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

2026-05-28 · Source: Artificial Intelligence · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

Multi-component LLM agents, which combine probabilistic claims from components with partial problem views, can exhibit global incoherence despite local coherence in each component. This phenomenon is formalized by the compositional residual eps*, an L2 distance from the composed quote to the joint coherent polytope, computable at runtime using system output and declared cross-component coupling constraints. A product-structure dichotomy identifies conditions where local coherence is sufficient, and a Rayleigh-quotient prediction estimates the residual within 7% across three of four relation classes. A hierarchical Boyle-Dykstra projection deterministically repairs the composition, while an anytime-valid e-process offers sequential coherence monitoring. Across 1,876 ensemble cliques on a four-LLM mid-tier panel, eps* was greater than zero in 33-94% of cliques, leading to +0.115 nats per bet of regret on 1,770 resolved bets under proportional allocation. Three LLM-side mitigations (retrieval, partition-aware prompting, aggregator-LLM) were found to fail or regress.

Key takeaway

For AI Scientists designing multi-component LLM agents, you must actively address compositional incoherence, as local coherence is insufficient. Quantify this risk by computing the eps* residual at runtime to identify violations of probability axioms. Implement a hierarchical Boyle-Dykstra projection to deterministically repair incoherent compositions, preventing significant regret. Your current LLM-side mitigations like retrieval or prompting may be ineffective or even detrimental.

Key insights

Multi-component LLM agents can be globally incoherent despite local coherence, quantifiable by eps* and repairable via projection.

Principles

• Local coherence does not guarantee global coherence in multi-component LLM agents.
• Compositional incoherence is measurable via the eps* residual.
• Probabilistic claims from LLM components can violate basic probability axioms.

Method

The paper proposes formalizing incoherence via compositional residual eps*, predicting it with a Rayleigh-quotient, and repairing it deterministically using a hierarchical Boyle-Dykstra projection. Sequential monitoring uses an anytime-valid e-process.

In practice

• Compute eps* at runtime to detect compositional incoherence.
• Apply Boyle-Dykstra projection for deterministic repair.
• Monitor coherence sequentially with an e-process.

Topics

• Multi-component LLM Agents
• Compositional Incoherence
• Probability Axioms
• Boyle-Dykstra Projection
• eps* Residual
• LLM Agent Coherence

Best for: Research Scientist, AI Architect, AI Engineer, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by Artificial Intelligence.