MF-LLM: Simulating Population Decision Dynamics via a Mean-Field Large Language Model Framework

Jun Wang (iWudao Tech) · Xu Chen (Renmin University of China) · Xiangning Yu (Tianjin University) · Mengyue Yang (University College London / University of Bristol) · Bo An (Nanyang Technological University) · Qirui Mi (Institute of Automation, Chinese Academy of Sciences) · Haifeng Zhang (Institute of automation, Chinese academy of science, Chinese Academy of Sciences) · Cheng Deng (Xidian University) · Zhiyu Zhao (University of the Chinese Academy of Sciences)

bidirectional interactionscoherent trajectoriescollective decision-makinghigh-fidelity foundationib-tuneinformation bottleneck principleintervention planningiterative process kl divergencemean field theorypopulation signalsquantitative alignmentsocial simulationtrend forecasting

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.