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Three laws for when a society of LLM agents will stop disagreeing

AspireAI community · arXiv
Emerging control planes would compose LLM agents that exchange interpreted conclusions, so hallucinations can propagate even over error-free transport. Modelling such a society as a cellular sheaf, this paper establishes three laws that hold on arbitrary topologies. The composition law: network-wide divergence exceeds the sum of per-agent audit scores by exactly their hidden total correlation, which masks up to 23% of joint divergence and overstates the cognitive signal-to-noise ratio by 1.14 dB purely through topology. The scaling law: reconciliation decouples across metric counters, so the worst-connected dimension sets the pace, and consistency time grows as Omega(n^(2/d)) on polynomial-growth topologies of degree d - paths breach a one-second near-real-time budget at 13 agents, while expanders and radius-3 local audits stay bounded. The consistency-time law: timing error from omitted correlations is one-sided and capped by the worst-measured link. The laws are validated on simulated topologies and deployed LLM societies, giving worst-case latency ceilings for near-real-time operation.
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