MF-LLM: Simulating Population Decision Dynamics via a Mean-Field Large Language Model Framework
Authors: Qirui Mi
Mengyue Yang
Xiangning Yu
Zhiyu Zhao
Cheng Deng
Bo An
Haifeng Zhang
Xu Chen
Jun Wang
Venue: NeurIPS 2025 poster ()
Keywords: social simulation
large langauge model
population
decision making
mean-field
Primary area: social_and_economic_aspects_of_machine_learning

Abstract: Simulating collective decision-making involves more than aggregating individual behaviors; it emerges from dynamic interactions among individuals. While large language models (LLMs) offer strong potential for social simulation, achieving quantitative alignment with real-world data remains a key challenge. To bridge this gap, we propose the \textbf{M}ean-\textbf{F}ield \textbf{LLM} (\textbf{MF-LLM}) framework, the first to incorporate mean field theory into LLM-based social simulation. MF-LLM models bidirectional interactions between individuals and the population through an iterative process, generating population signals to guide individual decisions, which in turn update the signals. This interplay produces coherent trajectories of collective behavior.
To improve alignment with real-world data, we introduce \textbf{IB-Tune}, a novel fine-tuning method inspired by the \textbf{I}nformation \textbf{B}ottleneck principle, which retains population signals most predictive of future actions while filtering redundant history. Evaluated on a real-world social dataset, MF-LLM reduces KL divergence to human population distributions by \textbf{47\%} compared to non-mean-field baselines, enabling accurate trend forecasting and effective intervention planning. 
Generalizing across 7 domains and 4 LLM backbones, MF-LLM provides a scalable, high-fidelity foundation for social simulation.

MF-LLM: Simulating Population Decision Dynamies via a Mean-Field Large Language Model Framework
Qirui Mi..2.3 Mengyue Yang', Xiangning Yu Zhiyu Zhao Cheng Deng
Bo An", Haifeng Zhang Xu Chen Jun Wang**
l Institute of Automation, Chinese Academy of Sciences
School of Artificial Intelligence, Chinese Academy of Sciences
Nanyang Technological University *University of Bristol
5 TTinjji University Shanghai Jiao Tong University
Renmin University of China University College London
Abstract
Simulating collective decision-making involves more than aggregating individual behaviors; it emerges from dynamic interactions among individuals. While large language models (LLMs) offer strong potential for social simulation, achieving quantitative alignment with real-world data remains a key challenge. To bridge this gap, we propose the Mean-Field LLM (MF-LLM) framework, the first to incorporate mean field theory into LLM-based social simulation. MF-LLM models bidirectional interactions between individuals and the population through an iterative process, generating population signals to guide individual decisions, which in turn update the signals. This interplay produces coherent trajectories of collective behavior. To improve alignment with real-world data, we introduce IB-Tune, novel fine-tuning method inspired by the Information Bottleneck principle, which retains population signals most predictive of future actions while filtering redundant history. Evaluated on a real-world social dataset, MF-LLM reduces KL divergence to human population distributions by 47 % compared to non- mean-field baselines, enabling accurate trend forecasting and effective intervention planning. Generalizing across 7 domains and 4 LLM backbones, MF-LLM provides a scalable, high-fidelity foundation for social simulation.
Introduction
Simulating how population-level decisions evolve over time is essential for predicting the spread of public opinion B.. household responses to policy shocks [17, and crowd dynamics during emergencies 15).. Unlike static aggregation of individual behaviors, collective decision-making 5l. where each agent's 's choices are shaped both by private observations and by the evolving actions of others [7]. These individual decisions, in turn, continuously reshape the population distribution, creating feedback loop that drives population dynamies. Classic agent-based models simulate this loop using handcrafted rules 6 25,. but often lack realism and fail to generalize beyond narrow scenarios.
emerges from dynamic interactions among individuals [33 34
Recent studies show that large language models (LLMs) can endow agents with rich world knowl- edge and generative capabilities, enabling simulations ranging from "generative towns" [3] 48) to
docial-media environments 43 45 351. election forecasting (44). and macrocconomic modeling 22
Shate-of-the-as simulations such as OASIS [33 and AgentSociety [32 excel at environment model- ing but remain prompt-centric in agent maaissio--aiiineeeleeee relying manually crafted role templates, heuristic memory-retrieval rules, and fixed interaction schedules. These expert-crafted heuristics
CCoresppoding author; jun wang wang@@ullac.uk @ichen@rac.du.ccn haifeng zhanggghanggeee @ia.ac.en
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Figure I: MF-LLM framework for simulating population decision dynamics. When an event occurs (e.g., rumor), individuals make sequential decisions by evolving collective behavior such as public opinion. Early decisions shape collective behavior, which in turn influences future actions, creating a feedback loop. MF-LLM captures this loop by alternating two LLM-based modules: policy model that generates individual decisions based on personal states and population signals, and a mean field model that updates population signals from new actions. This iterative process closely aligns with real-world population dynamics (top right).
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enhance qualitative plausibility but lack principled alignment real-world behavioral data. This limits their applications in tasks requiring quantitative fidelity to real-world behavior, such as ex-ante policy evaluation or counterfactual intervention planning. Bridging this realism gap-transforming qualitative simulations into social simulations that quantitatively match real data data-remains an open challenge [88.
Despite recent advances, three key challenges hinder progress toward social simulation that aligns with real-world data. (C1) Prompt-based heuristies lack data alignment. Many existing simulations rely on carefully crafted prompts or scripted interaction schedules. While these may produce plausible narratives, they fail to track the evolving dynamics of real-world populations. As shown in Fig. [ (top right), the prompt-based simulation (blue) initially follows the real-world rumor trend, but quickly diverges as collective behavior shifts. (C2) Supervised fine-tuning overlooks interaction dynamics. Supervised fine-tuning (SFT) offers a direct path to align LLM agents with real-world data. However, treats each decision as independent, ignoring how agents influence one another over time. As result, SFT may fit individual behavior but fails to reproduce collective dynamics (28 In Fig. (top right), SFT-based simulation (orange) fails follow the real-world rumor trajectory. (C3) Balancing fidelity and scalability remains core challenge. As agent population grows, simulating agents' interactions becomes increasingly complex and costly. Yet such interactions are essential for reproducing real-world dynamics, as collective behavior emerges from agent-to-agenn influence. Balancing fidelity to real-world behavior with scalability thus remains a core challenge.
Contributions. To address the challenges of quantitative population simulation (C1-C3), we make the following contributions:
1. MF-LLM: scalable simulation via mean-field egent-populatie interaction. We introduce Mean-Field LLM (MF-LLM; see Fig. (T) framework for simulating population dynamics. Inspired by mean-field theory [9), MF-LLM MF-LLM agent-to-agent interactions with agent-population interactions. This avoids the combinatorial cost of modeling all agent-to-agemt interactions (C3) while preserving key feedback dynamics (C2). To implement this, MF-LLM alternates between two LLM-based modules to generate the trajectory of collective decisions over time: (i) mean-field model that generates dynamically updated population signals based on past individual actions, and (ii) a policy model that generates subsequent individual actions informed by these population signals. This design reflects the bidirectional interaction between individual decisions and population behavior (C2), while remaining scalable large populations (C3).
2. IB-Tune: a data-driven algorithm for real-data alignment. To overcome the limitations of SFT (CI), we propose a fine-tuning algorithm, IB-Tune, to optimize the above LLM modules. (i) The mean-fiele field model is trained with an information bottleneck objective, extracting population signals that carry predictive information about future actions while discarding redundant history.

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(ii) The policy model is trained via negative log-likelihood supervision against real-worth actions. This creates feedback loop: accurate population signals lead to more human-like actions, which in turn improve the learning of decision-relevant population signals (C2).
3. Evaluation and key findings. We evaluate MF-LLM on the WEIBO corpus (~ 4,500 real-
world events): (i) ME-LLM aligns closely with real-world population trends (Fig. 2). reduces
KL divergence by 47 % over non-mean-field baselines, outperforms baselines across semantic dimensions (Fig. B. and generalizes across domains (Fig. 4 and LLM backbones (Table I (ii) Ablation results show that both the mean-field module and IB-Tune are critical, with up to 118% degradation when removed (Table [ (iii) We further examine MF-LLM's real-world forecbbbitttyoooottttnnnn and intervention planning (Fig. 5 and find that exogenous signal injection further improves fidelity (Fig. 8
Code is available at http:hhwww...c...aaaaaaee//aaaaa
2
Related Work
full discussion of related work appears in Appendix H we highlight key directions here.
Agent-Based Models (ABMs). ABMs have long served as foundation for modeling complex social systems through local agent interactions, with seminal applications in artificial societies [10], crowd behavior [15), markets [36], ecosystems [I4], and public policy 26). While effective for exploring emergent phenomena, classical ABMs often rely manually designed rules, limiting scalability and generalization to real-world complexity.
LLMs for Social Simulation. Recent work has explored using large language models (LLMs) to enhance social simulation, leveraging their generative capabilities and world knowledge. Systems such as OASIS 44 45,, ElectionSim [44). EconAgent [22 42, and toolkits like GenSim 33 and AgentSociety
demonstrate promising use cases across domains. However, many current I..M-based agents operate on prompt-engineered templates, scripted roles, and heuristic memory, with limited alignment to real-world data 88 233, hindering their quantitative reliability.
Mean Field Theory for Scalable Interactions. Mean field theory offers a principled way to model large-scale agent interactions by replacing explicit pairwise interactions with population-level dynamics [19 16 41 It has been applied in social influence 4 40 energy systems [9]. traffic [I]]
and economics [27 While prior work shows its success in reinforcement learning, extending it to LLMs is non -riviall..: modeling populations where each agent is an LLM makes dynamic updates computationally expensive. These challenges motivate our MF-LLM framework.
3 Mean-Field LLM
We begin by formalizing the problem of simulating population decision dynamics ($3.1) then introduce MF-LLM framework ($3.2) and IB-Tune algorithm ($3.3) to align with real-world data.
3.1 Problem Statement
We aim to simulate population decision-making in text-driven environments, where population dynamics capture evolving collective behaviors emerging from decentralized decisions of interacting agents (C2). Consider population of N agents making sequential decisions in shared, language- based space. At each timestep f, a subset of N, agents ( N₁ N) acts simultaneously based on textual states encoding personal attributes (e.g., roles, preferences) and environmental observations (e.g., task descriptions). We denote the agent states as 5, = (s!..... NN)) where sj E S represents agent i's state. Each agent selects an action oj A, forming joint action vector ā = (a....... ... .. ........aa")) which influences the environment and future behaviors. The parameter N, controls simulation granularity: larger N, enables efficient, coarse rollouts, while smaller N₂ captures finer dynamics.
Unlike traditional MDPs or Markov games with discrete actions, our language- simulation operates in open-ended natural language, where both state space S and action space A are unbounded free-form text. We model agent decision-making with an M-rvver policy, leveraging L.MMs' generative power produce context-aware, semantically rich behaviors grounded in broad priors.
3

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3.2 Mean-Field LLM Framework
To quantitatively simulate population dynamics, propose the Mean-Field LLM (MF-LLM) frame- work-thh the first to introduce mean-field theory [9 into LLM-driven social simulation. We now describe the core components of the MF-LLM framework.
Scalable Interaction Modeling via Mean Field. Simulating all agent-to-agent interactions be- comes intractable as population size and time horizon grow. While full interaction histories can be encoded for small groups, this approach does scale to realistic population settings (C3). To address this, MF-LLM introduces a mean-field approximation [41] 27 to model gggent-oopulatinn dynamics without tracking all pairwise interactions. Unlike and retrieve individual experiences [3 the mean field in MF-LLM encodes population-centee centric, continuously evolving signal that influences subsequent agent decision-making It is initialized as an empty string mo and recursively updated by an LLM μr, referred to as the mean field model:
memory designs that store
My p( 8 1.=1),
(I)
where (5-1), represent the latest agent states and actions. Instead of passively accumulating interaction histories, MF-LLM dynamically distills decision-critical information from evolving population trajectories. This mechanism preserves essential social dynamics while maintaining scalability within LLM context limits. Detailed mean-field prompts are provided in Appendix F:4
To stabilize early-stage simulation, we design a warm-up phase where the mean field is updated with real actions át from background context. After twarmup. the simulation proceeds with geniertee actions. Ewarmup is determined based on task-specific considerations, as discussed in the experiments.
Decision- Making via Policy Model. Given the current mean field my and individual state s each agent selects an action based on a language-model-dringg model-driven policy. This policy maps textual inputs to a distribution over possible textual actions:
of n s m.).
(2)
where n' S x M - A denotes the agent's LLM-based policy. By operating in unbounded language spaces, MF-LLM captures highly expressive, context-sensitice and adaptive decision- making, bridging closer to real-world complexity. Detailed policy prompts shown in Appendix [44
Environment Transition Dynamics. After all N₃ agents complete their decisions at timestep f, the system transitions to the next state. State transitions depend on the current joint state-action pair (3,, a.) and the mean field my:
$ P( St, ā, m.),
(3)
where P is the anvironment-specinn stochastic transition function. This setup enables MF-LLM to capture both individual decision-making and population-leva evolution over time. Pseudocode [ summarizes the overall framework. We also provide intuitive examples in Appendix Coto illustrate how MF-LLM models complex and heterogencous interactions.
Pseudocode Simulation Procedure of the MF-LLM Framework
1: Input: Number of subset agents Nr, time horizon I', warm-up horizon twarmup-
2: Initialize: Mean field mo as empty string, agent states {
3: for 0 to T do
4: if t < twanmup then
>> Warm-up phase using background actions
5: Retrieve real actions: d. + āz
6: else
Simulation phase using LLM policy
7:
for each agent in active set do Observe st, my; generate action of ~ x x-(
subset of N₂ agents active at time
8:
ss)m)))
s mz)
9:
Form joint action: ã + (a.
10:
Update mean field: m++1 < pmm,, St, σe)
11:
Environment transition: 5,-1 P(. 5t, Ce m))
Output: Sequence of simulated actions {7, T

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3.3 IB-Tune Algorithm
While MF-LLM captures population dynamics using pretrained LLMs, its alignment with real-world data can be further improved through targeted fine-tuning. We propose IB- (B-Tune, a fine-tuning algorithm that optimizes: (1) the mean field model, to extract predictive population- signals; and (2) the policy model, to generate behaviorally realistic actions conditioned on these signals.
Mean Field Model Optimization. In the MF-LLM framework (Section 3.2p, the mean field my serves as a dynamic population signal that encodes predictive information about future individual actions. To enhance its predictive value and compress irrelevant history, optimize my via the Information Bottleneck (IB) principle [] which learns representations that retain only task- relevant information. Formally, given input variables X and target variables Y, the IB objective seeks a latent variable Z that minimizes the trade-off:
minz [(; x) B ((; Y):
where -( is mutual information and / balances compression and prediction.
Applying this principle, we construct the mean field my as textual representation that retains the essential information to predict individual actions in the next step Y [att] Ji=1 irrelevant details from historical trajectories X = {(87, 07 )) This leads to the IB-style objective:
No while discarding
minm, [mm;; X) - [m,; Y).
(5)
To approximate the predictive term 7 [(m;; Y), we leverage the intuition that an informative mean field should enable the policy better reproduce real-world behavior. Following standard IB practice D. approximate it via the log- se-likklihhodd of observed actions under the policy model:
[mms Y) E log (a;"
|66 mz)-
(6)
For the compression term [mm;; X). we adopt a variational upper bound that makes the objective
tractable. Full derivation of this bound shown Appendix G.1 Let foa (m, X)) denote the learned
posterior distribution and r(m,) fixed prior induced by pretrained LLM. Following standard IB
approximations [.. we bound the term as:
[(m;; X) s E)(x) [[o X) [| ((m))) Ep(x) [ (m., [log (o(mm) X) ((m)))
In practice, we instantiate X as the immediate trajectory {m+-1, 1, 8, T,, }
balance predictive
richness and computational efficiency. Combining the above, the final objective for optimizing the mean field model rewrites Eq. 5
as:
Emean-fleld ΣT
(oxx)KK((C ExXx, KL (ms(me) X.) r(m)) B M log π (at" |
s/ mi.m
(7)
where m, pes(- | m 1, This objective encourages my to serve compact yet predictive population signal, improving the fidelity of the decision-making of the downstream agent.
Policy Model Optimization. The policy model governs individual decision-making conditioned on private states and the mean field. Each agent observes own state sf and the shared mean field my, selecting an action of accordingly. We assume a factorized policy structure, where the joint action distribution decomposes as:
((ā m.) = IIiiiaaa (af m.),
with all agents sharing the same policy model л. Agent-specific behavior arises naturally from personalized state inputs si, expressed in rich natural language. This design ensures scalability and generalization across heterogeneous populations.
To align the policy model with real-world agent behavior, we minimize the negative log-likelihood of observed actions:
(8) where a² denotes the ground-truth action of agent at time 1. This objective encourages the policy model to generate behaviorally realistic individual actions conditioned on both private states and evolving population signals, while continuously tracking the evolution of population dynamics.
Cpolicy = Σ ΣN log (a;"" ss,
5

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Experiments
We evaluate MF-LLM on ability to simulate population decision dynamics using the WEIBO corpus. Our experiments are structured around two core questions:
1. How Real is MF-LLM? Evaluating Its Fidelity and Generalization $4.3
We assess MF-LLM's ability to match real-world decision trajectories across temporal trends, semantic dimensions, and diverse social domains, and evaluate its robustness across multiple base LLMs.
What Drives MF-LLM? Dissecting the Mean Field and IB-Tune Mechanisms ($4.4)). We conduct ablations to assess the necessity of the mean-field module and the IB-Tune algorithm for ensuring simulation fidelity.
4.1 Evaluation Setup
Dataset. We conduct experiments on both the WEIBO corpus and TWITTER dataset. The WEIBO corpus [24] contains over 5,000 real-world events, hundreds of temporally ordered user responses per event, and rich user profiles. Its scale, accessibility, and granularity make it well-suited for modeling population decision dynamics. Details are provided in Appendix F. The TWITTER d
large collection of tweet-reply pairs centered on popular keywords, while MARKET BEHAVIOR dataset constructed from Bitcoin-related tweet-reply interactions is used to simulate collective bullish/bearish sentiment dynamics. Results on the TWITTER and MARKET BEIIAVIOR datasets show consistent trends with those on WEIBO; due to page limitations, these results are presented in Appendix B.2
Baselines. Our baselines are drawn from existing LLM-based frameworks (e.g., AgentSociety [32. OASIS 43
based on their designs for dynamic population interactions (Details in Appendix F22
State 44
LLM conditioned only user profile and event topic.
Recent 45
32
State k most recent actions from other agents (e.g., Top-k comments).
Popular 43
State + most popular actions from other agents (by followers, likes, etc.).
SFT Supervised fine-tuning on state action pairs; trained to convergence (Appendix Fig.
For evaluation, we compare the outputs our MF-LLM and baselines with ground-truth responses from the WEIBO corpus (hereafter Real data).
4.2 Evaluation Metrics
To evaluate the accuracy of L.LM simulation of population decision- decision-making dynamics, we adopt a micro-to-macro evaluation approach: (1) we first assess individual agent decisions (both real and generated actions); (2) then evaluate the decision distribution over a subset of agents at each timestep, capturing temporal trends in decision distribution over time. Accordingly, we design two types metrics: one for individual actions and one for action distribution similarity.
Metries for Individual Actions. To assess the policy model's ability to generate realistic actions for individual agents, we use 107-4omminil to evaluate both real and generated text actions. We define evaluation dimensions such as sentiment (e.g., happy, angry, calm, doubtful). attitude, behavior, stance, belief, suhjectivity, intent, and rumor, as informed by related work (29 12]. detailed list of evaluation dimensions, prompt templates, and the reliability and efficiency analysis of GPT-4o-mm -minii as an evaluator are provided in Appendix
Metrics for Action Distribution. Building on individual action evaluation, we compute the action distribution over N, text actions at each timestep To assess the similarity between generated and real distributions, we use: (I) KL Divergence and (2) Wasserstein Distance: measure distributional similarity, averaged across all timesteps; (3) Dynamic Time Warping (DTW) Distance: evaluates temporal alignment between time series, assessing how well generated trends follow real dynamics; (4) Negative Log-Likee Likelihhd (NLL) Loss: measures probability of ground -ruth actions; (5) Macro Fl and (6) Micro Fl: measure classification accuracy over generated action sets.
data
We use the version o4-min1-2025-04-5

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Figure 2: Comparison of collective decision trajectories in three events: our MF-LLM, Real data, and baselines-State Recent, Popular, SFT. Event (a) Liu Xiang rumors (top row): spread vs. counter-rumor rates and comment share behaviors. Event (b) Delayed retirement debate (middle row): calm vs. angry sentiment and neutral vs. opposing stances Event (c) Weibo speech-freedon freedom debate (bottom row): angry vs. happy sentiment over 900 timesteps (Real data spans 500). Our MF-LLM closely matches Real data trends in all events. Full curves see Appendix Fig.
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Figure 3: Radar plot comparing four baselines (State, Recent, Popular, SFT), and our MF-LLM (red)-on 5 distributional metrics and 8 semantic dimensions of actions. KL Divergence (Inverse), Wasserstein Distance (Inverse), and DTW Distance (Inverse) are inversely normalized so larger values indicate better performance, alongside Macro F1 and Micro F1. Larger areas denote superior performance, with MF-LLM (red) showing the highest semantic fidelity.
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Figure 4: Comparison of algorithms across seven event domains. Heatmaps show six metrics evaluating action distribution fidelity, with darker blue indicating better performance. MF-LLM (ours) demonstrates strong generalization across all domains, even in challenging cases like Culture.
4.3 How Real is ME-LLM? Evaluating Its Fidelity and Generalization
Facet A: Temporal Fidelity Matching
Decision Trajectories To demonstrate MF-LLM's ability to reproduce realistic decision trajectories over time, we simulate three events
7

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with increasing horizons and agent scale: (a) short- cooitohorizon rumor propagation, (b) mid-horizon
retirement debate, and (c) Long-horizon speech freedom discourse (Fig. 2. For each event, we track key action metries relevant to its topic (full curves in Appendix B Fig. Across all events, MF-LLM (red) closely aligns with ground-truth data (black), while baselines State, Recent, Popular, and SF7-often lag behind or smooth over critical transitions.
(a) Rumor Propagation. MF-LLM accurately captures the tipping point around step 75, followed by a realistic decline. Baselines over-predict virality and fail to reverse the trend. (b) Retirement Debate. MF-LLM matches the anger peak at T within three steps, while Popular and SFT lag by over 20 steps, missing the timing of sentiment shifts. (c) Speech Freedom. Beyond matching the real-world trajectory up to T=500, MF-LLM continues generating coherent trends up to T 900 by resampling states from historical distributions (see Appendix for for details).. This ability arises from the iterative generation between the mean-field and policy models, enabling natural long-horizon simulation. A detailed analysis of the scalability and computational complexity of MF-LLM, from both theoretical and empirical perspectives, is provided in Appendix E
Facet B: Semantic Fidelity - Capturing the Meaning of Collective Behavior Beyond trajectory alignment, we assess MF-LLM''s ability to model the semantic structure of collective decisions. We evaluate 20 real-world events involving up to 300 agents, measuring fidelity across five distributional metries and eight semantic dimensions of actions (Fig. 3) We exclude NLL Loss as it lacks semantic interpretability. To ensure fair comparison, distance- based metrics (KL, Wasserstein, DTW) are inversely normalized so that higher values indicate better alignment. MF-LLM (red) consistently achieves the largest radar area, indicating stronger semantic fidelity across all dimensions. A clear performance hierarchy emerges: MF-LLM outperforms all baselines, followed by SFT, with Popular, Recent, and State trailing behind. While SFT performs better than other baselines on semantic metrics, it fails track temporal shifts (see Fig. 2 In contrast, MF-LLM excels in both aspects, particularly on complex dimensions such as sentiment and stance, underscoring its strength in semantic decision modeling. See Appendix Table for full results.
for
Facet C: Cross-Domain Generalization Transferring Across Diverse Event Domains Having validated fidelity, we next test MF-LLM's generalization across diverse event domains without task- specific adaptation. The test events span seven domains-Criinn Culture, Health, News, Politics, Sports, and Technology- consistently lowers KL divergence (e.g., Culture 2.88 - 0.61) and DTW distance (e.g.. Sports 0.35 - 0.21), while boosting classification performance in Micro and Macro F1. Although SFT achieves the lowest NLL loss, MF-LLM sacrifices marginal one-step accuracy for improved temporal and semantic consistency- robust even in complex domains like Culture, where other baselines struggle.
exhibiting distinct collective behaviors. As shown in Fig. 4 MF-LLM
what KL, DTW, and F1 capture. Notably, MF-LLM remains
Facet D: Backbone Robustness - Generalizing Across Base LLMS The previous experiments, based on Qwen2-1. 5B- Instruct, validated ME-LLM's fidelity and generalization. We now ex- tend MF-LLM additional Mackbone--GPT-4----ie
DeepSeek-R1 Distill-Qwen-322 and -wen2-7B-Bnne In-stuct (Table []] Since some LLMs are closed-source, we evaluate MF-LLM without fine-tuning. Even without tuning, MF-LLM consistently outperforms State, Recent and Popular across all LLM backbones. Relative gains are most pronounced on GPT-4o-ming with KL di- vergence reduced by 60% and DTW by %. 1amm2-..5BIInsttt.
yields the best absolute performance. Here, MF-LLM achieves 33% (KI.) and 8% (DTW) improvements, which further increase to 47% and 16.8% with IB-Tune. Interestingly, smaller models outperform larger ones in simulating collective decision dynamics, with detailed analysis in Section D Overall, results highlight MF-LLM's robustness across diverse base LLMs-even without any model-specific adaptation.
4.4 What Drives MF-LLM? Dissecting the Mean Field and IB-Tune Mechanisms
Ablation variants. In
$.4 we evaluate six variants to assess the role of each MF-LLMM component:
MF-LLM (ours): full model with both modules fine-tuned via IB-Tune.
w/o IB-Tune MF: replace IB-Tune mean field model with pretrained Qwen2-1. 5B-Instruct.
w/o IB-Tune Policy: replace IB-Tune policy with pretrained; mean-field remains fine-tuned.
w/o IB-Tune: both modules use pretrained LLM without fine-tuning,
SFT (no MF): drop mean-field module; policy trained via supervised fine-tuning.
Pretrained (no MF): drop mean-field module; use pretrained policy without fine-tuning.
8

---

Table I: Comparison of base LLMs and baselines across multiple metrics. Lower is better ()) for all
metrics except Micro/Macro-F1 (t). Values denote mean with improvement rate (%) relative to State. Cells with positive improvement rates are colored by magnitude.
Backbone LLMs
KL Div. +
Wass. Dist.
DTW 4
Macro F1
Micro F1
NLL Loss 4
CPT-4o-nini
State
4.172
0.127
0.420
0.337
0.653
Recent
6.728 (61.1699)
0.145 (-141138))
0.485 (-154769))
0.270 (-19.8818)
0.625 (4.2665))
Popular
5,591 (390019))
0.128 640879)
0.447 (464299)
0,316 (-6252%)
0.650 (4.45995
ME-LLM (ours)
1.647 (0055393)
0.100 (21 2508)
0.329 (1106055))
0.399 (08 1889)
0.724 (1087799)
DeegSeek-R1-328
State
1996
0.110
0,348
0.398
0
Recent
6,435 (23000006)
0. 0.141 (20.129))
0.495 (-42 2419))
0.281 (99.99
0.617 (10.7095)
Popular
3.812 (45
0.113 622727%)
0.385 (-1003229)
0,353 (-113009)
0.682 (-1.022%)
MF-LLM (ours)
1,280 (34.23494)
0.088 (2000005)
0.307 (11.7825)
0.418 (5.0259)
0.724 (4.77996)
Qxen2-78-Inatruee
State
1.153
0.085
0.238
0.436
0.773
4,175
Recent
1,346 73933
0.081 (4.7099)
0.218 (s a0363)
0.434 (404495))
0.780 (U000S))
4,183 (0.19929)
Popular
1,066 (7.545%)
0.076 (10.5589)
0.199 (16.3871)
0,445 (2.0648)
0.794 (2.7179)
4.177 (0:0488)
MF-LLM (ours)
1.010 (12.402%)
0.075 (11.765%)
0.198 (16.807%)
0.447 (2.523%)
0.796 (2.97598)
4.132 (1.030%)
Qwen2 11.22-1..--.0 1.5B--Innttt Instruct
State
0.966
0.068
0.166
0.463
0.823
4.138
Recent
1.277 (-82,19243
0.077
(-13223593
0.202 (:21 687%)
0.441 6447822)
0.799 (-2.199))
4,056 (1.9819)
Populur
1,288 (/33 93593
0,080
(1776199)
0.199
6-19 s0099)
0,435 (-60009))
0.792
(6mm))
4,080 (1.400%)
MF-LLM (ours)
0.645 (38.23094)
0.065
(4.12%)
0.152
0.486 (4.668))
0.839
(194455)
4.085 (1.28193
ME-LLM IB-Tume (ours)
0.512 (47.)821))
0.062 (4.0245))
0.138 (163075)
0.495 (691119)
0.846 (2. 2.70666
2,809 (12.0015))
Table 2: Ablation study on MF-LLM. We evaluate the contribution of the mean-field module and
IB-Tune by comparing six variants. Cells show metric values and relative changes from MF-LLM (ours); darker shading indicates larger drops, reflecting the importance of the removed component.
Method
KL Div. 4
Wass. Dist.
DTW Dis. 1
NLL Loss J
Macro F' f
Micro F1 f
ME-LLM (Ours)
0,4813
0,0703
0.1581
2,9029
0.4891
0.8303
w/o Tu-Tuee MF
0.5312 (106%)
0,0702 (0.15)
0.1586 (0.5)
2,9802 (2.7%)
0,4865 (055%
0.8284 (0.2%)
w/o TB-Tune Policy
0.5882 (21.2%)
0.0704 (0.18)
0.1582 (.19)
4.0454 (9.45)
0.4846 (-00%)
0.8300 (009)
w/o TB-Tune
0.6166 (28 1993
0.0716 (188%
0.1636 (3.9%)
4.0933
0.4828 (-135%
0.8292 (4.19)
SFT (no MF)
0.7531 (56.5%)
0.0746 (5.)5)
0.1859 (17.5%
2.4217
(-168%)
0.4755 (228%%
0,8164 (-1.7%
Pretrained (no MF)
1.0526 (118.7%)
0.0792 (12.7))
0.1946 (23.19)
4.2088 (45.0%)
0.4561 (-6.7%) 0.8076 (s279)
Mean-Field Module Is Key to Population Dynamics. Sableeddmonstraatee the critical role of the mean-field module in achieving high-fidelity simulations. Removing it increases KL divergence by 118% and reduces Macro F1 by up to 7%. Although SFT (no MF) yields the lowest NLL Loss (2.4217), its KL divergence exceeds ours by over 50%. suggesting that low token-level loss alone may be insufficient for capturing social dynamics. These results confirm that the dynamic population signal captured by MF-LLM is essential for reproducing realistic decision trajectories over time.
Tu-Tune Enhances Woald Alignment. From Table 2 (i) Removing IB-Tune from both the mean-field and policy models (w/o IB- IB-Tune) increases KL by 28. 1% and NLL Loss by 41.0% relative to MF-LLM, demonstrating that combined fine-tuning is essential. (ii) Isolating IB-tuned mean-field (MF-LLM vs. w/o IB-Tune MF) cuts KL by 10.4% and NLL Loss by 2.7%, showing that IB objective is key to aligning population trends and suppressing noise. (iii) Tuning Policy model via IB-Tune yields large gains: it lowers KI. by up to 22.2% and NI.I Loss by up to 39.4% across variants, further boosting distributional fidelity. Together, these results highlight IB-Tune's two-stage role: refining the mean field for population alignment, then calibrating the policy for better action likelihoods-bott essential for aligning MF-LLM with real-world decisions.
5 Discussion and Conclusion
Key Findings from our experiments: (1) MF-LLM accurately captures real-world population decision dynamics, both in decision trajectories and semantic fidelity. (2) It generalizes well across diverse event domains and LLM backbones. (3) The mean-field module is the key for capturing population dynamics, while TB-e greatly enhances alignment with real-world data.
Applications and Discussion. Inspired by these findings, we explore MF-LLM's broader potential (Appendix D): (1) Enables forecasting of public opinion and pre-evaluation of intervention effeets

---

5m,
$14
[c]
[3] Simu ated Predictions Across Time
[b) Post-intervendon Forecasting Performance
1.0
Prelicinn Hical value: 99b
Predictio: 6G5
valuer 643
Cheer saac
Predictio:: Riaa valum 7C9
0.8
0.7
0.5
Roal volue: 0 702
Orece "Spoood
100
300
Triestop
Timestop
Figure MF-LLM for prediction and intervention: (a) Rumor spread predicted from four start points (20, 34, 43, 70); later starts improve accuracy. (b) Predictions under two interventions: single intervention at step 34 (with later rebound); second intervention step 80 yields desired effect.
(Fig. 5. (2) Injecting exogenous signals improves alignment with real-world dynamics (Fig. 8 We further observe: (3) Low NLL does not necessarily imply high rollout fidelity. (4) Smaller LLMs better capture agent diversity than larger ones in collective simulations.
Conclusion. MF-LLM integrates mrean-field theory with LLMs to model the interplay between individual decisions and population dynamics, enabling figh-fidelity simulation of collective behavior over time. IB-Tune further improves alignment with real-world data. These results suggest that uncovering collective behavior principles, combined with data-driven fine-tuning, provides a strong foundation for accurate and scalable social simulation.
Acknowledgments
We would like to thank Prof. Bo Li from Peking University for his valuable discussions and sugges- tions. This work was supported by the National Natural Science Foundation of China (NSFC) under the Original Exploration Program, Grant No. 72450002. We also thank the Program Chairs, Senior Area Chairs, Area Chairs, and Reviewers for their constructive feedback.
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Appendix
Appendix Table of Contents
A.
Training Curves and Hyperparameters
B.
Additional Experimental Results
C.
Modeling Complex and Heterogeneous Interactions MF-LLM
D.
Applications and Discussion of MF-LLM
E.
Scalability and Complexity Analysis of MF-LLM
F.
Detailed Experimental Setup and Prompts
G.
Details of MF-LLM Framework
H.
Full Version of Related Work
I.
Showcase of LLM-CGenrrttddd Content
A
Training Curves and Hyperparameters
We present the training loss curves for both the policy model and the mean field model optimized via our IB-Tune algorithm, along with the loss curve of the LLM trained using standard supervised fine-tuning (SFT), in Figure 6 All models are fine-tuned based on the Qwen2 1. 5B- IB-nnsruct language model. The corresponding training hyperparameters are summarized in Table 3 All experiments were conducted on a machine equipped with two NVIDIA A100-PCIE 4CGB-40GBB GPUs (CUDA 12.2, driver version 535. 183.01). each with 40GB of memory. The mean field model was trained for approximately 74 hours, the policy model for 64 hours, and the SFT model for 25 hours.
Meari Field!
IB-Tune: Policy Model adalm,
Loucod sida1
Monn Pltl Lou
-20
Stoocled
200
.013
10000
1,200 1900
2503
4.23
800
1000
1200
1902
230
420
600
900
1050
1290
Figure 6: Training loss curves for three LLMs (Qwen2-1.5m) 1.5B:: (left) SFT (No Mean Field), represent- ing standard supervised fine-tuning on state-action pairs; (middle) IB Tune: Policy Model ( m,, s), corresponding to the fine-tuning of the policy model via our IB-Tune method; and (right) IB- -une:: Mean Field Model, corresponding to the fine-tuning of the mean field model via IB- BunTun. The loss functions for the latter two models are detailed in Section 3.3 Each curve shows the moving average smoothed loss (window size 40), with shaded areas indicating the original unsmoothed losses. All models are fine-tuned to convergence.
Table 3: Training hyperparameters for IB-Tune (the mean field model, the policy model), and the standard SFT algorithm. All models are fine-tuned from Qwen2-1 1002-11.B-Inssuucc
Hyperparameter
Mean Field Model
Policy Model
Standard SFT
Base model
Quen2-1.58 Instruct
Qwen2-1.5B -..--rntt
Qwen2-1. 1.1.B---Instucc
Max sequence length
2048
2048
2048
Training dataset
Weibo
Weibo
Weibo
Training events (until converge)
400
400
400
Training batch size
256
256
256
Miero hatch size
8
8
8
Max epochs
1
Learning rate
x 10-7
x 10-7
1 10-6
LoRA rank
64
64
64
LoRA ulpha
64
64
64
Zero stage
2
2
Loss function
Cmen held of IB-Tune
Spolicy of IB-Tune
NLL Loss of <(a]s)
B in Eyean feld
14

---

B Additional Experimental Results
B.1
Additional Results WEIBO corpus
Results across Different Decision Dimensions. In Table we first present the similarity metrics comparing our MF-LLM method against the baselines State, Recent, Popul ar, and SFT across each decision dimension (base LLM is Qwen2-1. 1ann2-1.5B-00 10-55B-nm SB-Instruct), At each evaluation step, the action distribution is constructed from the actions the 16 nearest agents. Similarity is measured between the real and generated distributions using multiple metrics, including KL divergence, Wasserstein distance, DTW, Macro FI, Mícro FI, and NLL Loss. The reported results are averaged over 14 task scenarios. For each task, evaluation is performed by simulating agents from index 50 to 300.
Table 4: Evaluation results across different decision dimensions. All metrics reported with relative improvements (%) over State. MF-LLM (ours) consistently achieves the best performance.
Algorithm
KL Div.
Wass. Dist
DTW +
Macro F1
Micro F1 f
NLL Loss
Dimension: Rumor
State
2.2057
0.1061
0.1741
0.3731
0.8387
4.3154
Recent
1,9807 (10.28)
0.1050 (1,8)
0,1813 (-419)
0.3794
0,8399 (0.18)
3.8282 (11.38)
Popular
1.6488 (15 193
0.0993 (649)
0.1584 (9.0))
0.3997 (7.19))
0.8485 (1.29)
3.8379 (1.119
SFT (No MF)
1.5597 (29.1))
0.0948 (006)))
0.1459 (16.2%)
0,4060 (8.8%)
0.8536 (1.8%)
2.2280 (48.4%)
ME-LLM (ours)
1.0032 (54,5%)
0.0796 (25.0%
0.0926 (46.8%)
0.4481 (20.18)
0,8784 (4.7%)
2.8342
(34.5%)
Dimension: Sentiment
State
3,6245
0.0619
0.3895
0.2960
0.6960
4.3154
Recent
4.1686 (-15.0%)
0.0789 (27.5%)
0.4120 (:888)
0,2750 (7719%)
0.6711 (3.65)
3.8282 (11.3%))
Popular
3,8127 (6529)
0.0724 (-1698)
0.3862 (0.8%)
0,2862 (33,5%)
0.6824 (:208)
3.8379 (11.199)
SFT (No MF)
2,1504 (40.7%)
0.0504 (18.66)
0.3310 (15.0%)
0.3473 (17.3%)
0.7332 (5.4%)
2.2280
(08.0%)
MF-LLM (ours)
1.6850 (53,5%)
0.0550 (11.2%)
0.3087 (20.7%)
0.3530 (19.3%)
0.7464 (7.2%)
2.8344
(34.3%)
Dimension: Attitude
State
1.7155
0.0816
0,2973
0.4449
0.7601
4.3154
Recent
2.2148 (-29.19)
0.1052 (-289%)
0.3399
0.4185 (33.99)
0.7204 (:522%
3.8282 (11.386)
Popular
1.9632 (-14.5%)
0.0923 19)3
0,2983 (-0.3%)
0.4303 (-3.9%)
0.7396 (-2.8)
3.8379
(11.19)
SFT (No MF)
0.8818 (48)
0.0741 (92
0.2566 (13.9%)
0.4750 (6.89)
0.7854 (9.9%)
2.2280
(48.4%)
ME-LLM (ours)
0.4245 (75.3)
0.0730 (105%)
0.2272 (2.00))
0.4928
(108%)
0.7983
(5.0%)
2.8342
(34.3%)
Dimension: Behavior
State
0,2132
0.0901
0.1758
0,5446
0.7859
4,3154
Recent
0,2756 29.398
(3.19)
0,2208 ( 25.688
0,5317 (.44)
0.7489 (4.7%)
3.8282 (11.3%)
Popular
0.2963
0.0901 (0.05)
0,2411 (:37.1%)
0.5298 (.17%)
0.7437 (5.4%)
3.8379 (12.15)
SFT (No MF)
0,1505
0.0819 (9.9))
0.1467
0.5511 (1.2%)
0.7948 (1.19)
2.2280 (68,09)
ME-LLM (ours)
0.0956 (55.2%)
0.0802 (11.0%
0.1016 (42.2)
0.5688 (4.45)
0,8440 (3.48)
2.8342
(34.5%)
Dimension: Stance
State
2,2091
0.0861
0,3092
0.4376
0.7477
4.3154
Recent
2,7059 (-21.5%)
0.1059 (22305)
0,3302 (488%)
0.4177 (-4.5%)
0.7263 (:29%)
3.8282 (11.3%)
Popular
2,3616 (-.99)
0.0938 (-0,0%)
0.2955 (4.4%)
0.4339 (.0.8%)
0.7450 (-0.4)
3.8379
(11.15)
SFT (No MF)
1.0596 (52.09)
0.0771 (1055)
0.2485 (19.6%)
0.4776 9.19)
0.7874 (9.3%)
2.2280 (48.4%)
MF-LIM (ours)
0.4489 (79.9%)
0.0779
(9.5%)
0.2335 (14.9%)
0.5080 (16.19)
0.7907 (5.79)
2.8342
(94.9))
Dimension: Belief
State
1,2888
0.1159
0.2279
0.4695
0.7939
4.3154
Recent
2,1881 8:6)
0.1288 (-1111%)
0.2685 (-188%)
0.4247 (9.5%)
0.7763 (-2.%%
3.8282 (11.3%)
Popular
1.6316 26,06)
0.1170 (.0%
0.2416 (.0%)
0.4516 (38%)
0.7948 (0.1%)
3.8379 (11.1%)
SFT (No MF)
1.0178 (21.09)
0.1055
(909)
0.1691
(25.8%)
0.4927
0,8100 (2.088)
2.2280 (45,016)
MF-LLM (ours)
0.4432 (65
0.0811
(300%)
0.1345 (4100)
0.5270 (12.2%)
0.8498 (3.0%)
2.8344
(34.3%)
Dimension: Subjectivity
State
0.2348
0.0878
0.2054
0.5481
0.7857
4.3154
Recent
0.3237 57.8%)
0.0929 5.8%)
0,3271 (59.3%)
0.5130 6.4%)
0.6999 (10.9%)
3.8282 (11.3%)
Popular
0.2542 (8.3%)
0.0858 (239)
0.2627 (22.99
0,5299 (.3.9%
0.7369 (4.2%)
3.8379 (11.1%)
SFT (No MF)
0.1097 (53.3%)
0.0764 (13.0)
0.1326 (35.4%)
0.5678 (3.69)
0.8286 (5.5%)
2.2280 (48.4%)
MF-L.IM (ours)
0.0891 (62.19)
0.0724 (17.5%)
0.1030 (49.88)
0.5754 (5.0%)
0.8484 (8.0%))
2,8342
(34.39)
Dimension: Intent
State
0.6812
0.0770
0.2435
0.4602
0.7712
4.3154
Recent
0.7546 (-108%%
0.0841 (9.29))
0.3100 (9)
0.4424 (3.9%)
0.71774 (-70%)
3.8282 (11.39)
Popular
0.6901 (..2%)
0.0834 (8.3%)
0.3096 (22.2%)
0.4525 (1.7%)
0.7164
3.8379
(11.1%)
SFT (No MF)
0,5381 (21.0%)
0.0763 (0.9)
0.2137 (12.5)
0.4719 (2.5))
0.7889 (2.398)
2.2280 (48,036)
MF-LLM (ours)
0.3714 (45.59)
0.0720 (6.5%)
0.1747
(38.55)
0.4921
(6.9%)
0.8185 19)
2,8342
(34.95)
15

---

Full Dynamic Trend Simulations. In Appendix Fig. we present the full dynamic trend simu- lations under the Liu Xiang Rumor scenario. We illustrate the dynamic trends across all decision dimensions and compare the simulations of multiple baselines, including State, Recent, Popular, and SFT. Additionally, we include simulation curves for the ablation variants of our proposed MF-LLM. Due to the large number of baselines and evaluation dimensions, we report these detailed results in the appendix for clarity.
Purror Tap streal
Nurrer Tes 2: counict
Nuww KL Drectyotee
0.4
0.0
322
Sencheet
Amthate Top
Jet Diargeenc
32
Trmares
Detaufor Thp comment
Danacte* Tbx snore
Dataslor Dive "aance
06
25
68
3M
323
Top
The 2: opcoas
Stance Divergance
Thentte
Trandea
Sebrectiity Top:1: sdteedive
Subectiiety Tor dtjective
SuIjeTsRR Diveggrce
3.4
3.0
L00
25
226
122
Inwnt opiiion
promation
meett Divesgence
1.6
EG
1.5
6.
Figure 7: Comparison of dynamic trend simulations across multiple baselines (starting from step 48). At each timestep, the distribution of actions is estimated based on the actions of the 16 nearest agents.
16

---

B.2 Additional Results on TWITTER dataset
We extend evaluation beyond the WEIBO corpus to examine whether MF-LLM preserves distribu- tional fidelity and decision consistency on other datasets featuring different interaction patterns.
Hamous-Keywool Twitter Replies Dataset (Kaggle). The TWITTER datase contains a large collection of tweet-reply pairs centered on popular keywords, providing a suitable testhed for large- scale discussion dynamics. Testing on several base LLMs,, MF-LLLM outperforms baselines without any domain specifcc fine-tuning:
Table 5: Results the FAMOUS- KEYWORD TWITTER REPLIES dataset across different LLM backbones. Lower is better (L) for all metrics except Micro/Macro-F (t). MF-LLM consistently generalizes across backbones without domain-specifee fine-tuning.
Backhone LLMs
KL Div. 4
Wass. Dist. 4 DTW
Macro FI
Micro NLL Loss
Qwen2-1. 5B- 18-Instruct
0.8696
0.0673
0.1700
0.4977
0.8241
4.2121
Recent
1.5061
0.0922
0.2206
0.4471
0.7661
4.1053
Popular
1,0059
0.0725
0.1553
0.4864
0.8047
4.0697
MF-LLM (ours)
0.6883
0.0744
0.1587
0.4989
0.8093
3.9748
GPT-4o-mini
State
6.8382
0.1469
0.4513
0.2808
0.6282
Recent
6.5273
0.1491
0.4444
0.2843
0.6361
Popular
7.5150
0.4251
0.2526
0.6112
MF-LLM (ours)
5,9322
0.1506
0,3300
0.2934
0.6403
GPT-4o
State
7.8105
0.1711
0.5178
0.2388
0.5962
Recent
7.2690
0.1607
0.4576
0.2574
0.6200
Popular
8.8492
0.1818
0.5198
0,2138
0,5798
ME'LLM (ours)
2.2669
0.1085
0.2211
0,4103
0.7249
State
1.7496
0.1105
0.2847
0.4173
0.6999
Recent
2,4299
0.1192
0.3462
0.3941
0.6829
Popular
1,4311
0,0905
0,2198
0.4424
0.7256
ME-LLM (ours)
1.1814
0.0922
0.2042
0.4483
0.7204
Market Behavior Simulation. TwinMarker (42), ElectionSim 44
Following prior studies on market-style decision dynamics (e.g., construct Bitcoin-related tweet-reply dataset simulate bullish/bearish sentiment evolution. MF-LLM again achieves the best quantitative alignment:
Table 6: Results on the BITCOIN-RELATER MARKET BEHAVIOR SIMULATION dataset. Lower is better (L) for all metrics except Micro/Macro-F1 (t). MF-LLM achieves the best quantitative alignment across metrics with base LLM Qwen2-1. 5B- 5B-Instuuc)...
Method
KI. Div.
Wass. Dist. $
DTW 4
Macro Fl
Micro Fl 1
Loss +
State
1.2304
0.0854
0.4505
0.4723
0.6721
4.4320
Recent
2.0641
0.0800
0.4730
0.4550
0.6573
4.3438
Popular
1,4394
0.0853
0.3930
0.4834
0.6920
4.2537
MF-LLM (ours)
0.9316
0.0915
0.2364
0.5025
0.7741
4.1485
Across both datasets, MF-LLM maintains strong alignment in distributional metrics (KL, WD, DTW) and classification performance (Macro/Micro F1), indicating stable generalization under different social and linguistic contexts.
C Modeling Complex and Heterogeneous Interactions in MF-LLM
MF-LLM naturally models complex and heterogeneous interactions among agents in large populations. This section provides an intuitive explanation of its mechanism and several illustrative examples from real-world data, showing how MF-LLM captures diverse influence patterns and topic-specific behaviors.
dataset//
data

---

Intuitive Mechanism. In MF-LLM, the policy model maps the current population signal to individ- ual actions, while the mean field model updates the population signal from newly observed actions. The pathway
01 M
represents an indirect but generalizable interaction between any pair of agents. Unlike prior work with fixed influence weights, MF-LLM infers and updates interaction effects dynamically from online data, enabling robust modeling even in unseen structures.
Empirical Illustration. To better understand this mechanism, we present several examples demon- strating that MF-LLM effectively captures (I) heterogeneous interactions, (2) disproportionate influence, and (3) small close-knit groups, without manually defined interaction weights or structures.
(1) Heterogeneous Interactions. We compare two different actions taken by the same high-inftuence user.
Example of Heterogeneous Interactions
State: A non-verified user with high influence and many friends. Previous Mean Field: Most users express opposition and criticism toward the event, regard- ing it as unfair competition.
Action A: "Repost"
Action B: "Looking forward to the truth!"
Updated Mean Field:
After Action A: "Most users are criticizing the event rather than seeking factual verifica- tion."
After Action "Users call for investigation to uncover the cause. Many suspect that this might be genuine news report."
(2) Disproportionate Influence. We compare the same action taken by users of different influence levels.
Example of Disproportionate Influence
Action: "Looking forward to the truth!"
Previous Mean Field: Most users express opposition and criticism toward the event, regard- ing as unfair competition.
Agent States: High-Influence User: non-verified user with high influence and many friends.
Low-Inffuence User: A similar user with low influence and few friends.
Updated Mean Field:
After High-Influence User acts: "Many suspect that this might be a genuine news report."
After Low-Inftuence User acts: "A few users in the comments express a desire to
uncover the truth."
(3) Small, Close-Knit Groups. Finally, we illustrate localized topic-specific interactions.
Example of Small and Close-Knit Groups
Conversation Context: In entertainment discussion:
User A: "Taylor Swift will hold a concert!"
User B: "The city marathon route will be adjusted next month."
Updated Mean Field (after A + B): "Population sentiment surges around the concert... marathon news draws moderate interest from runners."
Policy Model Responses under the Same Mean Field:
Idol Fan User: "Can't believe it! Already organizing group to buy tickets and cheer!"
Marathon Enthusiast: "Good to know about the route change- II'll adjust my training."
18

---

This shows MF-LLM captures topic-specific shifts via the mean field and generates heterogeneous actions via the policy model, faithfully modeling "close-knit group" dynamics from real data.
Summary. These examples demonstrate that MF-LLM adaptively models heterogeneous and asymmetric agent behaviors through iterative mean-field updates.
D Applications and Discussion of MF-LLM
Exogenous Signal 1 boosts ramor spread.
Exogenous Signal 2 reduces rumor spread.
1.-
Signal
weo Exs Signu w Signal
w/s Cea. Signal ai Ero Signal
cach rerwecedd
cotarautively
data
Tutlo
0.7
0.5
Eon Skpnal 2: Pepricso-aahe "Reshh"'
Timestop
Timestes
Exogenous Signal boosts rumor spreed
Exogenous Signal reduces numor spreed
2.2
Bos Sgnal y Dints ritented villoa
0.2
malls
0.5
We Exi, 330nd wi Signa
0.5
Sigral
Hitarny vurlll the much
100
Figure 8: Simulation before or after key nodes. Key node I and 3 boost rumor spread, Key node and 4 reduce rumor spread.
We first highlight three key findings from our experiments. (1) MF-LLM accurately matches real- world decision dynamics, in both temporal shifts and semantic structure. (2) generalizes well across social domains and backbone LLMs without task-specific tuning. (3) The mean-field module either significantly degrades fidelity. These results
and IB-Tune are both validate MF-LIM as robust framework for simulating collective behavior. Inspired by them, we now explore more practical applications and further discussions.
Forecasting Public Opinion and Pre-evaluating Interventions. We demonstrate MF-LLM's utility in real-time forecasting and intervention design using a rumor propagation scenario (Fig. (5) The framework supports (i) trend forecasting, (ii) intervention planning, and (iii) evaluation of intervention outcomes. (a) Forecasting accuracy. Starting from partial observations at steps 20, 34, 43, and 70, MF-LLM generates forward rollouts of population behavior. Forecasts closely track ground-truth rumor prevalence (e.g., step 70: predicted 0.645 vs. actual 0.643), highlighting MF-LLM's temporal consistency and reliability. (b) Intervention planning. Simulation outputs enable data-driven planning. At step 34, the model anticipates rise in rumor spread, triggering an early warning for intervention. This offers actionable insights for proactive decision-making. (c) Intervention evaluation. We compare two intervention strategies. A single intervention at step 34 (green) slows spread temporarily but fails to prevent rebound. A second, later intervention at step 80 (red) stabilizes the trajectory. MF-LLM thus supports pre-deployment testing of multi-step interventions.
Incorporating Exogenous Signals to Improve Fidelity. While MF-LLM captures endogenous dynamics driven by agent interactions, many real-world events are shaped by rare, high- exogenous signals. We investigate their effect using the Liu Xiang rumor scenario, where a burst of "silent reposts" triggers widespread misperception. By injecting such signals into the simulation, we reproduce observed inflection points (Fig. K) and improve alignment with real-world dynamics. These findings underscore the importance of modeling rare, externally induced behaviors. Future work may explore dynamic event detection, uncertainty-awaat
responses, and automated signal injection to capture both endogenous patterns and exogenous shocks.
19

---

Low NLL does not Necessarily Imply High Rollout Fidelity. In Fig. SFT achieves the lowest NLL Loss at test time. However, token-level likelihood does not necessarily translate to rollout-level fidelity. MF-LIMM solves richer conditional generation problem by aligning each decision with the evolving population signal m. This additional constraint increases irreducible cross-entropy slightly but prevents overfitting and encourages long-term semantic consistency. As result, MF-LLM outperforms SFT on KL divergence, DTW distance, and FI metrics. The trade-off is favorable: sacrificing minimal one-step accuracy yields substantial gains in rollout quality and realism.
4 aand 2 we observe that
Smaller LLMs Outperform Larger Ones in Simulating Population Dynamics. In find that smaller backbones such as Qwen2-1.. Sheen-1..BBIInttii 5B-Instruc outperform larger models in simulating collective decision dynamics. Analysis of outputs from GPT-4o-m and DeepSeek-RI reveals highly homogeneous agent responses, even under identical prompts and hyperparameters across different LLMs (Appendix D. Larger models tend produce uniform responses over time, limit- ing their ability to capture diverse agent behavior and degrading long-horizon simulation fidelity. This likely stems from reduced sensitivity to subtle variations in prompt or agent state. In contrast, smaller models exhibit greater responsiveness and variability,, resulting in more realistic and dynamic population trajectories. These findings align with prior work showing that large LLMs often favor begh-probability outputs [18], and may underperform in tasks requiring structured behavioral diver- sity [47] These results provide key insights for social simulation: reducing output homogeneity may be more important than maximizing model size, and properly leveraging smaller models can preserve behavioral diversity while offering substantial efficiency gains.
I Limitations and Future Work While incorporating exogenous signals improves simulation fidelity, the current MF-LLM framework does not yet support real-time detection or integration of such signals. Future work could explore automated mechanisms for monitoring and injecting external events into the simulation loop. In addition, as simulation horizons increase, small deviations in carly steps may compound over time, leading to distributional drift. This effect is observed in Fig. 2 and highlights the need for long- horizon correction strategies, such as periodic recalibration or error-aware feedback mechanisms.
E
Scalability and Complexity Analysis of MF-LLM
Computational Complexity. MF-LLM aims to capture dynamic agent interactions that give rise to collective behavior. Modeling all pairwise agent interactions would incur O(N²) computational cost, whereas MF-LLM reduces this to O(N) through mean-field approximation. Specifically, the policy model generates one personalized action per agent, resulting in ((N) LLM inferences, and the mean-field model updates the population signal once per batch of K agents, producing O(N/K) mean-field inferences. Overall, MF-LLM achieves linear-time complexity while still modeling inter-agent effects and reproducing population-leve dynamics. This contrasts with baseline simulators that either ignore agent interactions entirely or approximate them through manual prompt engineering without dynamic coupling.
Empirical Validation of Complexity. To empirically validate the theoretical O(N) analysis, conduct two complementary experiments: (i) scalability testing under larger agent populations and (ii) runtime under increasing simulation scales.
(a) Scalability under Larger Populations. We evaluate MF-LLM's scalability by extending simu- lations up to 4,000 agents using (wee2-11.B-Ine Instructt (without fine-tuning). Results in Table 7 show that ME-LLM maintains consistent accuracy as population size increases, demonstrating stable performance and convergence in large-scale settings.
(b) Runtime Scaling, We further measure runtime on 10nm2-1.5B-Inttaae using the TWITTER dataset (no fine-tuning) on a single NVIDIA A100 GPU (40 memory). As shown in Table g runtime increases linearly with the number of agents, maintaining an almost constant per-agent cost (~,..66s), which empirically confirms the O(N) complexity of MF-LLM.
Summary. Both theoretical and empirical analyses demonstrate that MF-LLM scales linearly with population size while preserving simulation fidelity. This scalability enables efficient modeling
20

---

Table 7: Scalability of MF-LLM across different population sizes (500-4,00) agents). (L) for all metrics except Micro/Macro-FI (t).
Lower is better
Agents
KL Div.
Wass. Dist.
DTW 4
Macro F1 f
Micro F1 f
NLL Loss 1
500
1.2582
0.0645
0.1196
0.3688
0.8644
3.9916
1000
1,4638
0.0729
0.1220
0.3643
0,8436
4.0112
2000
1.1053
0.0685
0.0965
0,3569
0.8537
4.0236
3000
1.0668
0.0650
0.0837
0.3592
0.8611
4.0142
4000
1.5905
0.0698
0.1025
0.3548
0.8376
4.0237
Table 8: Runtime scaling of MF-LLM with respect agent population size. Results empirically
validate the ((N) complexity.
Agents
Total Time (s)
Time Agent (s)
512
280.88
0.55
1008
561.89
0.56
1504
832.31
0.55
2000
1113.41
0.56
2512
1404.34
0.56
3008
1687.50
0.56
3504
1966.29
0.56
4000
2249.15
0.56
of large-scale populations, bridging micro-level decision processes and macro-level population
dynamics.
Detailed Experimental Setup and Prompts
F1
Dataset
The WEIBO corpus 124 consists of approximately 5,000 real-world events across seven domains: Crime, Culture, Health, News, Politics, Sports, and Technology. Each event includes topic and responses from 100 to 1,000 users, with corresponding user profiles (e-g.. location, gender, follower count, activity level) and their posts. We use 4,000 events for training and 1,000 for testing. Training converged after 400 events, which point optimization was stopped (see Appendix Fig. 6).
F.2 Baselines.
Based related work, summarize the following baseline approaches for modeling other agents' decision-making:
State: The user profile and event topic serve the state and input to the LLM, independent of other agents' decisions, as ElectionSim 44].
Recent: Besides the state, the k most recent actions are provided as input. For instance, TrendSim
445 observes the Top-k comments, and AgentSociety 322 tracks event flow in time order.
Popular: In addition to the state, the actions with the highest popularity (followers, replies, likes, etc.) are included input to the LLM, in OASIS 43 and HiSim 29
SFT: Standard supervised fine-tuning 30 on state-action pairs for each agent. The baseline is
carefully trained to convergence (see training curves in Appendix Fig.
For evaluation, we compare the outputs our MF-LLM and baselines with ground-truth responses from the WEIBO corpus (hereafter Real data).
21

---

F.3 Evaluation Metries
Metrics for Evaluating Individual Actions. To provide fine-grained assessment of individual agent actions, we define eight evaluation dimensions, each capturing a critical aspect of decision realism. Below, explain the meaning and motivation behind each dimension.
Measures whether the agent is spreading or countering a rumor. spread: The com- ment believes, forwards, amplifies the topic discussed. counter: The comment challenges, questions, or refutes the truthfulness of the topic, aiming to clarify or correct misinformation.
Rumor.
Sentiment. Captures the emotional tone expressed in the comment, including implicit sarcasm or critique. Categories include angry, calm, happy, sad, fear, and surprise.
Attitude. Reflects the overall emotional orientation of the comment-whether negarive, neutral. Particular care is taken to detect subtle negativity when not explicitly stated.
positive,
Classifies the type of action taken: share if the agent reposts the content, and comment if the agent directly evaluates it.
Behavior:
Stance. Identifies the agent's position toward the appic-suports oppose. or neutral. Em- phasis is placed on recognizing implicit opposition or dissatisfaction within the comment.
Belief. Assesses whether the agent believes in the truthfulness of the discussed topic expresses doubt. Expressions of skepticism, calls for truth, or assertions of falsehood are categorized as doubt.
Subjectivity. Distinguishes whether the comment is based subjective personal opinions or on objective factual descriptions.
Intent. Captures the underlying purpose of the comment: question (asking for clarification), promotion (disseminating information), or opinion (expressing personal views).
Prompt Template for Evaluating Decision Dimensions. We employ GPT-4o-ming to evalu- both real and generated action texts. GPT-4o-mini offers highly cost-effective and fast API, enabling stable and consistent evaluation results. We benchmarked several alternatives, including emo- tion classification models, GPT-3.5 5.oTbob,,, GPT-4o, and DeepSeek, and selected GPT-4o-mine 4immmii for its balance between reliability, speed, and deployment cost.
To ensure evaluation reliability, conducted a human validation study 100 samples with domain experts (social science scholars, junior faculty, and senior PhD students), comparing human judgments with outputs from multiple LLMs. Table/9summmarin 91.25% agreement with human judgment- higher than GPT-3. 111-33.5-Turx 5-Turbo (79.13%) and comparable GPT-4o (89.38%) while maintaining the lowest cost and near-real-time speed.
the results. GPT-40-ming achieves
Table Reliability and efficiency comparison of different LLMs for semantic evaluation. GPT GPT-io-mini achieves high human alignment minimal cost and latency.
Metric
GPT-4o-mini GPT-3.5-Turbo
GPT-4o
GPT-4
Agreement w/ Human (%) Price (S/IM tokens, Input Output) Speed (s/sample)
91.25
79.13
89.38
94.13
0.15/0.60
0.5/1.5
2.5/10
30/60
1.25
0.83
0.96
4.02
Since semantic evaluation is not a highly complex task for modern LLMs, GPT-4o-mini provides the most cost-effective balance of accuracy, efficiency, and scalability. Below, we present the prompt template used for Docision-dimensse evaluation.
22

---

Prompt Template for Evaluating Decision Dimensions
You expert in public opinion content analysis. Task: Analyze multiple user comments objectively evaluate the sentiment, stance, and opinion orientation regarding the following topie: Discussion Topic: (topic)
Role:
Instructions: For each comment, perform analysis according the following nine dimensions and strictly return results JSON format. Special Note: The emoji "@ @" typically conveys feelings of "surprise, confusion, or being stunned".
rumor (Rumor propagation): Select from ["spread", "counter"].
counter": Comments that aim to refute, disbelieve, question the authenticity, expect further clarification, directly point out the falsity of the topic.
"spread": All other comments, including those expressing belief in the topic, reposting content, tagging usernames, repeating topic content, expressing emotional reactions to the topic.
2. sentiment (Emotional state): Capture the user's emotional state conveyed through the comment (including punctuation and tone). Choose from ["angry", "calm", "happy", "sad", "fear", "surprise"]] Note: Simple reposts are categorized as "calm".
attitude (Attitude polarity): Determine whether the user's sentiment is positive, negative, neutral. Choose from ("positive", "negative", "neutral"], Note: Pay close attention any implicit negative sentiment (e.g., sarcasm, criticism).
behavior (Behavior type): Select from ["comment", "share"].
"share": The comment is primarily forwarding or reposting content.
"comment": The comment expresses an evaluation, opinion, or reaction.
5. stance (Stance towards the topic): Select from ["support", "oppose", "neutral") "J. Note:
Pay attention implicit opposition, dissatisfaction, criticism.
belief (Belief in the topic): Select from ["believe", "doubt"].
"believe": The comment expresses belief in the topic (including reposting).
"doubt": The comment questions, refutes, expresses skepticism towards the topic.
keywords (Keyword extraction): Extract important keywords from the comment and return them as an array (c.g., ["policy", "economy"]) ")). If the comment is meaningless, return [""].
subjectivity (Subjectivity): Determine whether the comment based subjective opinions or objective facts. Select from ("subjective", "objective"] "].
9. intent (Intent classification): Select from ["question", "promotion", "opinion"].
"question": The comment primarily asks question.
"promotion". The comment primarily disseminates or promotes information.
"opinion": The comment primarily expresses opinion viewpoint.
Input Format: following are (len (comments)) user comments:
Comment 1:
"(comment__
Comment 2:
"[comment__
Strietly return JSON array evaluating the (len (comments)) comments. Do not output anything other than the JSON array.
Output Format:
Example Output:
"rumor:: "spread",
"sentiment_etate"" "calm",
"santinent.tendenyyy. "neutral", behavior_type "share",
"stance": "neutral",
"belief_der "eoreee_ "believe", "keyvords"; ["share", "veibo "],
23

---

"subjectivity" "objective",
"intent claten_claasiiication "promotion"
"rumor": "counter", "sentiment_state": "angry",
"sentimentt_tendengy" "negative", "behavior_type". "comment",
"stance": "oppose", bbelie_ddgreee: "doubt",
"keywords:: ["fake", "impossible"),
"subjectivity"; "subjective",
'intent "opinion"
}
]
F.4 Prompt Templates
In this paper, we design three prompt templates. (i) The first template guides the policy model to generate individual decision-making behaviors. (ii) The second template assists the mean field model in summarizing the evolving population distribution. (iii) The third template enables GPT-4o-a 4ommini to evaluate the dimensions of individual decisions with fine-grad mne-grained analysis. Together, these templates ensure coherent workflow across decision generation, mean field updating, and evaluation.
Prompt Template for Policy Model
You tasked with simulating plausible user action (reposting commenting) based on their profile and the current population information.
Inputs:
Discussion Topic: {topic}
Recent Comments (if available): (Recent_comment)
Popular Comments (if available): (Popular_comee comment)
Current Mean Field: fimea_ffeldd
User Profile Attributes:
Location
Description
Gender: Male Female
Number of Friends: Categorized
8 Very few: fewer than 10
Few: 30
Moderate: 31 to 1000
Many: 1001 3000
Very many: than 3000
Number of Followers (Influence Level): Categorized
Very low: fewer than 100
Low: 101 500
> Moderate: 501 to 1000
High: 1001 10000
*
Very high: more than 10000
Activity Level (Based on Total Interactions):
s Inactive: fewer than 10 interactions
Moderately active: 10 100 interactions
Highly active: more than 100 interactions
Verification Status:
Verified user (with verification type ID)
* Non-verified user

---

Intermediate Step (User State Construction): First, generate a concise user profile description in Chinese (or English), following the template:
A user from (user_location); described {user_desses desse__deccrpttonn iden- tified (gender), with {friends_levell levell] number of friends and {influence __evel_ level influence based on followers. user is factivity_levell.. in terms interactions, and the account is wverified_statss]
Note: If using GPT or DeepSeek models, we add an explicit instruction at the end of the prompt: "Ouiput only the final simulated text without any intermediate reasoning process. In the output generated by DeepSeek-a Distill-Qwen Mastill-Qwen-32B. any content enclosed within <think>... </think> tags removed, and only final generated text is preserved for evaluation.
Prompt Template for Mean Field Model
You tasked with summarizing the distribution of user comments regarding specific discussion lopic.
Inputs:
Discussion Topic: [topic}
Previous Mean Field: {previous_ment cactsss_eea__eeeeeeee
Recent User Comments: A list of user comments formatted "Comment I: xxx", "Com-
ment xxx", etc. etc.
Instructions: Based on the provided information, summarize the overall user discussion by addressing the following six aspects in order of importance:
Stance Distribution: Are users predominantly supportive or oppositional?
2. Opinion Distribution: What the major viewpoints expressed?
3. Emotion Distribution: Are emotions primarily anger, excitement, doubt, or anxiety? Overall, are sentiments positive, negative, or neutral?
Behavior Distribution: Are users more inclined repost or to comment?
5. Perception of Topic Authenticity: To what extent do users believe doubt the authenticity of the topic?
6. Intent Comments: Are users primarily asking questions, expressing opinions, or dissemi- nating information?
Response Requirements: Provide concise summary in Chinese (or English), approximately 200 words in length. Ensure the response is structured clearly, focuses on key points, and remains casy to comprehend.
G Details of ME-LLM Framework
G.1 Derivation of the IB-Tune Objective
Variational upper-bound on the [mm;;; X) term. We begin from the definition of mutual informa- tion and derive computable bound by introducing variational prior r(m4).
T(m;; X) = p(Xmm.) log p(m X)
(definition of mutual information)
p(m+)
= -Fx))
(p(m X) [l
(rewriting as an expectation of KT.)
~ xx(x) (Ko X) [Ip(m)))
(variational posterior μz)
= Bmo(me [log X) log logr(m:))
Next, we add and subtract the log-density of a fixed prior r (m²):
log μs log (log μs logr) + (logr log
25

---

Hence
[(m::X) K x) x))rr(m))) + Pp(x)Buu (x) [lo - log p( mz)
(A)
(B)
Observe that
( Bp())) [log rmm)) log p(m)] KL (p((())) [(mm)) S
Discarding this non-negative term yields the desired bound:
[[m; X) < (L XX ((()))
(pc mo X) - -log (mm)]
G.2 Scaling to More Agents via State Sampling
Simulating More Agents Our MF-LLM framework is inherently scalable and can simulate an arbitrary number of agents over time through iterative rollouts of the policy model and mean field model, as shown in Figure [ A key question how to obtain the state information for additional agents during simulation. If the profiles of future users or agents are available, they can be directly used as the input states for simulation. However, in scenarios where the profiles of future agents are as when predicting future participation- we extend our method by sampling agent states from an existing state distribution. Agent profile distributions tend to evolve much more slowly than opinion/decision distributions, especially relative to the fast dynamics of event-driven discussions. Therefore, for long-tern term simulations of collective decision trends, it is reasonable to sample agent states from historical user profiles. Our experimental results further suggest that the mean field model plays dominant role in shaping collective dynamics, while the specific agent state distribution has relatively minor impact.
H Full Version of Related Work
H.1 Agent-Based Models: Foundations and Limitations.
Agent- Agent-Based Modeling (ABM) has long served as a cornerstone for simulating complex social systems, enabling emergent phenomena to arise from local interactions among individuals. Seminal works such as Sugarscape [10, Bonabeau's 's survey 66. and domain- sppaciii applications in crowd dynamics 115 market simulations [6), ecosystems 14] and public policy 22 have demonstrated the versatility of ABMs across diverse domains. However, traditional ABMs often rely on manually crafted behavioral rules, limiting their adaptability and scalability cawelittt--seecallllyy
population size and environmental complexity increase 77 17 25). While effective at capturing rule-driven emergent patterns, ABMs typically lack the flexibility required to generalize across diverse and unseen scenarios. Recent advances large language models (LLMs) offer a promising direction to overcome these limitations by equipping agents with generative decision-making capabilities grounded in rich contextual knowledge.
H.2 LLMs for Social Simulation: Progress and Gaps.
The rise of LLMs has catalyzed
of social simulation systems, enabling agents son, adapt, and interact through natural language. Early works such as Generative Agents [31] and Sotopia [48] demonstrated the potential of LLMs to support small-scale, open-ended simu- lations. Recent efforts have sealed up to broader domains, including social media [43 45 32
elections 44 economic behavior 22 42 and misinformation spread (23) Toolkits such Gen-
Sim (35] AgentScope [13), and AgentSociety (32) have facilitated the construction of complex multi-agent environments. Despite these advances, key limitations remain. Many simulations rely on handcrafted prompts, fixed roles, and heuristic memory mechanisms that lack alignment with real-world behavior, limiting their quantitative fidelity. Agent interactions are typically governed by static or scripted schedules 43 45 g. preventing agents from adapting to changing collective dynamics. Although recent approaches attempt to incorporate peer behavior and scene evolution into memory [3 45 29 43), they often depend on heuristic retrieval or summarization strategies, lacking principled mechanisms to retain decision-critical information over long horizons. These constraints hinder the simulation of realistic, adaptive population behavior. Progress in L.M--bssed social simu- lation will require principled mechanisms to model the feedback loop between individual actions and evolving population signals- signals-allowingg allowing agents to both respond to and influence macro-level dynamics.
26

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H.3
Mean Field Approximation: Scalable Interaction Modeling.
Mean field approximation offers an effective way to model large multi-agent systems by replacing costly pairwise interactions with interactions between each agent and a shared population signal [T9]
This abstraction is formalized in Mean Field Game (MFG) theory, which enables scalable modeling of individual decisions and their aggregate influence on population dynamics. By collapsing
41)
multi-agent dependencies into compact population-level representation, MFGs significantly reduce the complexity of interaction modeling and have been applied to domains such as social influence [40
4. traffic control [ 39] energy optimization [9) economic policy [27], and imitation learning [46]
However, classical MFGs often assume stylized agent behaviors and lack the contextual reasoning
required for realistic social simulation. Recent neural variants (20 21 improve expressiveness,
but remain less flexible than large language models. Motivated by these limitations, we propose Mean-Field LLM (MF-LLM), which combines the scalability of mean-field approximation with the generative reasoning capabilities of LLMs. MF-LLM explicitly models the bidirectional feedback between individual behavior and evolving population dynamics, enabling scalable, high sechfiielitty social simulation.
I Showcase of LLM-Generated Content
In Appendix [ we present a subset of generated comments under the "Liu Xiang Olympic Rumor" scenario, corresponding to the decision distribution at a single time step (manifested as comments distribution in this context). We compare outputs generated by agents in identical states but using different methods and LLM backbones. All comments were initially generated Chinese and faithfully translated into English for presentation. The complete results are available in our GitHub repository.
I.1 Analysis of Generated Comments across Different Algorithms
To further evaluate the fidelity of generated comments, we conducted comparative analysis along three key dimensions: content richness and naturalness, intention distribution trumor-spreading vs. countering vs. neutral), and belief uncertainty. We compare the outputs from MF-LLM and State generation against real human comments collected from the same context.
Content Richness and Naturalness. Comments generated by MF-LLM exhibit a high degree of linguistic diversity and conversational naturalness, closely resembling real human discourse. Examples include casual expressions such "Haha Is this news real?" and mixed emotional cues like "This feels way too real... but let's wait for the official announcement." These stylistic features mirror the informal, fragmented, and emotion-driven nature of weal-world social media discussions. In contrast, State generation tends to produce more formal, structured outputs, often resembling official clarifications (e.g.. "Regarding the latest news, have contacted the relevant parties, please do not believe rumors."). Such responses, while coherent, lack the spontaneous variability observed in human comments.
Intention Distribution. MF-LLM successfully captures the coexistence of rumor-spreading, rumor- debunking, and neutral stances within the population. Some generated comments actively propagate suspicions (e.g., "Stop joking around."), while others explicitly advise caution against misinformation (e.g., "Fake people and fake stories are all rumors, don't believe them!"). Importantly, MF-LLM also generates comments that reflect passive spectatorship. mimicking users who merely observe without taking stance, In contrast, State generation skewed toward debunking or formal clarification, showing limited presence of rumor-sprees sumor-spreading or ambivalent behaviors. This mismatch leads to narrower and less realistic distribution compared to real-world discussions.
Belief Uncertainty. Real human comments display wide spectrum of belief, ranging from full acceptance to skepticism and outright denial. MF-LLM- --eeerrgeeeeteed comments faithfully reproduce this belief heterogeneity. Some comments show partial belief or hesitation (e.g.. "Is it true? Or fake? Too many rumors going around."), while others demonstrate firm rejection or concern. This spread reflects the nuanced and non-binary attitudes common in organic social discourse. Conversely, State generation primarily produces comments that firmly oppose rumor acceptance, lacking examples that inhabit the uncertain middle ground
27

---

Summary. Overall, MF-LLM significantly outperforms State generation in replicating the natural distribution of real human comments across multiple dimensions. It captures richer language pat- terns, more balanced intention distributions, and realistic belief spectrum, enabling more faithful simulation of public opinion dynamics.
1.2 Analysis of Repetition across Different LLMs
We further evaluate the quality of generated comments by examining content diversity. align- ment with real-world distributions, and model-specific generation tendencies. In particular, we compare GPT-4o-mine 4o-mini and DeepSeek-Ri Distill-Qwes MeBBn-3BBBB- against meen2-1.BB Instruct MF -FLLLM/State.
High Repetition Across Agent States. Both GPT-4o-mini and DeepSeek-RA R1 exhibit significant repetition across outputs, even when agent states vary. For example, GPT-4o-mini frequently repeats phrases like "really heartbreaking" and "sigh," while DeepSeek-RI consistently generates sensational headlines such as "shocking! Liu Xiang's withdrawal scandal exposed!" across different user profiles. We highlight repeated content using color in following tables. This redundancy indicates failure adapt responses to agent-specific contexts, limiting the models' ability to simulate diverse population behavior.
Deviation from Real Comment Distributions. Generated comments from GPT-4o-mini and DeepSeek-R1 deviate markedly from real-world comment patterns. Human comments naturally span rumor-spreading, debunking, passive observation, humor, and emotional venting. In contrast, both models collapse this diversity into narrow emotional templates, predominantly emphasizing grief or outrage. This leads to unrealistic collective behavior, missing the rich spectrum of opinions and intentions present in authentic discussions.
Distinct Narrative Biases. Each model also imposes distinctive stylistic biases, GPT-4o-mini favors sentimental and empathetic narratives, often regardless of the agent's initial belief state. DeepSeek-PP R1, in contrast, exaggerates sensationalism by systematically inserting attention -eentionggrabbing phrases. These narrative tendencies further distort the natural variance of social discourse, amplifying specific emotional tones beyond their prevalence in Real data.
Summary. Compared to Qwen2-1. Instruct MF-LLM, both GPT-4o-mini and DeepSeek-R1 R1 exhibit higher repetition, stronger narrative bias, and weaker aligmment with real-world collective decision-making dynamics. These results highlight the necessity of diversity-aware generation strategies when modeling large-scale social behaviors.
28

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Comparison between Real and Generated Comments (Qwen2-1.5B-Instiee MF-LIM)
Index
Real Comment
Generated Comment
Repost.
feel same way!! But wait for official announcement.
2 Stop spreading bullshit rumors, you brainless nationalists! [angry] Since when could the host country just change the IAAF competition rules whenever they want?! [angry] How much more stupid can you get just to suck up to someone?!
Haha-> Is this news real? Were we tricked again?
3
true? fake? Too many rumors going around.
RealNewsBot Fake people and fake stories are all rumors, don't believe them!
4 Repost.
This feels way too real. @CRNews @So- huVideo This whole thing is really confus- ing... @/CCNNws: Didn't expect this V(@SohuVides [haha] That was close [think- ing][sly smile]
5
[Watching]
Stop joking around. Only China would dare pull something like this. Heh.
6
it real or fake?
know what's 's up. Stop spreading rumors, haha, seriously.
7
No way, really? it true? @ @lovelingzi
@RealWorld @OnlyBelicvennSkill @ @portt sNews
8
[angry] Shameful.
@BejjingSportShhnnell
9
Looking the truth.
Repost.
10
Repost.
"Rumor says
11
Is this really how it happened?! [angry]
@ @Everyone Please pay attention~ Recently shocking piece of news been spreading oaline..[immage).. Let's check out this video together...
12
Repost.
Why are there so many people spreading fake news? Stop lying!! Is all of this even true? still hoping someone would tell the truth
13
Damn it! Inhumane! I'm boycotting British goods! [angry rant]
@ Tot @ChinaTrackTemm I'm really rious why this issue causing such huge debate? We need see there's any solid evidence proving this claim, because online ru- mors are every where now... e/@ BeijingSports: Very...
14
Repost.
@ @People's Daily:
15
Paranoia kicking in again.
@Hello everyone~ Here's the latest trending news As we all know, there shocking report carlier saying that China's track Liu Xiang might have messed up because the hur- dle spacing was deliberately altered.
29

---

Comparison between Real and Generated Comments (Qwen2-1.BB-Intrrull State)
Index
Real Comment
Generated Comment
Repost.
saw someone post a message about Liu ang withdrawing before the London Olympics. He said it was because hurdle spacing was lengthened...
2 Stop spreading bullshit rumors, you brainless nationalists! [angry] Since when could the host country just change the IAAF competition rules...
3
it true? fake? Tao many rumors going around.
[Regarding the latest news on topic, already contacted the relevant parties, plcase everyone don't 't believe in rumor spreading
4
Repost.
Shocked!! It's spreading wildly online that Liu Xiang accused of violating IAAF rules, and that improper setup of the competition venue...
5
[Watching]
Really? Does this maybe reveal some of own problems?
6
it real or fake?
[Shocking rumor online: Liu Xiang's with- drawal involved huge scandal? The hurdle spacing was actually widened...]
7
No way, really? Is it true? @lovelingzi
@ RRallWorld @ MeToo
8
[angry] Shameful.
[Shocking rumor online: Liu Xiang's with- drawal stumning inside story - London's 's care- lessness actually led to hurdle spacing in- crease!]
9
Looking for the truth.
#0lyymppiQuuiieeessstSotiieeeeee After Liu Xiang's hurdle misstep, how did still manage to break through?...
10
Repost.
"Rumor says
11
Is this really how it happened?! [angry]
[Reply] @ Anonymous: This topic very in- teresting. think key prohlem lies differ- ences in the venue and training levels...
12
Repost.
"Haha..... Netizen comment: Haha...
13
Damn Inhumane! I'm boycotting British goods! [angry rant]
@Liu Liu Xiang questioned for continuous hurdle mistakes this claim credible?
14
Repost.
@Peoplc's Daily:
15
Paranoia kicking again.
#Today Topic #OmlineRumorEveen
30

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Comparison between Real and Generated Comments (GPTT-4-mini State)
Index
Real Comment
Generated Comment
Repost.
Although Liu Xiang's withdrawal really re- grettable, this kind of hurdle spacing change is just way too unprofessional! He made many adjustments...
2
Stop spreading bullshit rumors, you brain- less nationalists! [angry] Since when could the host country just change the IAAF com- petition rules whenever they want?! [angry] How much more stupid can you get just to suck up to someone?!
Sigh, Liu Xiang's withdrawal this time is really heartbreaking! heard the hurdle spacing was actually changed, this is just way too unreason- able!...
3 Is it truc? Or fake? Too many rumors going
Liu Xiang's ' withdrawal is really hearthreaking, especially with the hurdle spacing problem in London, really should not have happened!...
around.
4
Repost.
After seeing this hehind-the-ssceee story, truly a mix emotions. Liu Xiang, as an excellent athlete, has been through so much...
5
[Watching]
Liu Xiang's 's withdrawal London was because of the hurdle spacing change, this is just too outrageous!...
heard
6
Is it real or fake?
Liu Xiang's 's withdrawal is really heartbreaking, seeing such behind-the-sceee feel emotional...
makes
7
No way, really? Is it true? @ @lovelingzi
Sigh, this is really hearthreaking! Liu Xiang has always been a hero our hearts, his seven-step technique...
8
[angry] Shameful.
As who been following Liu Xiang. am truly shocked the behind-the-scenee of this London event!...
9
Looking for the truth.
Sigh, Liu Xiang's withdrawal this time is really hearthreaking! have always supported him, and T never thought that...
10
Repost.
Secing Liu Xiang at the London Games originally thought he
ally heartbreaking! would perform well, unexpectedly...
11
this really how happened?! [angry]
This really regrettable! Liu Xiang always been our pride, but unexpectedly London, be- cause of the careless hurdle spacing design...
12
Repost.
this shocking piece of news, feel extremely regretful and disappointed. Liu Xiang's seven- step technique was classic skill...
13
Damn it! Inhumane! I'm boycotting British
The inside story of Liu Xiang's withdrawal in London is truly shocking! It turns out the hurdle spacing was actually increased 13.85 meters...
goods! [angry rant]
14
Repost
Seeing the inside story about Liu Xiang's with- drawal, my heart really feels full mixed emo- tions. Turns out, the hurdle spacing change...
15
Paranoia kicking again.
Sigh, it's really too disappointing! Behind Liu Xiang's 's withdrawal, there was actually such hidden story...
31

---

Comparison between Real and Generated Comments (DeepSeek-R) R1 Distill-Qwen-321)
State)
Index
Real Comment
Generated Comment
1
Repost.
Repost Weibo: Shocking! The real reason be- hind Liu Xiang's 's withdrawal scandal exposed! Carelessness the London Olympics led an increase in hurdle spacing...
2
Stop spreading bullshit rumors, you brainless nationalists! [angry]... ...
"The hurdle spacing increased by 0.13 meters, it looks like a tiny change, but had a huge impact on Liu Xiang's 's seven-step technique! This small detail at the London Olympies is really chilling...
3
Is it true? Or fake? Too many rumors going around.
Liu Xiang really unfortunate, the hurdle spacing adjustment affected his performance, and other athletes also had problems. This is so unfair! Hope the truth will be revealed!
4
Repost.
Shocked! London really screwed Liu Xiang this time! The hurdle spacing increased by 0.13 meters...
5
[Watching]
Shocking! Liu Xiang's withdrawal scandal exposed! The hurdle spacing the London Olympics was actually increased to 13.85 me- ters...
6
it real or fake?
Liu Xiang's 's withdrawal is indeed regrettable, but the hurdle spacing change at the London Olympics was definitely key factor...
7
No way, really? Is it true? @lovelingzi
Shocking! Liu Xiang's 's withdrawal scandal ex- posed! Carelessness at the London Olympics actually lengthened the hurdle spacing...
8
[angry] Shameful.
[Repost]Liu Xiang's 's withdrawal scandal posed! London Olympics adjusted the hurdle spacing, from 13.72 to 13.85...
9
Looking truth.
This is so unfair! Xiang's seven-step tech- nique was clearly designed for 13.72 meters...
10
Repost.
This way too unfair! Liu Xiang's seven- step technique was designed for a 13.72-meter distance, but London actually changed it...
11
Is this really how it happened?! [angry]
Netizen emotions: sadness, disappointment, support for Liu Xiang.
12
Repost.
Shocking! There's such big scandal behind Liu Xiang's withdrawal! Was the hurdle spac- ing the London Olympics really set so casu- ally?...
13
Damn Inhumane! I'm boycolting British goods! [angry rant]
This way too outrageous! The London Olympics actually changed the hurdle spacing, causing Liu Xiang to hit the hurdle directly...
14
Repost.
Oh my god, Liu Xiang's withdrawal is really too unfortunate! London increased the hurdle spacing 13.85 meters...
15
Paranoia kicking in again.
Sigh, this is way too outrageous! Liu Xiang's seven-step technique was his signature move...
32

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NeurIPS Paper Checklist
1. Claims
Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Question:
Answer: [Yes]
Justification: The abstract and introduction explicitly state the paper's main contributions,
which supported by the MF-LLM framework ($ 3 and experimental results ($
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or
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It is fine to include aspirational goals as motivation as long it is clear that these goals are not attained by the paper.
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Question:
Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
We provide a further discussion of experimental findings and limitations in Appendix [
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The authors encouraged to create separate "Limitations" section in their paper.
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The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairess.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
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Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
33

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Answer: [NA]
Justification:
This paper is not theoretical paper. The derivation of the loss function related
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Justification: The paper includes all necessary information for reproduction, including the algorithm pipeline [ the use of pre-trained large language models subsection 4.3 parameter
configurations Appendix A, and evaluation approaches subseection
(suooacctssubbbcttiio F33
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Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution is specific model and empirical evaluation, it may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access the model. In general. releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how replicate the results, access a hosted model (e.g.. in the of large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
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5. Open access to data and code
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39


Reviews:
[{"review_id": "7FMc2DZgMV", "reviewer": "Reviewer_f92d", "summary": "This paper introduces a framework to integrate mean field theory with LLMs for simulating population decision-making dynamics,. The authors develop IB-Tune, a  fine-tuning algorithm inspired by Information Bottleneck principles that optimizes both a mean field model and a policy model to generate realistic individual decisions. Evaluated on ~4,500 real-world events from the WEIBO corpus, MF-LLM reduces KL divergence by 47% compared to baselines and accurately captures population trends across multiple domains and LLM backbones, enabling applications like trend forecasting and intervention planning.", "questions": "- How does the mean field approximation handle scenarios where agent interactions are highly heterogeneous or when certain agents have disproportionate influence on population dynamics?\n- How would you validate MF-LLM's performance on entirely different cultural contexts where social interaction norms differ significantly?\n- How do you address potential bias from using GPT-4o-mini for semantic evaluation? Have you validated these automated assessments against human expert judgments?", "limitations": "The paper's scalability claims are undermined by the absence of computational complexity analysis and testing on truly large populations, with simulations extending only 900 timesteps and acknowledged compounding errors over time. While positioned as achieving \"quantitative alignment with real-world data,\" the framework is validated exclusively on WEIBO corpus discussions, raising questions about generalizability to other forms of collective decision-making like voting or market behavior that motivated the work. Despite testing across seven domains and four LLM backbones, all evaluation occurs within a single cultural context, and the mean field approximation may oversimplify real social dynamics by failing to capture heterogeneous interaction patterns and varying influence weights between agent types that are crucial in authentic social systems.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths\n- The integration of mean field theory with LLMs is  theoretically grounded, providing a principled approach to modeling population dynamics while maintaining computational scalability.\nThe paper demonstrates robust performance across multiple dimensions - 7 domains, 4 LLM backbones, 8 semantic dimensions, and ~4,500 real-world events, with consistent 47% improvement in KL divergence over baselines.\nWeakness\n- Evaluation is only restricted to the WEIBO corpus and thus very specific to the context within that corpus.\nAlthough", "was_revised": true, "final_justification": "The authors' rebuttal with extensive additional experiments has resolved my primary concerns about cultural generalizability (demonstrated through English Twitter datasets and market behavior simulation), scalability (empirical O(N) scaling up to 4000 agents), and evaluation methodology (91.25% human expert agreement validation). The controlled experiments on heterogeneous interactions and disproportionate influence effectively address the mean field approximation concerns, while cross-cultural validation demonstrates robust performance beyond the original WEIBO corpus.", "rebuttal": "Dear Reviewer f92d,  \n\nThank you for your detailed review and valuable feedback, and for recognizing MF‑LLM as a *“theoretically grounded”* approach with *“robust performance.”*\n\nDuring the rebuttal, we conducted extensive experiments and analyses to address your comments:\n\n- **Added experiments** on culturally diverse English datasets (Twitter) and market behavior simulation, confirming MF-LLM’s generalization cross different cultural contexts.  \n- **Provided mechanism explanation, empirical results** (Appendix C, Fig.8) and **new case studies**, showing MF-LLM handles heterogeneous interactions and disproportionate influence.  \n- **Added comparison** of GPT‑4o‑mini with human experts, GPT-4, GPT-4o, GPT-3.5, confirming it is the best balance of accuracy, cost, and speed for semantic evaluation.  \n- **Added computational complexity analysis** (O(N²)→O(N)) and **long-horizon experiments** (Twitter, 2000 steps), demonstrating scalability.  \n\n**Here are our detailed responses to each of your questions and suggestions. We have made every effort, with the utmost sincerity, to address every one of your concerns.** \n\n---\n\n\n\n> **Weakness & Q2: \"How would you validate MF-LLM's performance on entirely different cultural contexts where social interaction norms differ significantly?\"**\n\n**Answer:** Thank you for this important question. MF-LLM is inherently culture-agnostic, with no assumptions about language or cultural background. To validate its generalization ability, we added experiments on **culturally diverse English datasets** without domain-specific fine-tuning.\n\n**1. Famous Keyword Twitter Replies Dataset** (Kaggle)\n\n This dataset covers globally relevant topics (COVID, Vaccine, NFT, TikTok, WorldCup, etc.). Using Qwen2-1.5B-Instruct, MF-LLM consistently outperforms baselines:\n\n| Method     | KL↓        | WD↓        | DTW↓       | NLL↓       | Macro F1↑  | Micro F1↑  |\n| - | - | - | - | - | - | - |\n| State      | 0.8696     | **0.0673** | 0.1700     | 4.2121     | 0.4977     | **0.8241** |\n| Recent     | 1.5061     | 0.0922     | 0.2206     | 4.1053     | 0.4471     | 0.7661     |\n| Popular    | 1.0059     | 0.0725     | 0.1553     | 4.0697     | 0.4864     | 0.8047     |\n| **MF-LLM** | **0.6883** | 0.0744     | **0.1587** | **3.9748** | **0.4989** | 0.8093     |\n\n**2. Market Behavior Simulation**\n\n To assess MF-LLM’s generalization to market behavior, we refer to *TwinMarket* [1], which uses real-world transaction data from Chinese social platforms (Xueqiu, Guba), and *ElectionSim* [2], which uses Twitter data on elections. However, neither releases datasets, making direct comparison infeasible.\n\nFollowing their approach of using social media data to simulate collective decisions, we use Bitcoin-related tweet–reply data from Twitter to simulate dynamic **bullish/bearish sentiment** at the population level. Once again, MF-LLM achieves superior alignment:\n\n| Method     | KL↓        | WD↓        | DTW↓       | NLL↓       | Macro F1↑  | Micro F1↑  |\n| - | - | - | - | - | - | - |\n| State      | 1.2304     | 0.0854     | 0.4505     | 4.4320     | 0.4723     | 0.6721     |\n| Recent     | 2.0641     | **0.0800** | 0.4730     | 4.3438     | 0.4550     | 0.6573     |\n| Popular    | 1.4394     | 0.0853     | 0.3930     | 4.2537     | 0.4834     | 0.6920     |\n| **MF-LLM** | **0.9316** | 0.0915     | **0.2364** | **4.1485** | **0.5025** | **0.7741** |\n\nWe hope these additional results address your concern by showing that MF-LLM generalizes across languages and cultural settings. These findings will be incorporated into the revised paper.\n\n[1] TwinMarket: A Scalable Behavioral and Social Simulation for Financial Markets.\n\n[2] ElectionSim: Massive Population Election Simulation Powered by LLM Agents.\n\n\n\n\n\n---\n\n\n\n> **Q1: \"How does the mean field approximation handle scenarios where agent interactions are highly heterogeneous or when certain agents have disproportionate influence on population dynamics?\"** \n\n**Answer:** First, we clarify that **MF-LLM is evaluated on real-world data**, which naturally involves abundant heterogeneous agent interactions and cases of disproportionate influence. Below, we address this from both a **mechanism** and **empirical evidence** perspective:\n\n**1. Mechanism**: MF-LLM places no assumptions on agent homogeneity. At each step, the policy model generates personalized actions, while the **mean field model (an LLM) infers how these actions affect collective dynamics and outputs the key population signals (=mean field) that influences future individual decisions.** Unlike prior methods that manually encode interaction heterogeneity or assign fixed influence weights, our approach automatically generates these effects at each step.\n\n**2. Empirical**: **Experimental results in Appendix C and Fig. 8 (4) have already demonstrated disproportionate influence**: when the famous Chinese sports commentator \"@Huang Jianxiang\" was referenced to verify the truth, the population signal shifted toward skepticism, leading to reduced rumor spread.\n\n**3. We added two sets of controlled experiments** to demonstrate that the mean field model can capture heterogeneous interactions and disproportionate influence without any manual weighting or structural assumptions:\n\n**(1) Heterogeneous Interactions**\n\nWe compare the effects of two different actions taken by the same **high-influence user**.\n\n- **State**: A non-verified user with high influence and many friends.\n\n- **Previous Mean Field**:\n\n  `Most users express opposition and criticism toward the event, regarding it as unfair competition.`\n\n- **Action A**: `\"Repost\"`\n\n- **Action B**: `\"Looking forward to the truth!\"`\n\n\n\nThe mean field model takes the individual’s state and action as input and updates the mean field accordingly:\n\n- **After Action A**:\n\n  `\"Most users are criticizing the event rather than seeking factual verification.\"`\n\n- **After Action B**:\n\n  `\"Users call for an investigation to uncover the cause. … Many suspect that this might be a genuine news report.\"`\n\nDue to rebuttal length limits, only excerpts of updated mean field are shown here; the full version will appear in the revised paper.\n\n**(2) Disproportionate Influence**\n\n\n\nWe compare the effects of the **same action** taken by two users: one with **high** influence and one with **low** influence.\n\n\n\n- **Action**: `\"Looking forward to the truth!\"`\n- **Previous Mean Field**: *(Same as in Case Study 1)*\n\n\n\n- **Agent States**:\n\n- - **High-Influence User**: A non-verified user with high influence and many friends.\n  - **Low-Influence User**: Same description, but with low influence and few friends.\n\n\n\n**Updated Mean Field:**\n\n- After **High-Influence User** acts: `\"Many suspect that this might be a genuine news report.\"`\n\n- After **Low-Influence User** acts: `\"A few users in the comments express a desire to uncover the truth.\"`\n\n---\n\n### \n\n> **Q3: \"How do you address potential bias from using GPT-4o-mini for semantic evaluation? ...\"**\n\n**Answer:** To balance **evaluation cost and speed**, we chose GPT-4o-mini for semantic evaluation. We validated its reliability through **human evaluation** on 100 samples by domain experts (social science scholars, junior faculty, and senior PhD students), comparing GPT-4o-mini’s outputs with human judgments. We also tested other LLMs (GPT-3.5-Turbo, GPT-4o, GPT-4). Summary:\n\n| Metric|GPT-4o-mini| GPT-4   | GPT-3.5-Turbo | GPT-4|\n| - | - | - | - | - |\n| Agreement w/ Human (%) | 91.25 | 89.38   | 79.13 | **94.13** |\n| Price ($/M tokens)| **0.15/0.60** | 2.5/10  | 0.5/1.5 | 30/60   |\n| Speed (s/sample)| 1.25 | 0.96    | **0.83** | 4.02|\n\nSince semantic evaluation is not a challenging task for today’s advanced LLMs, **GPT-4o-mini balances accuracy and cost effectively**, offering higher human alignment than GPT-3.5-Turbo at a much lower cost. With an optimized prompt (Appendix D.3), GPT-4o-mini provides the best cost-effectiveness, **especially considering its low price**, making it ideal for large-scale simulations. We will include full results in the revised paper.\n\n---\n\n\n\n> **Limitation: \"computational complexity analysis and testing on truly large populations.\"**\n\n**Answer:** \n\n**1. Computational Complexity Analysis**: \n\nMF-LLM aims to capture dynamic agent interactions, which are fundamental to the formation of collective behavior. **Modeling all agent–agent pairwise interactions requires O(N²) complexity, while MF-LLM reduces this to O(N) linear complexity.** Specifically, the policy model generates one personalized action per agent, leading to O(N) LLM inferences. The mean field model updates the population signal once per batch of K agents, resulting in O(N/K) mean field inferences. \n\nOverall, MF-LLM reduces total LLM inference complexity to O(N) while still modeling agent interactions and producing population-level dynamics. This **contrasts with baselines** that either ignore agent interactions entirely or approximate them through manual prompt engineering without dynamic modeling.\n\n**2. Testing on Large Populations**: \n\nIn the original paper, the Weibo dataset naturally limited simulation horizons to ~900 steps due to the discussion length of real events. To further validate scalability, we extend evaluation to the English Twitter dataset with long-horizon discussions (up to 2,000 steps). **Results show that while error increases slightly with horizon, MF-LLM consistently outperforms baselines.**\n\n| Method | KL↓ | WD↓  | DTW↓ | NLL↓  | Macro F1↑  | Micro F1↑  |\n| - | - | - | - | - | - | - |\n| State| 1.1701 | 0.0714 | 0.1110  | 4.2050 | **0.3773** | 0.8456   |\n| Recent| 1.8701 | 0.0685 | 0.1178 | 4.1000  | 0.3210     | 0.8533 |\n| Popular | 1.4291 | 0.0722 | **0.0937** | 4.0863  | 0.3475     | 0.8438     |\n| **MF-LLM** | **1.1053** | **0.0685** | 0.0965 | **4.0236** | 0.3569     | **0.8537** |\n\n---\n\n**We hope these clarifications and new results will encourage you to reconsider your score. If you have any further questions, we are happy to discuss them.**"}, {"review_id": "IhusZ9bjnW", "reviewer": "Reviewer_GZm3", "summary": "This paper introduces the Mean-Field LLM (MF-LLM), a novel framework for simulating population-level decision dynamics. The core idea is to integrate mean-field theory into a large language model (LLM)-based agent simulation. This approach models the bidirectional feedback loop where individual decisions are influenced by an aggregate population signal (the \"mean field\"), and these decisions, in turn, update that signal. This replaces computationally expensive agent-to-agent interactions with a more scalable agent-to-population model. To improve the simulation's alignment with real-world data, the authors propose IB-Tune, a fine-tuning algorithm inspired by the Information Bottleneck principle. IB-Tune optimizes the LLM modules to generate population signals that are predictive of future actions while filtering out redundant historical information. The framework is evaluated on a large real-world social media dataset, demonstrating significant improvements in quantitative accuracy and forecasting capabilities compared to existing methods.", "questions": "The mean-field approximation is key to scalability. Could you elaborate on the types of social phenomena or network structures where this approximation might break down?\n\nThe finding that smaller LLMs outperform larger ones due to response homogeneity is interesting. Have you experimented with decoding parameters for the larger models (e.g., increasing temperature, top-p sampling) to see if encouraging more diversity could improve their performance in your framework?\n\nThe IB-Tune objective in Equation 7 includes a hyperparameter β, which balances compression and prediction. How sensitive is the model's performance to this parameter? Could you provide some details on how it was chosen and its impact on the learning process?\n\nThe framework uses a \"warm-up\" phase with real data before the simulation phase begins. How does the duration of this warm-up affect the long-term fidelity of the simulation? Is there a noticeable \"drift\" from the real-world trajectory, and does it correlate with the length of the warm-up?", "limitations": "The authors have clearly acknowledged and discussed the limitations of their work. In Section 5 and Appendix C, they identify important challenges. One issue is the accumulation of small errors over long simulation periods, which can cause the overall behavior of the system to drift away from realistic patterns. They also recognize that the current framework requires manual input of external signals, rather than detecting these exogenous events automatically. This limits the framework's usefulness in real-time or fully automated forecasting settings. In addition, the authors offer a thoughtful explanation for the surprising result that smaller LLMs sometimes perform better than larger ones. They connect this to the idea that smaller models may produce more diverse behaviors, which is important for simulating complex social systems. In general, the discussion is honest and clear, and it provides useful directions for future work.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\nThis paper presents a new and important idea by combining mean-field theory with large language model (LLM) based social simulation. This is a big improvement over older methods, which often use simple prompts or fine-tuning methods that do not consider how agents interact with each other. The proposed method, called MF-LLM, focuses on the feedback loop between individual agents and the whole population. This helps to understand how group behaviors appear and change over time. Solving this problem poses a challenge in computational social science, and MF-LLM provides a clear and scalable solution. The method could be useful in real-world applications such as predicting public opinion and planning social interventions.\nThe technical design is strong and well-structured. MF-LLM includes two LLM modules that work in turns: a policy model and a mean-field model. This structure is easy to understand and helps to capture how individuals influence the group and how the group influences individuals. Another key part is the IB-Tune algorithm, which uses the Information Bottleneck principle. It fine-tunes the models in a data-driven way, focusing on keeping only the most important parts of the population state that help predict future actions. This is a more advanced and effective method for aligning data compared to standard fine-tuning.\nThe paper is very clear and well organized. Figure 1 gives a helpful overview of how the full system works. The authors clearly explain the three main challenges they focus on: aligning data, modeling interaction dynamics, and scaling the method. They also show how their method addresses each of these problems. The appendices provide extra details such as prompt templates, hyperparameters, and additional results, which help readers better understand the work and reproduce the experiments.\nThe experiments are complete and convincing. The authors use a large and real-world dataset called WEIBO, which is better than using only simple or artificial data. They compare their method with strong baseline models and utilize a wide range of evaluation metrics, including KL Divergence, Wasserstein distance, Dynamic Time Warping, and F1 scores. These metrics help measure how well the model works in both time and meaning. The results are interesting. The model reduces KL Divergence by 47% compared to versions that do not use the mean-field module, and it performs well across seven different domains and four LLM backbones. The ablation study in Table 2 also shows clearly that both the mean-field module and the IB-Tune algorithm are very important. When the mean-field module is removed, performance drops by as much as 118%\n\nWeaknesses\nFirst, the mean-field approximation, although necessary to make the model scalable, reduces all interactions to a simple relationship between each agent and the overall population. This approach may miss more complex and local interactions, such as the spread of influence within small, close-knit groups or the impact of specific individuals who are highly influential. These types of local behaviors are important in many real-world social systems and may not be fully captured by the current model.\n\nSecond, the authors show that adding external signals, called exogenous events, can help improve the accuracy of the simulation. However, this process is still done manually. For real-world forecasting tasks, this is a major limitation. In many real situations, external events such as news, policy changes, or viral content happen suddenly, and the system needs to detect and include them automatically. Without this ability, the model may miss important changes in social dynamics.\n\nLastly, the paper presents an interesting and unexpected result: smaller LLMs sometimes perform better than larger ones. The authors suggest that this may be because larger models tend to produce more similar and less diverse responses. While this explanation makes sense, it would be more convincing if the authors included a deeper analysis. For example, testing different decoding methods such as increasing the temperature in larger models could show whether the lack of diversity is due to model size or decoding choices. More evidence would help support this claim and provide useful guidance for model selection.", "was_revised": true, "final_justification": "This paper combines mean-field theory with LLM-based simulation to create a scalable alternative to agent-to-agent interaction. The method is technically strong, and the IB-Tune algorithm offers a clear and effective way to align simulations with real-world data. The experiments use a large, real-world dataset and include strong baselines, many evaluation metrics, and clear ablation studies showing the importance of each part of the method. The paper is well written, reproducible, and openly discusses its limitations. Although automatic detection of external events and deeper study of the performance difference between small and large LLMs are still missing, the overall strengths are much greater than these issues. I recommend acceptance.", "rebuttal": "**Dear Reviewer GZm3**,\n\nThank you for your detailed and constructive review, and for recognizing our work with a *“strong and well‑structured” technical design, “complete and convincing” experiments, and a “clear and well‑organized” paper.*\n\nDuring the rebuttal, we have made every effort to address your comments through additional experiments, clarifications, and expanded analysis:\n\n- **Added case studies** of highly influential individuals (Appendix C, Fig. 8‑4) and small, close‑knit groups, demonstrating that MF‑LLM effectively captures complex interactions without manual design.\n- **Added new decoding experiments** (varying temperature and top‑p) and highlighted Appendix G outputs showing lexical homogeneity in larger LLMs.\n- **Conducted sensitivity analysis** over multiple β values, showing the relationship between β and loss values.\n- **Demonstrated that** longer warm‑up phases improve long‑term simulation fidelity (Appendix C, Fig. 5a).\n\n**Below, we provide detailed responses to each of your questions, with the utmost sincerity, to address every concern.**\n\n\n\n---\n\n\n\n> **W1 & Q1: \"Mean-Field Approximation ... may miss more complex and local interactions\"?**\n\n**Answer:** We respectfully clarify that MF‑LLM **does not** “miss more complex and local interactions” or “break down” in such cases. MF‑LLM is evaluated on real‑world data, which naturally includes \"small, close‑knit groups\" and \"highly influential individuals\". We address this via mechanism and empirical evidence: \n\n**1. Mechanism**  \n\nIn MF‑LLM, the **policy model** maps population signals to individual actions, while the **mean field model** updates the population signal from new actions. The pathway\n$$a_A→m_{t+1}→a_B$$\nrepresents an indirect but generalizable interaction between any pair of agents. Unlike prior work with fixed influence weights, MF‑LLM **infers and updates interaction effects dynamically from online data**, enabling robust modeling even in unseen structures.\n\n**2. Empirical Evidence**  \n\n**(a) Highly influential individuals**  \n**Appendix C and Fig. 8(4) show** \"impact of highly influential individuals\": when the famous Chinese sports commentator \"@Huang Jianxiang\" was referenced to verify the truth, the population signal shifted toward skepticism, leading to reduced rumor spread.\n\n**(b) Small, close‑knit groups**  \nIn an entertainment discussion:  \n\n- **User A**: `\"Taylor Swift will hold a concert!\" ` \n- **User B**: `\"The city marathon route will be adjusted next month.\"`\n\n**Updated Mean Field (after A+B):**  \n`\"Population sentiment surges around the concert... marathon news draws moderate interest from runners.\"`\n\n**Policy model responses under same mean field:**  \n\n- **Idol Fan User**: `\"Can’t believe it! Already organizing a group to buy tickets and cheer!\"  `\n- **Marathon Enthusiast**: `\"Good to know about the route change—I’ll adjust my training.\"`\n\nThis shows MF‑LLM captures topic‑specific shifts via the mean field and generates heterogeneous actions via the policy model—faithfully modeling \"close‑knit group\" dynamics from real data.\n\n\n\n\n\n---\n\n> **W2: Although the authors show that adding external signals improves simulation accuracy, how does the model handle the automatic detection in real-world scenarios?**\n\n**Answer:** We appreciate the reviewer’s recognition of our “honest and clear” limitation discussion. **Appendix C & Fig. 8 shows that** adding external signals preserves simulation fidelity, demonstrating MF‑LLM’s robustness. While automatic detection is beyond our current simulation-focused scope, we agree it is important for real-world forecasting and identify it as a future direction.\n\n\n\n\n---\n\n> **W3 & Q2: Can you provide more evidence for why smaller LLMs outperform larger ones, such as by exploring decoding parameters?**\n\n**Answer:** Regarding this \"interesting and unexpected result\", **we discussed it in Appendix G and presented a comparison of model outputs** (pp. 27–28 for larger LLMs vs. pp. 25–26 for smaller LLMs).  The larger LLMs’ generations exhibit clear lexical homogeneity—frequent repetition of similar phrasing and syntactic structures (highlighted by color)—whereas the smaller LLMs, under the same simulation context, show no such degree of lexical uniformity.\n\nFurther, **we conducted additional experiments varying decoding parameters for the larger models**. The following table presents the results for:\n\n1. **Higher temperature** (temp = 1.2, top‑p = 0.85)\n2. **Higher top‑p** (temp = 0.8, top‑p = 0.95)\n\nFor each metric, we report the absolute value together with its relative change (%) compared to the original decoding setup in the submitted paper (temperature = 0.8, top‑p = 0.85).\n\n*7B = Qwen2‑7B‑Instruct*\n\n| Model       |    Temp |    Top_p | KL↓               | WD↓              | DTW↓             | MacroF1↑         | MicroF1↑         | NLL↓             |\n| :---------- | ------: | -------: | :---------------- | :--------------- | :--------------- | :--------------- | :--------------- | :--------------- |\n| 7B          |     0.8 |     0.85 | 0.915             | 0.098            | 0.332            | 0.388            | 0.705            | 3.994            |\n| 7B          | **1.2** |     0.85 | **0.814(-11.0%)** | **0.098(-0.6%)** | **0.328(-1.2%)** | **0.389(+0.4%)** | **0.715(+1.5%)** | **4.044(+1.3%)** |\n| 7B          |     0.8 | **0.95** | 1.960(+114.3%)    | 0.116(+18.3%)    | 0.413(+24.6%)    | 0.362(-6.7%)     | 0.670(-5.0%)     | 4.076(+2.0%)     |\n| GPT‑4o‑mini |     0.8 |     0.85 | 0.990             | 0.106            | 0.357            | 0.380            | 0.687            | -                |\n| GPT‑4o‑mini | **1.2** |     0.85 | 2.673(+169.9%)    | 0.128(+20.6%)    | 0.467(+30.9%)    | 0.337(-11.3%)    | 0.636(-7.4%)     | -                |\n| GPT‑4o‑mini |     0.8 | **0.95** | 2.724(+175.1%)    | 0.132(+23.6%)    | 0.477(+33.7%)    | 0.337(-11.3%)    | 0.633(-7.9%)     | -                |\n\nThese results show that increasing diversity through **higher temperature or top‑p does not necessarily improve simulation performance**. For example, Qwen2‑7B‑Instruct showed only a marginal improvement when increasing temperature, but significant degradation at top‑p = 0.95 (KL more than doubled). Similarly, GPT‑4o‑mini exhibited worse performance when either temperature or top‑p was increased.\n\nDue to rebuttal time constraints, we report the additional results above. More extensive experiments on “increasing diversity” will be included in the revised paper for reference.\n\n---\n\n\n\n> **Q3: How sensitive is the model's performance to the β in the IB-Tune objective?** \n\n**Answer:** We thank the reviewer for raising the question regarding the sensitivity of hyperparameter β in balancing compression and prediction.\n\nIn our experiments, **we tested β values of 1.2, 1.6, and 2.0** and observed that the predictive term **$- \\sum_{i=1}^{N_t} \\log \\pi(a_t^{i} \\mid s_t^i, m_t)$** (denoted as $L_2$ hereafter) in Equation 7 shows a qualitative negative correlation with β. The following table summarizes the average $L_2$ over the final 100 steps of training:\n\n| **β** | **$L_2$** |\n| ----- | --------- |\n| 2.0   | 3.563     |\n| 1.6   | 3.978     |\n| 1.2   | 3.987     |\n\nAs shown, a lower $L_2$ indicates better predictive performance. Based on these qualitative observations, we selected **β = 2** for the final model.\n\nWe have already begun testing larger β values in additional experiments. However, due to the extensive fine-tuning time required for LLMs, we aim to obtain results before the discussion period ends. We will include these findings in the revised version of the paper.\n\n\n\n---\n\n\n\n> **Q4: How does the warm-up duration affect the long-term fidelity of the simulation?** \n\n**Answer:** We thank the reviewer for the insightful question regarding the warm‑up phase.\n\nAs discussed in **Appendix C** and shown in **Fig. 5(a)**, we evaluated simulations starting at different warm‑up lengths (20, 34, 43, 70 steps). **Longer warm‑up phases consistently yielded smaller deviation from the real‑world trajectory.** The figure also marked the prediction and real values, directly illustrating this improvement. This benefit arose because a longer warm‑up provided the simulation with a richer and more accurate prior, reducing early‑stage uncertainty.\n\n\n---\n\n**We hope these clarifications and new results will address your concerns. If you have any further questions, we are happy to discuss them.**"}, {"review_id": "ObbHvxIPnP", "reviewer": "Reviewer_U3Se", "summary": "This is a work on simulation of agent-based models of human social interaction using large language model agents.  The focus is on modeling social networks and phenomena such as the spread of rumors and collective decision making. The present work builds on the framework of Refs. [32] and [43], it studies the same task of using a stylized social network which generates a time sequence of \"tweets\" to model the Weibo corpus (Ref [24]), and it compares with previous results.  Two innovations are claimed.  The first is to use an LLM (the \"mean field\" agent) to summarize the vector of states and actions for all of the agents to produce a \"mean field\" summary text.  My understanding is that direct interactions between the agents (the \"tweets\") are replaced by the summary text.  The second innovation is to introduce a loss based on information bottleneck to train the mean field agent, balancing effectiveness of the summary in making subsequent predictions against compression of the information being summarized.  The results are compared with several ablations (leave out specialized training, leave out the summary) and the new method achieves a better fit.", "questions": "1. Given that the mean field summary depends on the states of all of the agents (equation 1), and considering that the actual social systems being modeled as well as the baselines do not (as I understand) include direct communication of the agents' states, how do we know whether the reported improvements in predictive fit might be because of this new and unrealistic form of interaction ?\n\n2. The paper includes examples of agent comments, but I didn't see any examples of mean field summaries.  This would help answer (1).\n\n2. Is there any estimate of the uncertainty and statistical significance of the results in tables 1,2 ?", "limitations": "I think it is adequate.  The study is methodological in nature so possible negative impact would be speculative.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths: adding the summary is an interesting idea which is probably new in this context and certainly has not been much explored.\n\nWeaknesses: I found the description of the simulation difficult to read and understand.  Basic attributes such as the connectivity of the network (are all agents connected pairwise or not?) are not clearly explained.  Especially, it was not clear whether the summary is used to *replace* agent-agent interactions (as stated on p. 2) or *in addition* to the other interactions listed under \"baselines\" on p. 6.   I guess that it is used to replace, but this seems like a very drastic change in the model compared to the previous work.  One also wonders whether the improvements in prediction are coming because the summary contains information about the agents' internal states which is not being communicated either in the real world social interactions being modeled or in the baselines.  In this case it would be a sort of contamination or \"cheating\" which would make the results less interesting.", "was_revised": true, "final_justification": "The authors responded to my comments and questions adequately.", "rebuttal": "**Dear Reviewer U3Se,**\n\nThank you very much for taking the time to review MF‑LLM and for your constructive feedback, as well as for recognizing the “interesting idea” and “better fit.”\n\nDuring the rebuttal period, we have made every effort to address your concerns through targeted clarifications, additional experiments, and concrete examples:\n\n- **Clarified the simulation mechanism and connectivity**.\n- **Added new case studies** on *Different Interactions* and *Different Users*.\n- **Provided explicit mean field summaries**, showing agent actions and corresponding updated mean field content.\n- **Demonstrated that the states in Eq. (1) are observable from real‑world data**, not unobservable “internal states.”\n- **Conducted control experiments by adding state information to baselines**, with MF‑LLM still outperforming all variants.\n- **Reported statistical significance** with mean ± standard deviation over multiple runs.\n\nBelow, we provide detailed responses to each of your questions, with the utmost sincerity, to fully address every concern.\n\n---\n\n\n\n> **W1 & Q2: Is the mean field summary used to replace agent-agent interactions or in addition to the interactions listed under 'baselines'? Could you provide examples of mean field summaries?**\n\n**Answer:** We thank the reviewer for the insightful comments. We will clarify the simulation description in the revised paper.\n\n**1. Mechanism:**\n\nMany existing works model the connectivity of the agent network, where each edge weight reflects the strength of influence between two agents. **While such network modeling is reasonable, manually specifying these edge weights is often inaccurate and may overlook important interaction patterns in unseen scenarios.**\n\nMF‑LLM replaces fixed, handcrafted connectivity with a **data-driven mechanism**:\n\n- The **policy model** generates individual actions based on the agent’s state and the current population signal.\n- The **mean field model** updates the population signal using these newly generated actions\n\nThis creates an indirect but generalizable interaction pathway:\n$$a_A→m_{t+1}→a_B$$\nwhere agent A’s action affects agent B via the updated population signal. Crucially, interaction strengths are **inferred and updated dynamically at each step from online data**, without any manually set network weights.\n\nThe baselines represent alternative agent interaction strategies:\n\n- **Recent** connects agents to the most recent actions.\n- **Popular** connects agents to the most popular actions.\n\nThese fixed heuristics may miss subtle interactions in new contexts. In contrast, MF-LLM allows interaction patterns to emerge adaptively from the data.\n\n\n **2. Experimental Evidence:**\n\nOur MF-LLM **do not** force the mean field model to attend to or ignore specific agents. It evaluates all available information to infer interaction effects. **The following two case studies illustrate this dynamic modeling, while also showcasing the content of the mean field**.\n\n**(1) Influence of Different Interactions**\n\nIn a *rumor propagation* scenario, we compare the effects of two different actions taken by the same **high-influence user**.\n\n- **State**: A user with high influence and many friends.\n\n- **Previous Mean Field**:\n\n  `Most users express opposition and criticism toward the event, regarding it as unfair competition.`\n\n- **Action A**: `\"Repost\"`\n\n- **Action B**: `\"Looking forward to the truth!\"`\n\n\n\nThe mean field model takes the individual’s state and action as input and **updates the mean field** accordingly:\n\n**Updated Mean field:**\n\n- **After Action A**:\n\n  `\"Most users are criticizing the event rather than seeking factual verification.\"`\n\n- **After Action B**:\n\n  `\"Users call for an investigation to uncover the cause. … Many suspect that this might be a genuine news report.\"`\n\nDue to rebuttal length limits, only excerpts of updated mean field are shown here; the full version will appear in the revised paper.\n\n\n\n**(2) Influence of Different Users**\n\nIn the *rumor propagation* scenario, we compare the effects of the **same action** taken by two users: one with **high** influence and one with **low** influence.\n\n\n\n- **Action**: `\"Looking forward to the truth!\"`\n- **Previous Mean Field**: *(Same as in Case Study 1)*\n\n\n\n- **Agent States**:\n\n  - **High-Influence User**: A user with high influence and many friends.\n  - **Low-Influence User**: Same description, but with low influence and few friends.\n\n**Updated Mean Field:**\n\n- After **High-Influence User** acts: `\"Many suspect that this might be a genuine news report.\"`\n\n- After **Low-Influence User** acts: `\"A few users in the comments express a desire to uncover the truth.\"`\n\n\n\n**Conclusion: MF‑LLM thus provides an indirect yet generalizable mechanism for modeling agent interactions and influence, without manually specifying network weights.**\n\n---\n\n\n\n> **W2 & Q1: \"How do we know whether the reported improvements in predictive fit might be because of this new and unrealistic form of interaction?\"**\n\n**Answer:** We thank the reviewer for raising this concern.\n\n1. **Observed states in Equation 1.** The “state” in Eq. (1) corresponds to **information observable in the real-world social interactions** being modeled. These states include attributes such as `location, description, gender, friend/follower counts, activity level, and verification status`. The *User State Construction* prompt template is shown in **Appendix D.4 (p. 20)** of the submitted paper. No hidden or unobservable “internal states” are introduced.\n\n\n2. **The mean field model processes these observable states, which is fully reasonable**. As illustrated in above Case Study 2 (*Influence of Different Users*), even when different users perform the same action, their states lead to different downstream effects on subsequent users. Processing these observable states enables the mean field model to analyze the corresponding influence of actions more accurately.\n\n\n3. **We conducted a control experiment by adding user state information to the baselines (Recent, Popular).** Recent (+state) improves, while Popular (+state) drops in performance. **MF-LLM still outperforms these enhanced baselines,** confirming that the improvement comes from its interaction modeling. Baselines ignoring user identity fail to capture heterogeneous agent influence, highlighting MF-LLM’s advantage.\n\n| **Model**  | **KL↓**   | **WD↓** | **DTW↓** | **Macro F1↑** | **Micro F1↑** |\n| - | - | - | - | - | - |\n| Recent (original)| 1.277±0.670| 0.077±0.008 | 0.202±0.060 | 0.441±0.032   | 0.799±0.026   |\n| Recent (+ state) | **0.9038±0.495** | **0.0664±0.012** | **0.1674±0.064** | **0.4667±0.024** | **0.8273±0.030** |\n| Popular (original)| 1.288±0.579 | 0.080±0.007| 0.199±0.055 | 0.435±0.032   | 0.792±0.025   |\n| Popular (+ state)| 1.4672±0.687   | 0.0821±0.017 | 0.2087±0.073   | 0.4358±0.023  | 0.7861±0.037  |\n| MF‑LLM  | 0.645±0.260    | 0.065±0.007 | 0.152±0.020 | 0.486±0.023   | 0.839±0.009 |\n| MF‑LLM IB‑Tune  | **0.512±0.238**| **0.062±0.007** | **0.138±0.025**| **0.495±0.024**| **0.846±0.009**|\n\n\n---\n\n> **Q3: \"Is there any estimate of the uncertainty and statistical significance of the results in tables 1,2?\"**\n\n**Answer:** We report **mean ± standard deviation and p-values** for Tables 1 and 2. The small standard deviations and consistent performance of MF‑LLM indicate statistical significance and stability.\n\nDue to rebuttal length limits, we only present the main results here; the full version will be included in the revised version.\n\n**Tables 1 - mean ± std:**\n\n| **Model** | **KL↓**   | **WD↓** | **DTW↓** |\n| - | - | - | - |\n| GPT-4o-mini | | | | | | \n| State | 4.172±2.618 | 0.127±0.022 | 0.420±0.092 |\n| Recent | 6.728±1.525 | 0.145±0.016 | 0.485±0.072 |\n| Popular | 5.591±2.298 | 0.128±0.017 | 0.447±0.096 | \n| MF-LLM | **1.647±0.702** | **0.100±0.017** | **0.329±0.118** | \n| DeepSeek-R1-32B |||| \n| State | 1.946±0.981 | 0.110±0.016 | 0.349±0.074 | \n| Recent | 6.435±1.226 | 0.141±0.018 | 0.495±0.105 |\n| Popular | 3.812±1.427 | 0.113±0.011 | 0.385±0.110 | \n| MF-LLM | **1.280±0.831** | **0.088±0.015** | **0.307±0.101** | \n| Qwen2-7B-Instruct | | | | \n| State | 1.153±0.667 | 0.085±0.012 | 0.239±0.077 |\n| Recent | 1.346±0.184 | 0.081±0.010 | 0.218±0.059 | \n| Popular | 1.066±0.378 | 0.076±0.012 | 0.199±0.062 |\n| MF-LLM | **1.010±0.354** | **0.075±0.014** | **0.198±0.068** | \n| Qwen2-1.5B-Instruct | | | |  \n| State | 0.966±0.491 | 0.068±0.009 | 0.166±0.046 | \n| Recent | 1.277±0.670 | 0.077±0.008 | 0.202±0.060 | \n| Popular | 1.288±0.579 | 0.080±0.007 | 0.199±0.055 |\n| MF-LLM | 0.645±0.260 | 0.065±0.007 | 0.152±0.020 |\n| MF-LLM IB-Tune | **0.512±0.238** | **0.062±0.007** | **0.138±0.025** | \n\nDue to character limits, we present the KL Divergence statistical significance for the Qwen2-1.5B-Instruct model. The following p-values highlight **significant differences** between algorithms:\n\n| **Algorithm Pair**| **p-value**|\n| -- | - |\n| Popular vs MF-LLM| **0.0095** (*) |\n| Popular vs Recent| 0.9718|\n| Popular vs State | 0.2236|\n| Popular vs MF-LLM IB-Tune | **0.0008** (*) |\n| MF-LLM vs Recent | **0.0132** (*) |\n| MF-LLM vs State  | 0.1293|\n| MF-LLM vs MF-LLM IB-Tune  | 0.4063|\n| Recent vs State  | 0.2510|\n| Recent vs MF-LLM IB-Tune| **0.0014** (*) |\n| State vs MF-LLM IB-Tune | **0.0179** (*) |\n\n(*) p-values < 0.05 indicate statistically significant differences.\n\n**Tables 2:**\n\n| **Method** | **KL↓** | **WD↓** | **DTW↓** | \n| - | - | - | - | \n| MF-LLM (Ours) | **0.481±0.236** | **0.070±0.018** | **0.158±0.042** | \n| w/o IB-Tune MF|0.531±0.212 | 0.070±0.018 | 0.159±0.045|\n| w/o IB-Tune Policy| 0.588±0.239 | 0.070±0.018 | 0.158±0.048 | \n| w/o IB-Tune|0.617±0.250 | 0.072±0.021 | 0.164±0.045 |\n| SFT (no MF)| 0.753±0.556 | 0.075±0.022 | 0.186±0.074 |\n| Pretrained (no MF) | 1.053±0.760 | 0.079±0.020 | 0.195±0.068 | \n\n---\n\n**We hope these clarifications and new results will encourage you to reconsider your score. If you have any further questions, we are happy to discuss them.**"}, {"review_id": "hRqe4I7y7L", "reviewer": "Reviewer_G3Ud", "summary": "This paper introduces MF-LLM, the first framework to integrate mean-field theory into LLM-based social simulation by iteratively exchanging population-level signals and individual agent decisions to capture coherent collective behavior. To improve alignment with real-world data, it proposes IB-Tune, an Information Bottleneck–inspired fine-tuning method that compresses population history into only those signals most predictive of future actions. Evaluated on a Weibo dataset, MF-LLM reduces KL divergence to human population distributions by 47% over non-mean-field baselines, generalizes across seven domains and four LLM backbones, and supports accurate trend forecasting and intervention planning.", "questions": "See Weaknesses.", "limitations": "See Weaknesses.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n-\tThis paper introduces a novel MF-LLM framework that seamlessly integrates mean-field theory with LLM-based social simulation to capture bidirectional dynamics between population signals and individual decisions.\n-\tExtensive experiments on a large Weibo dataset, across seven domains and four LLM backbones, demonstrate robust performance improvements and scalability.\n-\tA comprehensive analysis—including KL divergence comparisons, trend-forecasting results, and intervention-planning charts—provides clear, interpretable evidence of the framework’s effectiveness.\n\nWeaknesses:\n-\tThe paper claims a general-purpose social simulation framework but is evaluated on only a single Chinese Weibo dataset. As a general method, it should be tested on at least 2–3 diverse datasets. Besides, include at least one English dataset.\n-\tScalability is cited as a main motivation, yet the paper lacks any complexity analysis or detailed experiments on efficiency and scalability.\n-\tThe writing should be improved. For example, the contributions paragraph is overly lengthy and fails to highlight the core innovations succinctly.", "was_revised": true, "final_justification": "The rebuttal is convincing, and I have adjusted my score.", "rebuttal": "**Dear Reviewer G3Ud,**\n\nThank you very much for taking the time to review MF‑LLM and for your valuable feedback, as well as for recognizing our work with *“extensive experiments,” “robust performance improvements,” and “comprehensive analysis providing clear, interpretable evidence of the framework’s effectiveness.”*\n\nDuring the rebuttal, we have made every effort to address your concerns through additional experiments, detailed analysis, and writing refinements:\n\n- **Added experiments on diverse datasets** — including English Twitter replies and Bitcoin sentiment — showing that MF‑LLM generalizes across languages and diverse forms of collective behavior.\n- **Provided scalability analysis** — formally analyzing complexity reduction from O(N²) to O(N) and demonstrating efficiency gains in large‑scale simulation.\n- **Extended long‑horizon evaluation** — adding experiments up to 2,000 steps to confirm MF‑LLM’s robust performance at scale.\n- **Refined the contribution summary** — presenting the core innovations more concisely to directly address the reviewer’s clarity concerns.\n\n**Below, we provide detailed responses to each of your questions, with the utmost sincerity, to address every concern.**\n\n\n\n---\n\n\n\n> **W1: \"The paper claims a general-purpose social simulation framework but is evaluated on only a single Chinese Weibo dataset. As a general method, it should be tested on at least 2–3 diverse datasets. Besides, include at least one English dataset.\"**\n\n**Answer:** Thank you for this important question. MF-LLM is inherently culture-agnostic, with no assumptions about language or cultural background. To validate its generalization ability, we added experiments on **culturally diverse English datasets** without domain-specific fine-tuning.\n\n**(1) Famous Keyword Twitter Replies Dataset** (Kaggle)\n\n This dataset covers globally relevant topics (COVID, Vaccine, NFT, TikTok, WorldCup, etc.). Using Qwen2-1.5B-Instruct, MF-LLM consistently outperforms baselines:\n\n| Method     | KL↓        | WD↓        | DTW↓       | NLL↓       | Macro F1↑  | Micro F1↑  |\n| ---------- | ---------- | ---------- | ---------- | ---------- | ---------- | ---------- |\n| State      | 0.8696     | **0.0673** | 0.1700     | 4.2121     | 0.4977     | **0.8241** |\n| Recent     | 1.5061     | 0.0922     | 0.2206     | 4.1053     | 0.4471     | 0.7661     |\n| Popular    | 1.0059     | 0.0725     | 0.1553     | 4.0697     | 0.4864     | 0.8047     |\n| **MF-LLM** | **0.6883** | 0.0744     | **0.1587** | **3.9748** | **0.4989** | 0.8093     |\n\n**(2) Market Behavior Simulation**\n\n To assess MF-LLM’s generalization to market behavior, we refer to *TwinMarket* [1], which uses real-world transaction data from Chinese social platforms (Xueqiu, Guba), and *ElectionSim* [2], which uses Twitter data on elections. However, neither releases datasets, making direct comparison infeasible.\n\nFollowing their approach of using social media data to simulate collective decisions, we use Bitcoin-related tweet–reply data from Twitter to simulate dynamic **bullish/bearish sentiment** at the population level. Once again, MF-LLM achieves superior alignment:\n\n| Method     | KL↓        | WD↓        | DTW↓       | NLL↓       | Macro F1↑  | Micro F1↑  |\n| ---------- | ---------- | ---------- | ---------- | ---------- | ---------- | ---------- |\n| State      | 1.2304     | 0.0854     | 0.4505     | 4.4320     | 0.4723     | 0.6721     |\n| Recent     | 2.0641     | **0.0800** | 0.4730     | 4.3438     | 0.4550     | 0.6573     |\n| Popular    | 1.4394     | 0.0853     | 0.3930     | 4.2537     | 0.4834     | 0.6920     |\n| **MF-LLM** | **0.9316** | 0.0915     | **0.2364** | **4.1485** | **0.5025** | **0.7741** |\n\n\n\n**We hope these additional results address your concern by showing that MF-LLM generalizes across languages and cultural settings.** These findings will be incorporated into the revised paper.\n\n\n\n[1] TwinMarket: A Scalable Behavioral and Social Simulation for Financial Markets.\n\n[2] ElectionSim: Massive Population Election Simulation Powered by LLM Agents.\n\n---\n\n\n\n> **W2: \"Scalability is cited as a main motivation, yet the paper lacks any complexity analysis or detailed experiments on efficiency and scalability.\"**\n\n**Answer:** \n\n**(1) Computational Complexity Analysis**: \n\nMF-LLM aims to capture dynamic agent interactions, which are fundamental to the formation of collective behavior. **Modeling all agent–agent pairwise interactions requires O(N²) complexity, while MF-LLM reduces this to O(N) linear complexity.** Specifically, the policy model generates one personalized action per agent, leading to O(N) LLM inferences. The mean field model updates the population signal once per batch of K agents, resulting in O(N/K) mean field inferences. \n\nOverall, MF-LLM reduces total LLM inference complexity to O(N) while still modeling agent interactions and producing population-level dynamics. This contrasts with baselines that either ignore agent interactions entirely or approximate them through manual prompt engineering without dynamic modeling.\n\n**(2) Testing on Large Populations**: \n\nIn the original paper, the Weibo dataset naturally limited simulation horizons to ~900 steps due to the discussion length of real events. To further validate scalability, we extend evaluation to the English Twitter dataset with long-horizon discussions (up to 2,000 steps). **Results show that while error increases slightly with horizon, MF-LLM consistently outperforms baselines.**\n\n\n| Method     | KL↓        | WD↓        | DTW↓       | NLL↓       | Macro F1↑  | Micro F1↑  |\n| ---------- | ---------- | ---------- | ---------- | ---------- | ---------- | ---------- |\n| State      | 1.1701     | 0.0714     | 0.1110     | 4.2050     | **0.3773** | 0.8456     |\n| Recent     | 1.8701     | 0.0685     | 0.1178     | 4.1000     | 0.3210     | 0.8533     |\n| Popular    | 1.4291     | 0.0722     | **0.0937** | 4.0863     | 0.3475     | 0.8438     |\n| **MF-LLM** | **1.1053** | **0.0685** | 0.0965     | **4.0236** | 0.3569     | **0.8537** |\n\n---\n\n\n\n> **W3: \"The writing should be improved. For example, the contributions paragraph is overly lengthy and fails to highlight the core innovations succinctly.\"**\n\n**Answer:** We thank the reviewer for the valuable suggestion. **We will further polish the writing in the revised paper**. Below is a more concise summary of the contributions, highlighting the core innovations:\n\n**(1) MF‑LLM framework** — We introduce MF‑LLM, the first framework to integrate mean‑field theory into LLM‑based social simulation, by iteratively updating population signals and individual decisions to capture the evolving trajectories of collective behavior.\n\n**(2) IB‑Tune alignment** — To improve alignment with real‑world data, we introduce IB‑Tune, an Information Bottleneck–inspired fine‑tuning method that compresses population history into only those population signals most predictive of future actions.\n\n**(3) Empirical validation** — MF‑LLM achieves up to **47% lower KL divergence** than baselines, generalizes across **seven domains** and **four LLM backbones**, and supports real‑world forecasting and intervention planning.\n\n---\n\n\n\n**We hope these clarifications and new results will encourage you to reconsider your score. If you have any further questions or would like additional clarifications, we would be very happy to discuss them.**"}]

Author rebuttal:

Meta-review: The authors present a new method for LLM-based social simulation for modeling phenomena like rumor spread and decision making in social networks. The contributions include introducing a “mean-field” LLM agent to summarize agent observables to align with population data, and an objective based the information-bottleneck to train this agent. Empirical results show improvements vs. existing LLM social simulation frameworks. 

All reviewers appreciated the overall approach, describing it as principled, interesting, and novel. They also found the experiments on the Weibo dataset to be convincing, concluding that the model showed robust performance and improvements over baselines. Two reviewers commented that the evaluation on a single dataset was limited, and encouraged authors to explore one or more settings beyond Weibo. During the rebuttal period, the authors presented results for two additional settings including English language tweets. Other questions about strength of evidence such as computational complexity were also addressed during the rebuttal. One reviewer commented that clarity could be improved, especially giving more direct explanations of the method and agent interactions. Clarity was also reflected in several of the questions asked by reviewers. The author responses in the rebuttal were generally adequate on these issues, and the authors are encouraged to improve these explanations in the final paper. 

Overall, reviewers were satisfied with the rebuttal and two raised their scores, leading to a positive overall assessment.
Decision: Accept (poster)