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

2026-06-27

AI Summary

This work addresses the challenge of quantifying genuine coupling effects in multi-agent large language model systems, where existing methods often conflate true interactions with artifacts introduced by system design. The authors propose a contagion tensor framework that introduces the Coupling Amplification Factor (CAF) to measure coupling strength across modalities, agents, and temporal dimensions. To disentangle authentic coupling from spurious biases, they develop a modular ablation protocol and block-orthogonal simulations, complemented by Bootstrap confidence intervals, validated in both synthetic and real-world API environments. Experiments reveal that CAF under visual conditioning drops from 1.40 to 0.87 in simulation, while in real API tests, GPT-4o-mini exhibits a CAF of 1.72 under visual input—significantly higher than under textual input—providing empirical evidence for superlinear coupling effects.

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.

Problem

• output-distribution coupling
• multi-agent LLM systems
• contagion tensor
• coupling amplification factor
• falsifiability

Innovation

• Contagion Tensor
• Coupling Amplification Factor
• output-distribution coupling
• multi-agent LLM systems
• ablation protocol