Title: MF-LLM: Simulating Population Decision Dynamics via a Mean-Field Large Language Model Framework
Venue: NeurIPS 2025
Accepted: yes
Keywords: social simulation

large langauge model

population

decision making

mean-field
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.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\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.\n\nQUESTIONS:\nSee Weaknesses.\n\nLIMITATIONS:\nSee Weaknesses.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths: 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.\n\nQUESTIONS:\n1. 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 ?\n\nLIMITATIONS:\nI think it is adequate.  The study is methodological in nature so possible negative impact would be speculative.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\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.\n\nQUESTIONS:\nThe 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?\n\nLIMITATIONS:\nThe 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.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\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\n\nQUESTIONS:\n- 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?\n\nLIMITATIONS:\nThe 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.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-03"}