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This paper investigates the impact of delayed verification in multi-agent large language model (LLM) systems, revealing that such delays can lead to the propagation of false claims among agents. By modeling the verification process as delayed consensus on a graph with corrector nodes, the authors derive a closed-form stability threshold that highlights how excessive or tardy corrections can destabilize consensus. Experimental results across five open models validate the theoretical predictions, demonstrating that the most significant instability occurs when communication and verification delays align, with implications for optimal corrector placement in agent networks.
Delayed verification can turn consensus into oscillation, with the most unstable regime occurring when communication and verification delays coincide.
Multi-agent large language model (LLM) systems often rely on verifier and critic agents to suppress hallucinations, but verification is delayed. During this delay, false claims can propagate through the agent network. We model this process as delayed consensus on a graph with grounded corrector nodes. Spectral decomposition by the grounded Laplacian yields a closed-form stability threshold for the verification dose: correction that is too strong or too delayed can turn consensus into oscillation. The most unstable regime occurs when the communication and verification delays coincide; for delay two, the threshold is the inverse golden ratio. The same framework gives a supermodular placement objective and a greedy (1-1/e)-approximation rule for assigning a limited corrector budget to influential nodes. Experiments across five open models confirm the predicted dose-delay oscillations. By contrast, grounded factual answering makes truth an absorbing boundary and eliminates the effect, suggesting that the instability is specific to signed-belief tasks while grounded verification remains stabilizing
