CoE: Collaborative Entropy for Uncertainty Quantification in Agentic Multi-LLM Systems

TL;DR

This paper introduces Collaborative Entropy (CoE), a new information-theoretic metric for semantic uncertainty in multi-LLM systems, capturing both intra-model entropy and inter-model disagreement to improve uncertainty estimation.

Contribution

The paper proposes CoE, a novel system-level uncertainty measure for multi-LLM collaboration, along with a simple post-hoc heuristic, demonstrating improved uncertainty estimation over existing methods.

Findings

CoE outperforms standard entropy and divergence baselines in experiments.

CoE's effectiveness increases with more heterogeneous models.

Properties of CoE clarify when reducing per-model uncertainty suffices.

Abstract

Uncertainty estimation in multi-LLM systems remains largely single-model-centric: existing methods quantify uncertainty within each model but do not adequately capture semantic disagreement across models. To address this gap, we propose Collaborative Entropy (CoE), a unified information-theoretic metric for semantic uncertainty in multi-LLM collaboration. CoE is defined on a shared semantic cluster space and combines two components: intra-model semantic entropy and inter-model divergence to the ensemble mean. CoE is not a weighted ensemble predictor; it is a system-level uncertainty measure that characterizes collaborative confidence and disagreement. We analyze several core properties of CoE, including non-negativity, zero-value certainty under perfect semantic consensus, and the behavior of CoE when individual models collapse to delta distributions. These results clarify when reducing per-model uncertainty is sufficient and when residual inter-model disagreement remains. We also present a simple CoE-guided, training-free post-hoc coordination heuristic as a practical application of the metric. Experiments on \textit{TriviaQA} and \textit{SQuAD} with LLaMA-3.1-8B-Instruct, Qwen-2.5-7B-Instruct, and Mistral-7B-Instruct show that CoE provides stronger uncertainty estimation than standard entropy- and divergence-based baselines, with gains becoming larger as additional heterogeneous models are introduced. Overall, CoE offers a useful uncertainty-aware perspective on multi-LLM collaboration.