona, and the reading that an assigned role gives way to the model's own stance is the wiki's.
sources
- Probine, C., Bayiz, Y. E., Fotiadis, F., Li, S., Yang, Y., & Topcu, U. (2026). Characterizing Opinion Evolution of Networked LLMs. arXiv:2606.18276.