The Contagion Tensor: A Framework for Measuring Output-Distribution Coupling in Multi-Agent LLM Systems -- and Auditing the Claims It Enables
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Computer Science > Machine Learning
arXiv:2606.28839 (cs)
[Submitted on 27 Jun 2026]
Title:The Contagion Tensor: A Framework for Measuring Output-Distribution Coupling in Multi-Agent LLM Systems -- and Auditing the Claims It Enables
Authors:Zewen Liu
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Abstract: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.
| Comments: | 26 pages, 2 figures |
| Subjects: | Machine Learning (cs.LG) |
| ACM classes: | I.2.7; I.2.11; I.6.4 |
| Cite as: | arXiv:2606.28839 [cs.LG] |
| (or arXiv:2606.28839v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.28839
arXiv-issued DOI via DataCite (pending registration)
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View a PDF of the paper titled The Contagion Tensor: A Framework for Measuring Output-Distribution Coupling in Multi-Agent LLM Systems -- and Auditing the Claims It Enables, by Zewen Liu
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