# Attributing Emergence in Million-Agent Systems

arXiv: https://arxiv.org/abs/2605.11404 · HTML: https://mlsanity.com/paper/2605.11404/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 29 of its 48 references that are in the map.
- First posted on arXiv 12 May 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- LLM agents and tool use / [Social simulation and multi-agent debate](https://mlsanity.com/agents/social-simulation-and-multi-agent-debate/)

## Builds on (most cited first, 29 of 29)

- [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)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [MetaGPT: Meta Programming for A Multi-Agent Collaborative Framework](https://mlsanity.com/paper/2308.00352/) (2023)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [CAMEL: Communicative Agents for "Mind" Exploration of Large Language Model Society](https://mlsanity.com/paper/2303.17760/) (2023)
- [ChatDev: Communicative Agents for Software Development](https://mlsanity.com/paper/2307.07924/) (2023)
- [Out of One, Many: Using Language Models to Simulate Human Samples](https://mlsanity.com/paper/2209.06899/) (2022)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Why Do Multi-Agent LLM Systems Fail?](https://mlsanity.com/paper/2503.13657/) (2025)
- [AgentSociety: Large-Scale Simulation of LLM-Driven Generative Agents Advances Understanding of Human Behaviors and Society](https://mlsanity.com/paper/2502.08691/) (2025)
- [Which Agent Causes Task Failures and When? On Automated Failure Attribution of LLM Multi-Agent Systems](https://mlsanity.com/paper/2505.00212/) (2025)
- [EconAgent: Large Language Model-Empowered Agents for Simulating Macroeconomic Activities](https://mlsanity.com/paper/2310.10436/) (2023)
- [Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms](https://mlsanity.com/paper/1908.08619/) (2019)
- [Data Banzhaf: A Robust Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2205.15466/) (2022)
- [Emergent social conventions and collective bias in LLM populations](https://mlsanity.com/paper/2410.08948/) (2024)
- [AgenTracer: Who Is Inducing Failure in the LLM Agentic Systems?](https://mlsanity.com/paper/2509.03312/) (2025)
- [From Individual to Society: A Survey on Social Simulation Driven by Large Language Model-based Agents](https://mlsanity.com/paper/2412.03563/) (2024)
- [Shapley Q-value: A Local Reward Approach to Solve Global Reward Games](https://mlsanity.com/paper/1907.05707/) (2019)
- [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)
- [Who is Introducing the Failure? Automatically Attributing Failures of Multi-Agent Systems via Spectrum Analysis](https://mlsanity.com/paper/2509.13782/) (2025)
- [SHAQ: Incorporating Shapley Value Theory into Multi-Agent Q-Learning](https://mlsanity.com/paper/2105.15013/) (2021)
- ["I'm in the Bluesky Tonight": Insights from a Year Worth of Social Data](https://mlsanity.com/paper/2404.18984/) (2024)
- [Measuring user influence on Twitter: A survey](https://mlsanity.com/paper/1508.07951/) (2015)
- [Interpreting Emergent Extreme Events in Multi-Agent Systems](https://mlsanity.com/paper/2601.20538/) (2026)

## Abstract (arXiv)

Large language models (LLMs) can simulate human-like reasoning and decision-making in individual agents. LLM-powered multi-agent systems (MAS) combine such agents to simulate population-scale social phenomena such as polarization, information cascades, and market panics. Such studies require attributing macro emergence to individual agents, but existing axiomatic methods scale combinatorially in N and have been confined to N lesssim 103, while the phenomena they explain occur at N ≥ 106. We address this gap by adapting Aumann--Shapley path-integral attribution to LLM-powered MAS at million-agent scale; the resulting method satisfies all four axioms, runs three to five orders of magnitude faster than sampled Shapley on the same hardware, and extends feasible axiomatic attribution by over three orders of magnitude (a 1670× jump). We use this method to test the scale gap empirically: across 14 days of public Bluesky data (1,671,587 active users, five topics), we compute the attribution at both full scale and the visibility-biased N = 102 convenience sample used by small-scale studies, and the two disagree structurally. At full scale the long tail and middle tier jointly carry the majority; the biased small panel shifts about twice that share onto the upper follower tiers (48% versus 24%). We then prove that the disagreement cannot in general be reduced by post-hoc rescaling: an Attribution Scaling Bias theorem shows that a reconciling global rescaling factor exists exactly when the macro indicator is linear over agents, and our nonlinear indicators give residuals of 0.10--0.98. For such nonlinear indicators, full-scale attribution is therefore a requirement rather than a methodological choice.