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Local Predictability and Collective Fidelity in LLM-Agent Societies

Igor Itkin

arXiv:2609.35813v1physics.soc-phcs.AIcs.CLcs.MA

TL;DR

The paper asks whether better prediction of individual LLM-agent decisions translates into more accurate collective dynamics, a distinction that matters when surrogates generate their own interactions. It compares predictor inputs and forecast settings on public and new opinion-trajectory data, finding that individual gains do not guarantee group-forecast gains.

  • Problem

    It is unclear when improvements in predicting individual decisions translate into more accurate collective dynamics, because surrogate-generated interactions can propagate prediction errors through a population.

    Source: §I · p. 1

  • Method

    The paper compares probabilistic opinion-update policies using global, neighbor, and history information, evaluating both recorded transitions and the collective trajectories the policies generate.

    Source: §II · p. 2

  • Results

    Neighbor information improves individual prediction in all public-data point estimates and pooled group forecasts on held-out questions, but collective gains vary across transfer settings and new tests do not confirm earlier contrasting initial-state history effects.

    Source: §XIII · p. 21

  • Takeaways & Limitations

    Accurate individual prediction is insufficient evidence of accurate group forecasts, so collective quantities require direct evaluation.

    Source: §XIII · p. 21

    The Gemma–Qwen contrast compares fitted simulators rather than testing intrinsic LLM memory, because short histories may not identify their autonomous continuations.

    Source: E. Selection effects and parameter… · p. 20

Abstract

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Compact surrogates could reduce the cost of simulating large language model societies, but must reproduce collective behavior. We compare individual predictions and collective forecasts using 9,455 published trajectories and new experiments on opinion dynamics. Neighbor information improves individual prediction in all 16 public-data settings and pooled collective forecasts on held-out questions, although collective gains depend on transfer conditions. Tests on 24 new statements do not confirm earlier contrasting history effects in forecasts from the initial state. Qwen benefits from history after three observed rounds. These findings motivate direct collective validation, explicit limits on available observations, and comparisons with simple baselines.

I. INTRODUCTION

Neighbor information can improve predictions of individual opinions without consistently improving forecasts of collective behavior. The paper reanalyses public LLM-agent histories and tests how predictor inputs and observed history affect simulated opinion dynamics.

I. INTRODUCTION

  • Predicting recorded individual decisions and generating a sequence of decisions are distinct tasks because a surrogate’s errors can alter later interactions and collective behavior.Thus, better individual prediction need not imply a more accurate group forecast.Source: §I · p. 1

II. STUDY SCOPE AND INFORMATION COMPARISONS

  • The analysis compares predictor inputs on public histories and separately collected LLM trajectories, including transfer to new questions and graphs and forecasts after observed rounds.It also varies group size, forecast duration, questions, and LLM backends.Source: §I · p. 1, A. Related work · p. 2

I. INTRODUCTION

  • Neighbor opinions improve individual prediction in all reported public-data point estimates and improve pooled group forecasts on held-out questions, but group gains vary by transfer setting.The new 24-statement test does not confirm the earlier contrasting history effects for forecasts from the initial state; Qwen benefits from history after three observed rounds.Source: §I · p. 1

A. Related work

  • Related work distinguishes prediction of recorded decisions from generating future sequences, while projection methods explain why discarded state information can make past observations predictive.Neither connection identifies an intrinsic memory mechanism in an LLM.Source: A. Related work · p. 2

A. Retained information and policy features

  • The public-data policies compare global means, neighbor counts and opinions, and past opinions, while retaining individual agents in simulation.The global policy adds the population mean; graph policies add neighbor information, and history policies add past-round values.Source: A. Retained information and policy… · p. 3

B. Local scoring rules and collective fidelity

Local probabilistic accuracy and collective fidelity are related but distinct evaluation targets. The section explains a path-divergence bound and why it does not replace direct evaluation of group forecasts.

B. Local scoring rules and collective fidelity

  • Log loss is a proper score for probabilistic transitions, yet lower log loss need not mean smaller error in a chosen group-level quantity.Direct autonomous evaluation remains necessary for the collective observables of interest.Source: B. Local scoring rules and collective… · p. 4
  • The path-divergence decomposition includes total correlation in the next-spin distribution at a fixed history, with subsequent expectations averaging over histories.Summing the one-step identity over time yields the conditional chain rule for path divergence when initial-state laws match.Source: B. Local scoring rules and collective… · p. 4
  • Lower expected one-step cross entropy decreases path divergence for the product-kernel surrogate family, but does not guarantee lower error for a particular group observable.Finite test data estimate cross entropy, not the unknown entropy or conditional total correlation, and per-node gains alone cannot certify small absolute path divergence.Source: B. Local scoring rules and collective… · p. 4

IV. DATA, PROTOCOL, AND EVALUATION

The public-data analysis uses an audited set of binary opinion trajectories and separates question-level training, validation, and test data. Its two transfer settings differ in whether the test set also shifts graph type.

A. Snapshot and integrity audit

  • The audited primary analysis retains 9,455 complete episodes from 9,600, after excluding episodes with nonbinary histories or disagreement with raw-vote majorities.Each episode has 32 nodes and nine recorded states; the dataset covers 60 questions and four backbones.Source: A. Snapshot and integrity audit · p. 4

B. Question-level separation and two transfer settings

  • Surrogate calibration fits response probabilities, while validation data select regularization and history depth and test data measure performance.A test on a calibrated question and a test on a question never used in fitting assess different generalization claims.Source: B. Question-level separation and two… · p. 5
  • Questions are split into training, validation, and test partitions without overlap, and the same assignment is used across backbones, graphs, and replicas.The split is 50/20/30 within each question mode, with assignment preserved across the analyses.Source: B. Question-level separation and two… · p. 5
  • Question-plus-graph transfer tests held-out questions on unsigned lattices after training and validation on signed graphs, so it changes both questions and graph distribution.That test population is a subset of the question-transfer population, not an independent dataset.Source: B. Question-level separation and two… · p. 5

C. Observed transitions and autonomous collective observables

The section evaluates individual transition predictions and autonomous group forecasts separately. Neighbor opinions improve local prediction, but collective gains vary with transfer setting, normalization, and history.

C. Observed transitions and autonomous collective observables

  • One-step log loss is averaged over nodes and rounds, then episodes within questions and test questions; pooled intervals resample whole questions.Backbones are repeated measurements, not independent questions, and intervals are descriptive rather than multiplicity-adjusted.Source: C. Observed transitions and autonomous… · pp. 5–6
  • Collective evaluation uses autonomous rollouts from accepted initial states, recomputing surrogate features without observed future states or lags.The primary outcome is ensemble-mean trajectory MAE; terminal W1 and absolute-magnetization error are secondary outcomes.Source: C. Observed transitions and autonomous… · pp. 5–6

A. Graph information and collective prediction

  • Graph fields improve one-step log loss in all 16 cells; on held-out questions, pooled reductions are 0.1518 nats per node-transition and 0.0315 in trajectory error.The pooled terminal-distribution error reduction is 0.0526.Source: A. Graph information and collective… · p. 6
  • Under the joint question-and-graph shift, the local reduction is 0.1412, while collective trajectory and terminal-distribution reductions remain unresolved.The intervals for both collective comparisons cross zero.Source: A. Graph information and collective… · p. 6

B. Degree normalization and lagged features

  • Normalization reduces held-out log loss by 0.0057, but its trajectory-error reduction is unresolved; under joint shift, collective outcomes favor unnormalized graph fields.Under joint shift, the trajectory reduction from graph to normalized policy is −0.0253 and terminal W1 reduction is −0.0537.Source: B. Degree normalization and lagged… · p. 6
  • The validation-selected history policy improves pooled test log loss in both transfer settings, but neither setting shows a resolved mean-trajectory or terminal-distribution gain.Pooled log-loss improvements are 0.0116 for question transfer and 0.0103 for combined transfer.Source: B. Degree normalization and lagged… · p. 6
  • The local benefit of history supports predictive relevance within this model family, but does not establish finite-memory closure or improved collective simulation.Optimizing one-step history depth does not demonstrate improvement in the selected collective outcomes.Source: B. Degree normalization and lagged… · p. 6

C. Absolute fidelity, simple controls, and Monte Carlo sensitivity

Absolute collective fidelity can diverge from local predictive gains, and simple controls sometimes perform well. Sensitivity analyses preserve several conclusions while underscoring limits from observed data, splits, and scoring choices.

C. Absolute fidelity, simple controls, and Monte Carlo sensitivity

  • In Llama subjective-question combined transfer, graph log loss improves from 0.183 to 0.145 even as trajectory MAE worsens from 0.421 to 0.531.The interaction-free policy has trajectory MAE 0.171 despite worse log loss of 0.224, illustrating distinct evaluation targets.Source: C. Absolute fidelity, simple controls,… · pp. 6–7
  • The graph policy beats persistence in mean-trajectory error in 11 of 16 cells, although some systems with little collective motion favor simpler controls.Mean-trajectory agreement alone does not identify the microscopic interaction mechanism.Source: C. Absolute fidelity, simple controls,… · p. 7
  • Increasing simulator draws from 200 to 1,000 changes trajectory MAE by at most 0.0032 and terminal W1 by at most 0.0058 across 48 policy–cell combinations.This checks simulator Monte Carlo error, not uncertainty from the observed LLM ensemble, question split, or model specification.Source: C. Absolute fidelity, simple controls,… · p. 7

D. Semantic, integrity, and split sensitivity

  • Matched semantic augmentation makes the joint-shift graph trajectory reduction 0.0308 with an interval excluding zero, while history retains no resolved mean-trajectory gain.The semantic history comparison remains locally positive in both transfer settings.Source: D. Semantic, integrity, and split… · p. 8
  • Five additional question-split seeds retain positive pooled graph log-loss intervals, but collective intervals include zero in three of five question-transfer splits and all joint-transfer splits.The overlapping splits are sensitivity analyses, not independent replications; integrity checks do not identify valid outcomes for episodes with nonbinary states.Source: D. Semantic, integrity, and split… · p. 8

A. Design, calibration, and incomplete outcomes

  • New trajectories use balanced initial spins on signed degree-four rings, with global or signed-neighbor inputs, and evaluate size and initial-condition transfer rather than unseen questions.Questions overlap calibration and test; each agent retains its own state and public message.Source: A. Design, calibration, and incomplete… · p. 8
  • Ten of 440 planned episodes fail the frozen binary-output schema, all in the global-input regime; missingness cannot be treated as random.The balanced primary panel contains 304 test episodes across 22 backend/question pairs.Source: A. Design, calibration, and incomplete… · pp. 9–10
  • The new-experiment score compares simulated ensemble means with a single observed path, so it is a noisy reference and cannot alone establish fidelity of expected magnetization or its distribution.Absolute loss is consistent for a conditional median rather than a conditional mean.Source: A. Design, calibration, and incomplete… · p. 10

B. Finite-grid outcomes and calibration dependence

Across the finite-grid tests, local graph-versus-scalar comparisons do not establish a consistent advantage, and calibration-dependent results caution against reading error trends as universal. The 12-round follow-up finds a resolved Qwen local log-loss gain under longer calibration, but no resolved collective improvement.

B. Finite-grid outcomes and calibration dependence

  • The primary pooled-regime local graph-versus-scalar comparisons show no resolved advantage for either backend, and the four tested sizes establish neither a universal decrease with N nor an asymptotic floor.Qwen’s ∆ℓ is 0.0039 [−0.0206, 0.0265] and ∆Enew_m is −0.0101 [−0.0343, 0.0121]; Gemma’s ∆ℓ is −0.0057 [−0.0244, 0.0098] and ∆Enew_m is −0.0005 [−0.0056, 0.0035].Source: B. Finite-grid outcomes and… · pp. 10–11
  • With separately calibrated regimes, Gemma’s local graph advantage becomes resolved, but its collective comparison remains unresolved; Qwen’s local and collective comparisons both remain unresolved.The two-question DeepSeek local panel changes direction collectively under separate calibration, so the pooled-regime estimates do not establish that local graph information is unhelpful or always preserves collective dynamics.Source: B. Finite-grid outcomes and… · p. 11
  • The finite-grid analysis holds calibration sample size fixed as test N grows, so an apparent error plateau may reflect calibration bias or regularization as well as discarded interaction correlations.For single-class calibration, the smoothed constant probability already differs from a deterministic consensus response.Source: B. Finite-grid outcomes and… · p. 11

A. Calibration design and technical replay

  • The 12-round follow-up reuses four known questions, tests horizons T = 3, 6, 12, and compares short-frozen fits with separately refitted models using validation-only selection.The short-frozen round covariate extrapolates beyond its original range, and recalibration changes sample count and temporal coverage together, so the comparison does not isolate their effects or intervene on LLM memory.Source: A. Calibration design and technical… · p. 11

B. Local and collective effects of recalibration

  • At T = 12, longer calibration reduces Qwen scalar log loss by 0.1142 [0.0747, 0.1632], while its trajectory-error reduction is −0.0472 [−0.0853, 0.0100] and includes zero.The local gain is resolved in this panel, but a collective improvement is not; the study does not claim statistically resolved collective harm.Source: B. Local and collective effects of… · p. 11
  • With short-frozen Qwen weights, adding two lags reduces log loss by 0.0647 [0.0210, 0.1115], but its trajectory-error reduction is −0.0367 [−0.0679, 0.0036]; both comparisons are unresolved under long-refit weights.Gemma’s calibration intervals include zero for both metrics, and there is no uniform graph advantage across calibration choices.Source: B. Local and collective effects of… · pp. 11–12

VIII. QUESTION TRANSFER UNDER TWO CALIBRATION STRATEGIES

The new-question studies compare source-frozen policies with question-specific calibration, then test graph and history policies on local and API backends. Topic-calibrated graph comparisons remain unresolved, while history effects vary by backend and calibration arm.

A. Source-frozen and topic-calibrated evaluation

  • The new-question design contrasts unchanged source-frozen policies with topic-calibrated policies, which use training responses for each new question; both arms share held-out test episodes.Only the source-frozen arm tests a new question without fitting to its responses; the set contains 20 preselected statements that are not 20 independently sampled semantic domains.Source: A. Source-frozen and topic-calibrated… · pp. 12–13

B. Graph and history effects on new questions

  • Neither local backbone has a resolved graph-versus-scalar advantage in log loss or trajectory MAE after topic-specific calibration; all four primary intervals include zero.The result is neither an equivalence test nor evidence that graph information can never help.Source: B. Graph and history effects on new… · p. 13
  • In the source-frozen local arm, adding two lags improves Gemma log loss by 0.0200 [0.0056, 0.0376] but worsens trajectory error by 0.0149 [0.0043, 0.0240]; Qwen improves on both metrics.Qwen’s reductions are 0.0067 [0.0029, 0.0104] for log loss and 0.0186 [0.0140, 0.0227] for trajectory error; Gemma’s collective effect is sensitive to post-hoc multiplicity analysis.Source: B. Graph and history effects on new… · p. 13
  • For local-input scalar policies, topic calibration reduces trajectory MAE from 0.5467 to 0.2234 for Gemma and from 0.2806 to 0.2100 for Qwen.The regimes also differ in question conditioning, temporal coverage, and training count, so these results do not isolate the effect of more calibration data.Source: B. Graph and history effects on new… · p. 13

IX. TRANSFER TO ADDITIONAL API BACKBONES

  • On the prespecified API comparison, GLM intervals do not clearly favor either policy, while Qwen Max shows an individual-prediction gain but an uncertain group-forecast difference.The API grid tests only N = 16; one test trajectory per question also limits separation of surrogate bias from stochastic variation in the observed population.Source: §IX · pp. 13–15
  • The secondary source-frozen API Qwen comparison improves both scores, but its collective interval includes zero under broader post-hoc multiplicity sensitivity.These are within-arm contrasts, not a formal test of differences between calibration-arm effects.Source: §IX · p. 15

X. POST-HOC SENSITIVITY TO THE COLLECTIVE SCORE

The post-hoc analysis evaluates alternative collective scores on saved policies and episodes without refitting. It retains contrasting history outcomes and adds diagnostics showing that observed-prefix interventions do not validate forecasts made from the initial state.

X. POST-HOC SENSITIVITY TO THE COLLECTIVE SCORE

  • The sensitivity analysis retains saved policies, episodes, horizons, fitting choices, and random seeds; it regenerates only autonomous rollouts and does not fit or select policies using the new scores.The resulting intervals are conditional sensitivity diagnostics, not a new confirmatory test or guaranteed family-wise coverage.Source: §X · pp. 16–17
  • The fair ensemble CRPS scores each round’s predictive distribution, but averaging marginal scores over time does not test the full joint trajectory law or remove uncertainty from few reference paths.The single-path absolute-loss score can prefer a misspecified deterministic forecast over a true predictive mean in the example given, whereas squared loss ranks them differently.Source: §X · pp. 15–16
  • None of the four graph-versus-global comparisons shows a clear collective improvement under fair MSE or CRPS, and graph information does not show a consistent benefit across the reported comparisons.With source-frozen policies, adding two past rounds worsens Gemma forecasts and improves local Qwen forecasts under both scores; the additional scores were selected after inspecting the same questions and policies.Source: §X · p. 17

A. Surrogate and message-content interventions

  • Conditioning on Gemma’s first three observed updates reverses its mean graph-history ranking on later updates, while generated past opinions amplify its deviation toward agreement.An intercept adjustment reduces Gemma’s error but does not establish an advantage over a two-state model fitted to the same rounds; these extra observations do not correct initial-state forecasts.Source: A. Surrogate and message-content… · p. 17
  • Capping Qwen history-2’s round coordinate reduces late fair MSE from 0.3306 to 0.1885, while Gemma does not improve under the same cap.The 608-response message test finds Gemma’s average stance-only effect concentrated in Qwen-origin contexts, but does not identify what caused the original Gemma penalty.Source: A. Surrogate and message-content… · p. 17

XI. PROSPECTIVE REPLICATION ON 24 ADDITIONAL STATEMENTS

The prospective test evaluates fixed surrogate policies on 24 additional statements, comparing autonomous forecasts with forecasts conditioned on observed updates. Qwen benefits from history in conditional forecasts, but the earlier autonomous history contrast is not confirmed, and a simple two-state policy outperforms the conditional graph policy on the tested targets.

A. Fixed predictors, adaptation rules and forecasting targets

  • The prospective protocol fixed predictors, adaptation rules, and forecast targets before collection, using 24 additional hand-selected statements and 192 episodes.The frozen protocol used two local backends, two population sizes, two replicas, and six synchronous updates; the statements are not random samples of domains.Source: A. Fixed predictors, adaptation rules… · pp. 17–18
  • The primary forecast comparisons use fair MSE and fair marginal CRPS, equal question and population-size weights, and adjusted intervals conditional on the fixed panel and policies.Intervals including zero are unresolved, not evidence of equivalence.Source: A. Fixed predictors, adaptation rules… · p. 18, Table VII · p. 19

B. Autonomous and conditional transfer

  • The test does not confirm earlier autonomous history effects or clock-cap gains; the earlier Gemma history penalty and Qwen advantage remain unresolved on this panel.The adjusted intervals for the earlier Gemma result include zero, and its CRPS point estimate changes direction.Source: B. Autonomous and conditional transfer · p. 18
  • For conditional Qwen forecasts with three observed updates, history-2 reduces mean fair MSE by 11.8% and fair CRPS by 7.3% relative to graph, with both adjusted intervals positive.Source: B. Autonomous and conditional transfer · p. 18
  • For Qwen, the benefit of adding past opinions is larger after observing the first three updates than when forecasting from the initial state, for both scores.The adjusted intervals for this change are positive; both forecasts are scored on updates 4–6.Source: B. Autonomous and conditional transfer · p. 18
  • Conditional Qwen two-state scores are 0.01350 and 0.05784, versus 0.14431 and 0.26070 for offset graph; both adjusted baseline comparisons favor two-state.The result is evidence against an advantage for this graph-retaining policy on these targets and horizon, not evidence that graph information is unnecessary.Source: B. Autonomous and conditional transfer · p. 18

A. Local prediction and collective transfer

  • On the public data, graph features reduce one-step log loss in all 16 point estimates and reduce pooled mean-trajectory MAE on held-out questions, while collective gains depend on transfer conditions.Under joint question/graph shift, the primary MAE-reduction interval includes zero; after matched semantic augmentation, it excludes zero on the positive side. Separately fitted policies did not yield a statistically clear group-forecast improvement under fair MSE or CRPS.Source: A. Local prediction and collective… · p. 19

B. Population size and scope of generalization

C. Reference uncertainty and calibration scope

The analyses qualify the forecasts with reference, calibration, and identification limits. They recommend validation that specifies targets and available observations, while concluding that individual accuracy alone does not establish accurate group forecasts.

C. Reference uncertainty and calibration scope

  • 18 held-out questions and only two to four accepted reference replicas per configuration limit the public-data analysis; additional surrogate draws reduce Monte Carlo error, not uncertainty in the LLM reference.The bootstrap intervals are descriptive and conditional on fitted models, prompts, retained cases, and the split; they are not multiplicity-adjusted coverage guarantees.Source: C. Reference uncertainty and… · pp. 19–20

D. Post-hoc multiplicity sensitivity

  • Both source-frozen collective-error intervals include zero, and the broader post-hoc sensitivity analysis does not provide guaranteed family-wise population coverage.The MAE conclusion must not be generalized to every collective score.Source: D. Post-hoc multiplicity sensitivity · p. 20

E. Selection effects and parameter identifiability

  • Panel selection can be nonrandom, public-data estimators omit or encode source-author information differently, and short histories do not uniquely identify later autonomous continuations.The Gemma–Qwen contrast compares fitted simulators, not intrinsic memory; longer histories can separate inputs without guaranteeing transfer.Source: E. Selection effects and parameter… · p. 20

F. Validation criteria and open questions

  • Validation should prespecify targets, reference ensemble, horizon, information sets, uncertainty units, and simple baselines, while separating autonomous simulation from forecasting after an observed prefix.Stronger claims require new questions from a prespecified sampling frame, independent reference replicas, content-controlled multi-round interventions, and size sweeps that separate calibration budget from N.Source: F. Validation criteria and open… · pp. 20–21

XIII. CONCLUSION

  • Graph information improves individual prediction in public-data point estimates and pooled held-out group forecasts, but collective benefits vary by transfer setting; accurate individual prediction alone is insufficient evidence of accurate group forecasts.Evaluation must specify group quantities, available observations, and permitted refitting; short histories do not uniquely determine all history coefficients.Source: §XIII · p. 21

DATA, CODE, AND RELATION TO PRIOR WORK

  • This article is an empirical companion to Poor Man’s Agentic Modeling [4], reporting public-data reanalysis, separately collected LLM trajectories, exploratory controls, and a 24-statement test; overlapping questions are not independent replications.Its coarse-graining derivations and fitted-response experiments are not reproduced here.Source: DATA, CODE, AND RELATION TO PRIOR WORK · p. 21

Appendix A: Public-data inclusion criteria and numerical implementation

The appendices document data filtering, scoring, sensitivity analyses, and experimental procedures. They distinguish matched comparisons and descriptive estimates from independent confirmation or causal interpretations.

Appendix A: Public-data inclusion criteria and numerical implementation

  • The strict integrity filter rejects histories with nonbinary states and then episodes with majority disagreement; Table VIII reports accepted episode counts, not faulty-vote counts.The appendix records 5,214 raw zero votes, 53 zero-valued recorded node-time states, and 120 node-time disagreements, which are different counting units.Source: Appendix A · pp. 21–22, Table VIII · p. 22

Appendix B: Complete public-data scores

  • Graph-policy four-way balanced accuracy ranges from 0.717 to 0.922 across the 16 public-data combinations, while observed-transition, mean-trajectory, and terminal-distribution scores remain distinct outcomes.The accuracy values are not directly comparable with published headline accuracies based on different splits, covariates, or target processing.Source: Appendix B · p. 22

Appendix C: Public-data split and integrity sensitivity

  • The 14 pooled graph-versus-global sensitivity comparisons reuse the underlying 60-question corpus, and majority-reconstructed rows reproduce the primary outcomes rather than independently confirming them.Each setting has 18 test questions; the table compares paired reductions with 95% question-cluster intervals.Source: Appendix C · p. 23, Table X · p. 23

1. Model and generation settings

  • Local campaign generation uses temperature 0.7, a 128-token cap, JSON mode, and disabled thinking; neutral votes are not recoded as binary spins.Technical pilot responses are excluded from scientific fitting.Source: §1 · p. 23

2. Missing episodes and calibration comparison

  • Of 440 planned episode records, 430 are complete; the primary balanced test panel has 304 episodes, and incomplete question panels are not substituted into it.Complete calibration permits 23 backend/question pairs.Source: §2 · p. 23

Appendix E: Long-horizon results and missing-case sensitivity

  • Long-horizon policies fitted on three-round data are compared with policies refit on designated 12-round training and validation episodes, but longer calibration changes both sample count and temporal coverage.The comparison does not isolate either effect.Source: Appendix E · p. 24

1. Technical replay and panel restoration

  • Restoring the missing Gemma test episode expands its comparison from three to four questions; because the question set changes, the before/after difference does not isolate a replay effect.The replay adds neither an independent test realization nor a previously unseen question.Source: §1 · p. 24, Table XIII · p. 25

Appendix F: New-question results and missing-case sensitivity

The new-question appendix describes calibration, evaluation, and technical replacements for missing episodes. Its tables distinguish primary comparisons, secondary contrasts, and descriptive uncertainty rather than treating replays as new test realizations.

1. Calibration and evaluation

  • The source-frozen arm uses earlier training and validation episodes without current-topic embeddings or responses, while the topic-calibrated arm uses designated new-topic data.Evaluation uses 1,000 autonomous draws and nested prefixes at T = 3 and 6; its macro metric compares ensemble-mean surrogate trajectories with observed LLM trajectories.Source: §1 · p. 25

2. Technical replay and unmatched question sets

  • The final panel contains 20 Gemma and 19 Qwen questions, so cross-backbone comparisons use different question sets and are not paired quality rankings.The graph-versus-scalar tables use descriptive intervals, and the Gemma replay sensitivity changes question composition from 19 to 20.Source: §2 · pp. 25–26, Table XVI · p. 26

1. Generation and calibration

  • Source training uses 192 node transitions per backend, while new-topic training uses 96 per question; the frozen source-policy fits precede all new-topic calls.The supplied model identifiers do not establish parameter counts or static internal snapshots.Source: §1 · p. 26

2. Validation-episode replacement

  • The GLM validation replay restores a missing calibration panel and enables matched evaluation, but supplies no additional test trajectory.Original failures, the replacement, and the complete-panel analysis remain separately retained.Source: §2 · p. 27

Appendix H: Prompts, personas and statements

The appendix records the fictional-agent instructions, input construction, personas, and fixed opinion statements used in the campaigns.

1. System instruction and input construction

  • Agents are instructed to agree or disagree with a statement, may keep or change their opinion, and must return a two-field JSON response.The response contains a binary opinion and a public explanation capped at 25 words.Source: §1 · p. 28
  • Global inputs add the population mean, whereas local inputs instead provide neighbors’ relationships, opinions, and messages; prior message history is not appended.Personas are assigned by node index modulo four.Source: §1 · p. 28
  • The four personas emphasize careful evidence assessment, tradeoffs, skepticism, and assumptions or long-term consequences.The roster assigns one persona to each index modulo four.Source: §1 · p. 28

2. Original eight statements

  • The original statement set pairs objective items, such as a prime-number claim and coin-toss misconception, with subjective policies on cycling, workweeks, museums, and recorded lectures.The source-frozen follow-ups retain the four subjective statements.Source: §2 · pp. 28–29

3. Twenty new subjective statements

  • New statements include disputes over return fees, sports review, anonymous auditions, street lighting, book budgets, cats, and reservation deposits.These examples come from the fixed new subjective statement set.Source: §3 · p. 29
  • Other new topics cover research-data exclusivity, historic-building preservation, social-media ordering, disaster relocation, school phones, and cash acceptance.The statements also include zoo priorities, space exploration, and delivery drones.Source: §3 · p. 29
  • The remaining new statements concern community gardens, data-center waste heat, tied competition prizes, and charity reserves.Together these are part of the fixed, nonrandom statement set.Source: §3 · p. 29

Appendix I: Post-hoc investigation of the history-policy contrast

The appendix tests why history-policy advantages change across forecast conditions, including source exposure, observed-prefix initialization, prefix adaptation, clock extrapolation, and message content. Its analyses identify limits on transfer and interpretation, while retaining unresolved and adverse comparisons.

1. Common target and source-only controls

  • Longer source exposure resolves the unpadded nine-update history advantage for Gemma but not Qwen, while equal-sized early/late comparisons remain unresolved for both.Longer exposure does not isolate a unique memory mechanism or guarantee transfer.Source: §1 · p. 30

2. Observed initialization and feedback allocation

  • The Gemma lag-error component falls from 0.1307 autonomously to 0.0198 after observed-prefix initialization; these signed components are not causal mediation or fractions of MSE.The decomposition symmetrically allocates nonlinear interaction, and initialization resets the entire history rather than only its lag channel.Source: §2 · p. 30

3. Prefix adaptation and simple negative controls

  • The simple two-state forecast shows no adjusted Gemma advantage for offset graph/history policies, while Qwen’s offset history-2 remains much worse than the baseline at 0.1726/0.2916 fair MSE/CRPS.The gains over unadapted source policies do not establish an advantage over the simpler model fitted to the first three observed rounds.Source: §3 · p. 31

4. Extrapolation of the surrogate’s time coordinate

  • Qwen’s capped clock reduces late history-2 MSE by 43.0%, but its autonomous history advantage remains +0.0286 and +0.0242 on the reported scores.The clock intervention affects the fitted surrogate’s time feature, not an internal LLM clock.Source: §4 · p. 31

5. Message-content intervention at fixed spin states

  • The Qwen-minus-Gemma agreement-effect difference is −10.5263 percentage points, while all three reported flip-probability contrasts include zero.The overall effect does not establish a textual cause of Gemma’s penalty on its own paths; the intervention changes text features together.Source: §5 · pp. 31–32

6. Uncertainty and retained negative results

  • The post-hoc stages reuse inspected topics and reference paths, so they neither isolate intrinsic LLM memory or architecture effects nor establish general explanations.The 24-statement test limits transfer of earlier autonomous history and clock-cap contrasts; the appendix is not a multiplicity correction for the full investigation.Source: §6 · p. 32

Appendix J: Prospective replication: protocol, absolute scores and statements

The prospective test fixes collection and forecast boundaries for 24 new statements, then reports descriptive absolute scores and audits numerical precision in adjusted intervals. The statements are new by exact wording, but are not a representative or necessarily independent sample of topics.

1. Collection and information boundaries

  • All 24 questions meet the fixed completeness rule; forecasts score updates 4–6, with autonomous runs observing state 0 and conditional runs observing states 0–3.The 14 forecasts use 1,000 draws per episode; fair MSE targets the predicted mean and fair CRPS the per-time marginal distribution, not the joint trajectory law.Source: §1 · p. 32

2. All absolute scores on the common late window

  • Table XXII reports 56 descriptive absolute scores across two backends, 14 forecasts, and two scores; lower is better, and autonomous and conditional forecasts have different information budgets.The table does not provide an additional ranking selected for significance.Source: Table XXII · p. 33

3. Monte Carlo precision of adjusted bootstrap intervals

  • Two adjusted-interval classifications are numerically non-robust: 8 of 10 Gemma diagnostics include zero, and 3 Qwen diagnostics turn positive.The other 26 classifications remain unchanged; the diagnostic repetitions assess bootstrap endpoint precision, not experimental replication or hypothesis probability.Source: §3 · pp. 33–34

4. The 24 frozen subjective statements

  • The 24 statements were fixed before collection and have no exact wording overlap with the specified earlier lists, but are not representative and may have appeared in pretraining.Prompts and collection parameters were not revised after responses were observed.Source: §4 · p. 34
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