# The Contagion Tensor: A Framework for Measuring Output-Distribution Coupling in Multi-Agent LLM Systems -- and Auditing the Claims It Enables

arXiv: https://arxiv.org/abs/2606.28839 · HTML: https://mlsanity.com/paper/2606.28839/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 17 of its 30 references that are in the map.
- First posted on arXiv 27 Jun 2026.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 17 of 17)

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- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
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- [CrowS-Pairs: A Challenge Dataset for Measuring Social Biases in Masked Language Models](https://mlsanity.com/paper/2010.00133/) (2020)
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- [MultiAgentBench: Evaluating the Collaboration and Competition of LLM agents](https://mlsanity.com/paper/2503.01935/) (2025)
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- [Do Large Language Models Solve the Problems of Agent-Based Modeling? A Critical Review of Generative Social Simulations](https://mlsanity.com/paper/2504.03274/) (2025)
- [Emergent Coordination in Multi-Agent Language Models](https://mlsanity.com/paper/2510.05174/) (2025)
- [EcoLANG: Efficient and Effective Agent Communication Language Induction for Social Simulation](https://mlsanity.com/paper/2505.06904/) (2025)
- [Detecting Perspective Shifts in Multi-agent Systems](https://mlsanity.com/paper/2512.05013/) (2025)
- [CASPIAN: Online Detection and Attribution of Cascade Attacks in LLM Multi-Agent Systems via Cross-Channel Causal Monitoring](https://mlsanity.com/paper/2605.19240/) (2026)

## Abstract (arXiv)

We introduce the Contagion Tensor, a measurement framework for quantifying how large language model (LLM) output distributions couple across modalities, agents, and time steps. From the tensor we derive the Coupling Amplification Factor (CAF), a family of ratio-based metrics sharing the form CAF = E[T_condition] / E[T_baseline], providing unitless, baseline-referenced measurement with bootstrap confidence intervals. We instantiate CAF in four variants and evaluate the strongest in a complete 2x2x2 block-orthogonal simulation design with modality-specific ablation. The ablation reveals that an apparent image-condition super-linear effect (CAF = 1.40) collapses to sub-linear (CAF = 0.87) when the image perturbation module is disabled, a shift of -0.53 with zero effect on text conditions. We supplement with real-API experiments across two model families: DeepSeek-Chat (R=30) and GPT-4o-mini (R=15, real vision). Under uniform personas, text-only communication produces CAF approx 1.0 in both models. Diverse personas drive convergence (CAF = 0.88). A within-model comparison on GPT-4o-mini reveals: C3 (text) CAF = 1.02 vs. C5 (real vision, R=30) CAF = 1.72 [1.700, 1.733], delta = +0.70, validating the simulation's super-linear image-condition prediction. Of 11 conditions, 5 have been tested on real APIs and 6 remain unverified. Our contribution is two-layered: (1) a measurement instrument that makes output-distribution coupling quantitatively falsifiable; and (2) a transferable ablation protocol that any modular multi-agent simulator can adopt to distinguish genuine coupling from design artifacts.