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

arXiv: https://arxiv.org/abs/2504.21582 · HTML: https://mlsanity.com/paper/2504.21582/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 51 references that are in the map.
- First posted on arXiv 30 Apr 2025.

## Builds on (most cited first, 23 of 23)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Generative Agents: Interactive Simulacra of Human Behavior](https://mlsanity.com/paper/2304.03442/) (2023)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [SOTOPIA: Interactive Evaluation for Social Intelligence in Language Agents](https://mlsanity.com/paper/2310.11667/) (2023)
- [S3: Social-network Simulation System with Large Language Model-Empowered Agents](https://mlsanity.com/paper/2307.14984/) (2023)
- [Mean Field Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1802.05438/) (2018)
- [AgentSociety: Large-Scale Simulation of LLM-Driven Generative Agents Advances Understanding of Human Behaviors and Society](https://mlsanity.com/paper/2502.08691/) (2025)
- [EconAgent: Large Language Model-Empowered Agents for Simulating Macroeconomic Activities](https://mlsanity.com/paper/2310.10436/) (2023)
- [Simulating Opinion Dynamics with Networks of LLM-based Agents](https://mlsanity.com/paper/2311.09618/) (2023)
- [OASIS: Open Agent Social Interaction Simulations with One Million Agents](https://mlsanity.com/paper/2411.11581/) (2024)
- [AgentScope: A Flexible yet Robust Multi-Agent Platform](https://mlsanity.com/paper/2402.14034/) (2024)
- [Unveiling the Truth and Facilitating Change: Towards Agent-based Large-scale Social Movement Simulation](https://mlsanity.com/paper/2402.16333/) (2024)
- [Learning in Mean Field Games: A Survey](https://mlsanity.com/paper/2205.12944/) (2022)
- [From Skepticism to Acceptance: Simulating the Attitude Dynamics Toward Fake News](https://mlsanity.com/paper/2403.09498/) (2024)
- [GenSim: A General Social Simulation Platform with Large Language Model based Agents](https://mlsanity.com/paper/2410.04360/) (2024)
- [TwinMarket: A Scalable Behavioral and Social Simulation for Financial Markets](https://mlsanity.com/paper/2502.01506/) (2025)
- [Scalable Deep Reinforcement Learning Algorithms for Mean Field Games](https://mlsanity.com/paper/2203.11973/) (2022)
- [ElectionSim: Massive Population Election Simulation Powered by Large Language Model Driven Agents](https://mlsanity.com/paper/2410.20746/) (2024)
- [On learning agent-based models from data](https://mlsanity.com/paper/2205.05052/) (2022)
- [TaxAI: A Dynamic Economic Simulator and Benchmark for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2309.16307/) (2023)
- [TrendSim: Simulating Trending Topics in Social Media Under Poisoning Attacks with LLM-based Multi-agent System](https://mlsanity.com/paper/2412.12196/) (2024)
- [A Mean Field Games approach for multi-lane traffic management](https://mlsanity.com/paper/1711.04116/) (2017)

## Built on by (most cited first, 12 of 12)

- [Simulating Society Requires Simulating Thought](https://mlsanity.com/paper/2506.06958/) (2025)
- [PolicySim: An LLM-Based Agent Social Simulation Sandbox for Proactive Policy Optimization](https://mlsanity.com/paper/2603.19649/) (2026)
- [AIvilization v0: Toward Large-Scale Artificial Social Simulation with a Unified Agent Architecture and Adaptive Agent Profiles](https://mlsanity.com/paper/2602.10429/) (2026)
- [Collaborative QA using Interacting LLMs. Impact of Network Structure, Node Capability and Distributed Data](https://mlsanity.com/paper/2511.14098/) (2025)
- [Recognize Your Orchestrator: An Entropy Dynamics Perspective for LLM Multi-Agent Systems](https://mlsanity.com/paper/2606.01351/) (2026)
- [Aligned Alone, Misaligned Together: Forecasting Adversarial Capture in LLM Agent Populations](https://mlsanity.com/paper/2608.22444/) (2026)
- [SocietyBench: Forecasting Counterfactual Social-World Evolution](https://mlsanity.com/paper/2608.04009/) (2026)
- [ToMPO: Training LLM Strategic Decision Making from a Multi-Agent Perspective](https://mlsanity.com/paper/2509.21134/) (2025)
- [Cyberbullying Governance on Social Media: A Unified Framework from Content Identification to Intervention](https://mlsanity.com/paper/2605.27584/) (2026)
- [AgentSchool: An LLM-Powered Multi-Agent Simulation for Education](https://mlsanity.com/paper/2605.30144/) (2026)
- [MASS: Deep Research for Social Sciences with Memory-Augmented Social Simulation](https://mlsanity.com/paper/2606.09198/) (2026)
- [Poor Man's Agentic Modeling: Simulating Large LLM-Agent Societies on a Laptop](https://mlsanity.com/paper/2608.11215/) (2026)

## Abstract (arXiv)

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, a 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.