Contagion Tensor Measures LLM Output Coupling in Multi-Agent Systems.

As Large Language Model (LLM) systems become more complex, especially in multi-agent and multi-modal configurations, understanding how their outputs influence each other is crucial. This research introduces the Contagion Tensor, a novel measurement framework designed to quantify the coupling of LLM output distributions across different modalities, interacting agents, and sequential time steps. From this tensor, the authors derive the Coupling Amplification Factor (CAF), a family of ratio-based metrics. CAF provides a unitless, baseline-referenced measurement, complete with bootstrap confidence intervals, allowing for rigorous quantitative analysis. The framework was tested through a comprehensive simulation design, revealing that an apparent super-linear effect under image conditions (CAF = 1.40) collapsed to sub-linear (CAF = 0.87) when the image perturbation module was disabled, indicating a design artifact rather than genuine coupling. Further validation involved real-API experiments with models like DeepSeek-Chat and GPT-4o-mini. These experiments showed that text-only communication generally resulted in a CAF near 1.0, while diverse personas could drive convergence (CAF = 0.88). Crucially, GPT-4o-mini demonstrated a significant super-linear effect (CAF = 1.72) under real vision conditions compared to text-only, validating the simulation's prediction. This framework provides a robust instrument for falsifying claims about output-distribution coupling and offers a transferable ablation protocol for auditing modular multi-agent simulators.