Every Response Counts: Quantifying Uncertainty of LLM-based Multi-Agent Systems through Tensor Decomposition

LLM-based multi-agent systems (MAS) solve complex tasks through communication among role-specialized agents. However, inter-agent dependencies introduce reliability risks beyond isolated agent failures. For instance, errors in intermediate messages could be inherited and amplified by downstream agents. Existing uncertainty quantification (UQ) methods mainly target isolated responses or single-agent reasoning, and therefore fail to capture uncertainty propagation in MAS. To this end, we propose PropUQ-MAS, an error propagation-aware UQ framework that represents MAS execution as a communication-structured graph and estimates each step's reliability by combining local uncertainty with uncertainty inherited from upstream messages. Extensive experiments demonstrate that PropUQ-MAS consistently improves UQ in MAS, with average relative gains of +6.10% in AUROC and +47.58% in PRR.

LLM-based multi-agent systems (MAS) have attracted growing attention for improving reasoning through interaction among multiple agents. In this work, we focus on parallel multi-agent reasoning systems, where several agents solve the same problem over multiple rounds and aggregate their outputs into a final answer. Despite their strong reasoning performance, uncertainty estimation for such systems remains underexplored: the reliability of a MAS depends not only on individual generations, but also on how agents interact and evolve across rounds. We propose SAUCE (Sequential Agent Uncertainty through Consensus Evolution), a lightweight, training-free uncertainty estimator that formulates MAS uncertainty as sequential inference over a latent system-level belief. SAUCE aggregates round-level agreement and generation-uncertainty signals through a filtering-style update. Across five backbones, five benchmarks, and two MAS protocols, SAUCE improves misclassification detection, selective prediction, and calibration over a broad set of uncertainty estimation baselines, including standard log-likelihood-based methods and MAS-specific estimators.

As large language model (LLM)-based multi-agent systems become increasingly capable, coordinating agents under uncertainty becomes a fundamental challenge. Existing orchestration strategies typically rely on fixed interaction patterns and often lack mechanisms for assessing the reliability of intermediate reasoning steps, allowing errors and hallucinations to propagate through the system. This paper introduces a semantic-uncertainty-guided orchestration approach, HASSUM as a general framework for uncertainty-aware coordination in multi-agent systems. The method estimates uncertainty using semantic entropy and semantic density, which measure trust at the level of answer semantics rather than output probabilities. These signals enable adaptive orchestration decisions, including output verification, selective reprompting, additional deliberation, and confidence-aware response selection. Because the approach operates independently of any particular agent architecture, it can be integrated into a broad range of hierarchical and collaborative multi-agent systems. The evaluations demonstrate an implementation within a hierarchical agent framework and evaluate it on StrategyQA, JailbreakBench, and TruthfulQA benchmarks. Across tasks that require complex reasoning and are prone to ambiguity or hallucinations, uncertainty-guided orchestration yields more reliable outcomes than uncertainty-unaware coordination. Semantic entropy and semantic density in tandem outperformed either metric alone. Ablations testing different thresholds and model sizes demonstrated that both influence the effectiveness of semantic metrics. The results suggest that semantic uncertainty is a practical and general-purpose signal for improving robustness and trustworthiness in agentic AI systems.