Coherence-Driven Belief Formation and Population Dynamics of Contagion in LLM Agents

AI summary

Overview

• Research area: Multi-agent AI systems, social contagion theory, and LLM belief dynamics.
• Technical level: Intermediate. The paper combines network-contagion concepts (thresholds, cascade windows, hysteresis) with LLM prompting and logit-based measurement; readers need some familiarity with both, but the paper defines its terms.
• Scope: The paper measures empirically how LLM agents decide to adopt a belief under peer pressure, shows that three separate factors collapse into one "coherence" dimension, and then simulates how beliefs spread, cluster, and persist across networks of 30 agents.

What This Paper Is About

Most models of social contagion assume a rule for how individuals adopt beliefs and then derive population-level behavior from that assumption. This paper reverses the direction: it measures the adoption behavior of LLM agents directly, quantifying the probability that an agent accepts a claim as a function of how many peers endorse it. The goal is to characterize that "adoption kernel" and then ask what collective dynamics emerge when many such agents influence one another on a network.

Key Contributions

1. An empirically measured adoption kernel. Rather than assuming an adoption rule, the authors read the ADOPT/DECLINE decision logits from a single forward pass and compute p_adopt(k) = σ(ℓ_A − ℓ_D) for k = 0 to 10 endorsing peers, producing a sigmoidal (threshold) adoption curve characteristic of complex contagion.
2. A coherence account of belief adoption. Claim plausibility, source reliability, and agent disposition each shift the adoption threshold, and installed priors (about the world, the source, or the agent's own weighting of social input) move thresholds in the direction a coherence account predicts. The three axes are shown to collapse onto a single effective dimension.
3. Population-level signatures of complex contagion. In agent-driven simulations on Watts-Strogatz networks, clustered networks produce significantly larger cascades than random networks of equal density, alongside a bifurcating cascade window with bimodal outcomes.
4. Self-sustaining hysteretic consensus. Using a separately measured "retention" kernel (MAINTAIN/ABANDON) and permanent zealots as external pressure, the authors show that once consensus is reached it stays locked at full adoption even after all pressure is removed, with loops that widen as claim plausibility falls.

Main Findings

• Adoption is sigmoidal and threshold-like. Sweeping k from 0 to 10 peers yields an adoption kernel whose threshold θ is defined as the linearly interpolated k at which p_adopt crosses 0.5 (θ = 11 if it never crosses, θ = 0 if it begins above).
• Plausibility, source, and persona each move the threshold. A plausible claim that needed only 3 endorsing expert peers required 9.4 unreliable peers before being accepted. Credulous agents adopted both plausible and implausible claims from a single peer, while hardened and skeptical agents were immune (never adopted regardless of plausibility or social reinforcement), and only trusting agents were sensitive to the claim's plausibility.
• Priors move thresholds in the coherence-predicted direction. For example, 22 °C had a relatively low threshold under a normal prior, but when the model expected a heat wave or a cold snap, the threshold for adopting that temperature was substantially higher. Source priors and disposition priors moved thresholds similarly.
• The three axes reduce to one dimension. Kernels shifted by their own thresholds collapsed onto a single master curve; the first principal component of the threshold tensor accounted for 98% of the variance in thresholds; and a main-effects model with no interaction terms achieved R² = 92%.
• A bifurcating cascade window. Sweeping coherence via claim plausibility produced a sharp, saddle-node-like transition from full adoption to low adoption (ignition defined as final believing fraction above 0.5). Away from the transition the population was monostable; within it, outcomes were bimodal, so identical conditions produced qualitatively different collective outcomes across replicates.
• Complex contagion on clustered networks. At matched mean degree, clustering coefficient fell from C = 0.60 (ring lattice) to C = 0.20 (essentially random). Clustered networks produced significantly larger cascades (mean final size 0.67 vs. 0.43; one-sided Mann-Whitney U, p = 2.7e-6; rank-biserial effect 0.37).
• Hysteresis and self-sustaining consensus. The up-path required substantial zealot pressure to ignite, but the down-path remained locked at full adoption even as all pressure was removed. Loop area widened with implausibility: 0.067, 0.096, and 0.252 for plausible, borderline, and implausible claims.
• Mechanisms replicate across models and domains. On Mistral-7B-Instruct-v0.3 (temperature domain): first PC 96%, additivity R² 80%, clustering p = 4.1e-3 with effect +0.21, hysteresis loops 0.000 and 0.248 for plausible and implausible claims. On Qwen2.5-3B-Instruct in the traffic domain (next-day commute times): first PC 97%, additivity R² 91%, clustering p = 7.1e-3 with effect +0.20, hysteresis loops 0.065 and 0.248. What varied was calibration, not mechanism: Mistral weighted its own priors over social pressure more than Qwen, producing a wider plausibility range, a sharper bifurcation, and wider hysteresis loops.

Methodology in Plain English

Each "agent" is an off-the-shelf language model given a system prompt that defines its persona and a user prompt presenting a claim plus a summary of peer opinion. At k endorsing peers out of 10, the prompt states that k of 10 peers have already accepted the claim and the other 10 − k have not weighed in. The agent answers with one word, ADOPT or DECLINE.

Instead of generating that word, the researchers read the model's logits for the first sub-word token of each option and take p_adopt(k) = σ(ℓ_A − ℓ_D), then sweep k ∈ {0, …, 10}. This yields the adoption kernel. For the network simulations, each undecided agent computes the fraction of believing neighbors expressed as a count out of ten peers (k_i) and adopts with probability p_adopt(k_i) from a live forward pass, making the simulation agent-driven rather than an averaged response. N = 30 agents sit on a network, a fraction ρ₀ are seeded as initial believers, and the final believing fraction is the cascade outcome.

For clustering experiments, the authors generate Watts-Strogatz networks of fixed mean degree while varying only the rewiring probability, comparing the clustered ring lattice against the essentially random configuration. For hysteresis, they add a retention kernel measured with a MAINTAIN/ABANDON prompt for agents that already hold the belief, so believers abandon with probability 1 − p_retain(k_i). A fraction of agents are permanent zealots who never abandon; ramping the zealot fraction up and then back down traces the hysteresis loop.

Claims are next-day Boston temperatures of the form "Tomorrow it will be T °C in Boston," chosen because they are unverifiable predictions, free of moral content, and easy to make more or less plausible by varying T. The pipeline is replicated on next-day commute times into Boston. All measurements use a single sampling-free forward pass in half precision, and every reported quantity is deterministic given the prompt and random seed.

Why This Matters

Impact on research. The paper provides an empirical alternative to assumed adoption rules in contagion modeling: instead of positing a threshold rule, it measures one and shows that a reasoning, content-sensitive agent reproduces regularities previously derived from simple mathematical assumptions. The one-dimensional reduction is presented as a behavioral analogue of the linear representation hypothesis, raising the question of whether the model's internal basis for belief adoption is itself lower-dimensional than the space of factors influencing it.

Real-world applications.

• Misinformation resilience in agent teams: installing a simple prior tunes an agent across the full behavioral range, from readily accepting social input to never accepting it, which the authors suggest could protect agents against adopting misinformation.
• Multi-agent system safety: a consensus reached by a population of agents, even a false one, may be hard to correct once established, which matters for any deployed system where agents act on one another's conclusions.
• Contagion risk in AI-generated text ecosystems: the introduction cites a large-scale study estimating that roughly one third of newly published web text is now AI-generated or AI-assisted, a channel through which beliefs can propagate indirectly between agents.
• Intervention design: the clustered-versus-random contrast and the hysteresis results give concrete guidance about where and when interventions to suppress a belief are likely to succeed or fail.

Industry relevance. Any organization deploying multiple LLM agents that exchange information and converge on decisions — for planning, negotiation, or recommendation — faces the dynamics described here. The finding that consensus is far harder to remove than to establish is directly relevant to monitoring and correction pipelines.

Future Directions

• Connect behavior to internal representations. The authors characterize coherence in behavior, not in the model's internal representations, and suggest connecting the findings to an internal mechanism of belief adoption.
• Give agents explicit belief networks. In non-LLM agents, a model built on signed, weighted belief networks reproduces both simple- and complex-contagion dynamics depending on how well an incoming belief coheres with priors; installing LLM agents with explicit networks of prior beliefs could bridge behavior and mechanism.
• Study competing contagions. The current work considers a single belief spreading in isolation; a natural extension is competing claims and the question of how to suppress an undesirable belief while allowing a desirable one to spread.
• Scale and diversify. Populations are small (N = 30) and networks stylized, and only two models and two belief domains are studied, which separates model effects from domain effects but cannot establish the pattern across scales or model families. Because the claims are unverifiable predictions, results may not carry over to factual, morally charged, or multi-claim beliefs where fact retrieval and cross-claim consistency would introduce dynamics absent here.

Target Audience

Researchers working on multi-agent LLM systems, agent safety, and opinion-dynamics modeling will benefit most. The paper is also useful for computational social scientists interested in whether classic contagion findings transfer to AI agents, and for practitioners building or monitoring multi-agent deployments who need to understand how beliefs spread, stabilize, and resist correction. Readers without background in contagion theory or LLM prompting should expect an intermediate learning curve.

Authors’ abstract

Models of social contagion usually assume how individuals adopt beliefs and derive population behavior from it. We instead empirically measure belief adoption in language model agents, quantifying the probability an agent adopts a claim given how many peers endorse it. We find this adoption kernel to be sigmoid, a characteristic of complex contagion, with a threshold that is sensitive to three sources: the claim's plausibility, the source's reliability, and the agent's disposition. These three dimensions are well approximated by a single effective dimension which we propose can be understood as the coherence of the incoming belief with the LLM agent's prior beliefs. Further, we observe a characteristic of complex contagion in the collective dynamics of belief adoption in a system of AI agents: further spread on clustered than random networks. These systems also exhibit a bifurcating cascade window, and self-sustaining hysteretic consensus which lead to consensus being far harder to remove than to establish.