Locally Coherent, Globally Incoherent: Bounding Compositional Incoherence in Multi-Component LLM Agents

• URL: http://arxiv.org/abs/2605.30335v1
• Date: Thu, 28 May 2026 17:58:55 GMT
• Title: Locally Coherent, Globally Incoherent: Bounding Compositional Incoherence in Multi-Component LLM Agents
• Abstract summary: Multi-component LLM agents assemble probabilistic claims from components that each see only part of a joint problem.<n>We formalise this locally coherent, globally incoherent failure via the compositional residual eps*.<n>A hierarchical Boyle-Dykstra projection repairs the composition deterministically.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Multi-component LLM agents assemble probabilistic claims from components that each see only part of a joint problem; the composition can violate basic probability axioms even when every component is locally coherent. We formalise this locally coherent, globally incoherent failure via the compositional residual eps*, the L2 distance from the composed quote to the joint coherent polytope, computable at runtime from system output and the declared cross-component coupling constraints. A product-structure dichotomy characterises when local coherence suffices, and a Rayleigh-quotient prediction matches the observed residual within 7% on three of four relation classes. A hierarchical Boyle-Dykstra projection repairs the composition deterministically; an anytime-valid e-process gives sequential coherence monitoring. Across 1,876 ensemble cliques on a four-LLM mid-tier panel (frontier-panel rerun in Section 5.5), eps* > 0 on 33-94% of cliques, translating to +0.115 nats per bet of regret on 1,770 resolved bets under the proportional allocation rule (the gain collapses to +0.006 under bettors that themselves coherentise). Three intuitive LLM-side mitigations(retrieval, partition-aware prompting, aggregator-LLM) each fail or regress.

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