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

1 Introduction

• Erroneous or manipulated beliefs can spread between AI agents directly or indirectly through AI-generated text.A cited estimate places AI-generated or AI-assisted text at roughly one third of newly published web text [2].Source: §1 · p. 1
• Human social-contagion research distinguishes single-interaction spread from reinforcement by multiple peers and studies how prior beliefs and source reliability shape adoption [7].Prior work also includes threshold, epidemic-style, opinion-averaging, bounded-confidence, Bayesian, and confirmation-bias models [14].Source: §1 · p. 1
• Unlike predefined-rule models, LLM agents can interpret claim content and sources and can be conditioned to reproduce fine-grained, demographically realistic responses [3] [15].Related work uses generative agent societies and multi-agent debate to study social behavior [16] [17].Source: §1 · pp. 1–2
• The paper measures adoption probability against peer endorsements and reports sigmoid adoption, coherence-linked thresholds, greater spread on clustered networks, and hysteretic consensus.It frames plausibility, agent disposition, and source reliability as factors acting through coherence with prior beliefs.Source: §1 · p. 2

Social contagion and social influence

• Social contagion research distinguishes simple contagion from reinforcement-dependent complex contagion, and clustered-network advantage is conditional on low unsupported and high reinforced adoption [19].Persuasion research identifies social reinforcement, claim credibility, source expertise, and prior belief as recurring factors [7].Source: §2 · p. 2

Classical agent-based models of opinion dynamics

• DeGroot models average neighbors’ opinions, while bounded-confidence models ignore sufficiently dissimilar neighbors; these frameworks use fixed update rules regardless of claim content or source.A cognitive model of interacting beliefs can produce simple- or complex-contagion curves as an emergent property [20].Source: §2 · p. 2

Belief updating in language models

• Prior LLM studies report sycophancy [21] [22], sigmoid-like networked adoption [23], and persona-dependent misinformation resilience [24], [25]; this paper studies these factors together.The prior networked-agent study did not examine variation with credibility, expertise, or clustering [23].Source: §2 · p. 2

3.1 Agents and the adoption kernel

• Agents received a persona and peer-endorsement summary, then answered ADOPT or DECLINE; adoption probability was computed from decision-token logits across endorsement counts.The adoption threshold was the interpolated peer count where adoption probability crossed 0.5, with specified boundary values when it never crossed or began above that level.Source: §3.1 · p. 3

3.2 Beliefs and coherence manipulations

• The study varied temperature claims, source reliability, and agent disposition, then installed claim, source, or disposition priors to test threshold shifts.Boston temperature predictions were unverifiable, non-moral claims; results were also replicated using next-day commute-time claims.Source: §3.2 · p. 3

3.3 Low-dimensional approximation

• A 3×3×3 grid of claim, source, and persona kernels formed a threshold tensor, tested for dimensionality and for fit by a no-interaction main-effects model.The analysis unfolded the tensor into a 3 × 9 matrix for singular-value decomposition and recorded the main-effects model’s R2.Source: §3.3 · p. 3

3.4 Population model

• Population simulations placed 30 agents on a network, seeded initial believers, and used live model calls for adoption; clustering comparisons held mean degree fixed while varying rewiring.Hysteresis experiments measured a retention kernel, allowed agents to abandon beliefs, and ramped permanent zealots up and down to trace the loop.Source: §3.4 · pp. 3–4

3.5 Models

• Qwen2.5-3B-Instruct was the primary model, and the pipeline was replicated on Mistral-7B-Instruct-v0.3.Further implementation details and replicate counts are given in Appendix C.2.Source: §3.5 · p. 4

4.1 Belief adoption is driven by coherence

• Adoption kernels were sigmoidal and sensitive to claim plausibility, source reliability, and persona; implausible claims needed more peer reinforcement, while hardened or skeptical agents never adopted.Credulous agents adopted plausible and implausible claims from one peer, whereas only trusting agents responded to plausibility.Source: §4 · p. 4, §4.1 · p. 4
• Installed priors shifted adoption thresholds in the direction predicted by coherence, including claim priors, source-reliability beliefs, and instructions weighting personal knowledge against social input.For example, the 22°C claim had a low threshold under a normal prior but a substantially higher threshold under heat-wave or cold-snap expectations.Source: §4.1 · p. 4

4.2 Reduction to a one-dimensional effective coherence

• Threshold-shifted kernels collapsed onto a master curve; the first principal component captured 98% of threshold variance, and a no-interaction additive model achieved R2 = 92%.The figure presents the kernel collapse and additive-model comparison across the 3×3×3 grid.Source: §4.2 · pp. 4–5, Figure 1 · p. 5

5 Population dynamics of belief adoption

• The population experiment swept claim plausibility as a proxy for coherence and counted a belief as ignited when more than half the agents believed it.Agents could adopt through the adoption kernel and abandon through the retention kernel as the fraction of permanent believers rose and fell.Source: §5 · p. 5, §5.3 · p. 6

5.1 The cascade window and its bifurcation

• Ignition probability dropped steeply through a saddle-node-like transition as claim plausibility fell, with bimodal outcomes within the transition and monostable outcomes on either side.The bimodality means identical conditions could yield qualitatively different collective outcomes across replicates.Source: §5.1 · p. 5, Figure 2 · p. 6

5.2 Complex contagion: cascade size on clustered networks

• At matched degree, clustered networks produced larger cascades than random networks (mean final size 0.67 vs. 0.43; p = 2.7e-6).The comparison used Watts-Strogatz networks with clustering coefficients C=0.60 and C=0.20 in the marginal regime.Source: §5.2 · p. 6, Figure 2 · p. 6

5.3 Hysteresis: consensus is self-sustaining

• Consensus remained at full adoption as external pressure fell to zero, and the hysteresis loop widened as claims became less plausible.Loop areas were 0.067, 0.096, and 0.252 for plausible, borderline, and implausible claims, respectively.Source: §5.3 · p. 6, Figure 2 · p. 6

• Across the primary condition and both robustness conditions, the adoption kernel remained sigmoidal, the three factors acted as coherence relations, and population dynamics retained bifurcation, clustering, and hysteresis signatures.Calibration varied: Mistral weighted priors more than Qwen, while traffic-domain beliefs tracked temperature-domain results closely.Source: §6 · p. 7

7 Discussion

• LLM agents show sigmoidal adoption kernels, and plausibility, source reliability, persona, and prior beliefs appear to act through a single effective coherence dimension.The authors characterize this as a behavioral reduction, not evidence that the internal representation is one-dimensional.Source: §7 · p. 7
• A consensus, even a false one, may be difficult to correct once established, while installing a prior could protect naive agents against misinformation.The authors also describe prior installation as a way to tune agents from readily accepting social input to never accepting it.Source: §7 · p. 7

7.1 Limitations and Future Directions

• The one-dimensional result concerns adoption behavior, not the model’s internal representations.Explicit networks of prior beliefs are proposed as a way to connect the behavioral findings to an internal mechanism.Source: §7.1 · pp. 7–8
• The study tests one isolated belief, small stylized populations, two models, and two domains, so it cannot establish whether the pattern generalizes across scales or model families.Because the claims are unverifiable predictions, the findings may not carry over to factual, morally charged, or multi-claim beliefs.Source: §7.1 · p. 8

• Every result reproduced qualitatively on Mistral, whose more categorical weighting of priors and sources yielded a wider plausibility range, an all-or-nothing source axis, a sharper bifurcation, and wider hysteresis loops.The replication used the same temperature domain and prompts as the primary Qwen condition.Source: A Full Temperature domain with Mistral… · p. 10

The three axes

• Claim plausibility and source reliability shape thresholds: expert sources lower them, while unreliable sources produce near-total rejection even for plausible claims.The immune-to-credulous resilience ladder persists, though even the credulous persona retains a prior-based floor for implausible claims.Source: §A.1 · p. 10

Coherence tests

• Installing beliefs about claim context, source reliability, or coherence weighting shifts adoption thresholds in coherence-predicted directions.The source-reliability belief moves the threshold by up to 8.9 peers; coherence weighting reproduces the resilience ladder without personality descriptors.Source: §A.1 · p. 10

The reduction

• Mistral’s threshold tensor is one-dimensional, with its first principal component capturing 96% of threshold variance.The additive model explains 80% of the variance, lower than Qwen’s 92%, as Mistral’s categorical thresholds introduce more interaction.Source: §A.1 · p. 10

A.2 Population dynamics of belief adoption

• Mistral’s cascade window closes sharply near 34°C, with monostable outcomes on either side and bimodal outcomes in the narrow transition zone.The transition is sharper and the marginal regime narrower than Qwen’s.Source: §A.2 · p. 10
• At matched degree, clustered networks produced larger cascades than random networks (mean final size 0.83 vs. 0.65; p = 4.1e-3).The effect was moderate; Mistral’s higher baseline ignition in the marginal regime compressed the topology-related headroom.Source: §A.2 · p. 10
• Consensus remains at full adoption as pressure is removed, and hysteresis loop area grows with implausibility (0.000, 0.159, and 0.248).The plausible loop is near zero because adoption saturates immediately on the upward path.Source: §A.2 · pp. 10–11
• Across Mistral’s results, coherence-driven resistance, its one-dimensional reduction, cascade bifurcation, clustering signature, and self-sustaining consensus recur, while magnitudes and dominant resistance axes are model-specific.The authors attribute these model-specific differences to Mistral’s stronger, more categorical weighting of priors and sources.Source: §A.2 · p. 11

B Full traffic-domain with Qwen results

• The traffic-domain replication uses Qwen2.5-3B-Instruct and next-day commute-time claims, an unverifiable prediction with a graded prior and a softer plausibility ceiling than temperature.The authors report that every result reproduces and that the traffic results track the temperature results closely, including reduction statistics and hysteresis loop areas.Source: B Full traffic-domain with Qwen results · p. 13

B.1 Individual belief adoption

• For traffic claims, adoption thresholds are 3.3, 3.6, and 7.1 peers for plausible, borderline, and implausible commutes; the borderline commute is softer than its temperature counterpart.Source authority compensates for implausibility, and the resilience ladder persists, with plausibility discriminating only in the sensitive band.Source: §B.1 · p. 13
• In the traffic domain, road-condition priors shift thresholds in coherence-predicted directions, while source-reliability beliefs and coherence instructions also modify thresholds.A gridlock prior lowers thresholds for long commutes and raises them for short ones; a clear-roads prior acts in the opposite direction.Source: §B.1 · p. 13
• The traffic-domain threshold tensor is one-dimensional (first principal component 97% of variance), and its additive model explains 91%.These values closely match the temperature primary’s 98% and 92%.Source: §B.1 · p. 13

B.2 Population dynamics of belief adoption

• The cascade transition crosses 0.5 ignition probability at approximately four hours, with monostable outcomes on either side and bimodal outcomes in the transition zone.The authors describe the transition as clean and monotonic.Source: §B.2 · p. 13
• At matched degree, clustered networks produced larger cascades than random networks (mean final size 0.62 vs. 0.48; p = 7.1e-3).The comparison was measured in the marginal regime identified by the bifurcation.Source: §B.2 · p. 13
• Consensus remains at full adoption as pressure is removed, while hysteresis loop area increases with implausibility (0.065, 0.080, and 0.248).The areas are nearly identical to the temperature-domain values (0.067, 0.096, and 0.252).Source: §B.2 · p. 13
• The traffic-domain results closely match the temperature primary, and together with the model replication support robustness across both model and domain.The reported mechanisms are invariant across both, while model shifts magnitudes and the dominant resistance axis and domain shifts little.Source: §B.2 · pp. 13–14

C Reproducibility details

• The pipeline uses a single sampling-free forward pass in half precision, reading decision logits rather than generating tokens.Measurements are deterministic given the prompt and random seed; the appendix also identifies the models’ license and code/configuration location.Source: C Reproducibility details · p. 16

C.1 Prompt templates

• At k=10, the adoption template says that zero peers have not weighed in; measured adoption remains a smooth continuation from k=9.For the few conditions whose 0.5 crossing falls between k=9 and k=10, the interpolated threshold depends on that endpoint.Source: §C.1 · p. 16
• Prompt templates specify belief-maintenance and adoption decisions, peer-count wording, installed priors, and four resilience personas.The adoption template can include a source descriptor and an installed prior in the relevant experiments.Source: §C.1 · pp. 16–17

C.2 Decision tokens

• Table 2 lists the first sub-word token identifiers per model, verified as distinct and consistent with greedy decoding on a clear prompt.Token identifiers were recomputed per model.Source: §C.2 · p. 17, Table 2 · p. 17

C.4 Source and reliability descriptors

• Source experiments compare expert, ordinary, and unreliable descriptors, while the reliability-coherence test holds the source label fixed and varies the installed belief.Source: §C.4 · p. 17

C.5 Population and network parameters

• Table 4 specifies fixed population-simulation parameters per experiment, with replicate stochasticity coming from the random seed.Source: Table 4 · p. 18

C.6 Statistical procedures

• Clustered-versus-random contrasts use a one-sided Mann-Whitney U test, and rank-biserial correlation reports effect size.Ignition probability is the fraction of replicates whose final belief fraction exceeds 0.5.Source: §C.6 · p. 18

C.7 Compute

• A full model-domain condition takes approximately one GPU-hour on a single NVIDIA L4 GPU in half precision.Population simulations dominate compute because each cascade step requires a forward pass per distinct believing-neighbor count.Source: §C.7 · p. 18