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

Researchers identify a critical failure mode in multi-component LLM agent systems where individually coherent components produce globally incoherent outputs that violate probability axioms. The study proposes metrics to detect and repair these failures, finding them present in 33-94% of tested multi-LLM ensembles with measurable economic impact on prediction tasks.

Multi-component LLM systems represent a scaling strategy where different language models handle specialized subtasks within a larger agent architecture. This research exposes a fundamental architectural vulnerability: when individual components optimize locally without global coordination, their probabilistic outputs can violate basic probability theory even when each component functions correctly. This compositional incoherence emerges from incomplete information sharing between components that must jointly solve problems.

The technical contribution formalizes this problem through the compositional residual (eps*), a measurable quantity computed from system outputs and component coupling constraints. Critically, the authors demonstrate this metric appears in 33-94% of real multi-LLM ensemble cliques tested across 1,876 configurations. The economic impact proves tangible: under proportional allocation rules for betting tasks, the incoherence generates 0.115 nats of regret per decision across 1,770 resolved predictions.

This finding challenges the assumption that scaling LLM agents through ensemble methods automatically improves reliability. While the paper proposes repair mechanisms like hierarchical projection and monitoring approaches, attempted LLM-side mitigations including retrieval augmentation and specialized prompting failed to resolve the underlying issue. This suggests the problem requires architectural solutions rather than prompt engineering workarounds.

The research has implications for deployed systems relying on LLM agent composition. Organizations implementing multi-model architectures for critical decisions—financial forecasting, medical diagnosis support, autonomous planning—face previously unmeasured coherence failures. The deterministic repair methods proposed offer practical solutions, but the gap between local and global optimization in distributed LLM systems appears more fundamental than previously recognized.

• →Multi-component LLM agents violate probability axioms on 33-94% of test cases despite having locally coherent components, creating measurable prediction errors worth 0.115 nats per decision.
• →Compositional incoherence stems from incomplete information coupling between components rather than individual model failures, requiring architectural rather than algorithmic fixes.
• →Standard LLM mitigation techniques like retrieval augmentation and specialized prompting fail to address the underlying global coherence problem.
• →Deterministic repair methods using hierarchical projection can restore coherence, enabling monitoring and correction at runtime without retraining.
• →The findings suggest deployed multi-LLM agent systems may suffer systematic biases from undetected compositional failures in production environments.