Reliability-Contagion Feasibility in LLM Multi-Agent Networks

2026-07-23

AI Summary

This work addresses the dual challenge of information aggregation and error propagation in large language model (LLM)-based multi-agent systems, where communication facilitates collective reasoning yet risks amplifying false claims. Introducing an epidemiological framework to this domain for the first time, the study proposes a corrected-aware information propagation model with susceptible, exposed, infected, and corrected states. Integrating majority-voting baselines with graph-theoretic analysis, it reveals opposing structural constraints imposed by reliability and error containment. Theoretical analysis and simulations across 21,000 trajectories identify an intermediate connectivity regime that simultaneously satisfies both objectives. Experiments with the real-world LLM Grok-4.3 across diverse topologies further demonstrate that as node degree increases from 2 to 5, the average number of erroneous first-generation descendants rises from 0.667 to 1.667, with non-seed nodes exhibiting error adoption rates up to 0.333—providing quantitative guidance and optimal regular graph structures for designing robust multi-agent networks.

Abstract

Communication allows large language model agents to pool evidence, but it also creates paths along which an erroneous claim can spread. We formulate a correction-aware network model that tracks susceptible, exposed, infectious, and corrected agents and derive its early-invasion condition for heterogeneous communication networks. We then couple this propagation model to an analytic majority-vote benchmark in which a clean-task reliability target imposes a minimum connectivity requirement. Under fixed exposure per communication edge, reliability and error control impose opposing graph constraints. We characterize when their intersection is empty and when it contains an intermediate connectivity range, and identify regular graphs that attain the smallest invasion factor within the reliable graph class when such graphs exist. Under a fixed sender budget, the homogeneous first-order threshold is independent of network density, showing that the communication-budget convention determines whether added edges increase early propagation risk. Finite-network simulations on 21,000 trajectories illustrate these directional predictions. A controlled grok-4.3 experiment then evaluates three six-node topologies on 36 new closed-world tasks, with a balanced 12-task subset continued to full cascades. Mean first-generation offspring increased from 0.667 to 1.333 and 1.667 as degree increased from 2 to 4 and 5, while the adoption fraction among exposed neighbours remained 0.333. Mean non-seed erroneous adoption in the full-cascade subset was 0.200, 0.333, and 0.333. Together, these results provide a tractable basis for selecting connectivity under explicit reliability and propagation constraints.

Problem

• reliability
• contagion
• multi-agent networks
• error propagation
• connectivity constraints

Innovation

• multi-agent LLM networks
• error propagation
• reliability-contagion tradeoff
• SEIR modeling
• network connectivity constraints