GUT: Quantifying and Optimizing the Reasoning Uncertainty of LLMs via Graph Complexity

Large-Language Models (LLMs) can be prone to flawed and unfaithful reasoning that decoding strategies like Self-Consistency (SC) fail to detect as they evaluate only final-answer agreement while ignoring the logical validity of intermediate steps. This raises three fundamental questions: How can we reliably quantify uncertainty in LLM reasoning? Can semantic, structural, and causal awareness select more faithful reasoning compared to naïve majority voting? and How robust is reasoning topology under adversarial conditions? To address these questions, we introduce GRAPHEVAL, a graph-based reasoning framework that re-frames uncertainty quantification (UQ) as a holistic reasoning fidelity problem. We propose a novel UQ metric, Graph Reasoning Coherence Score (GRCS), that quantifies semantic-structural consensus of the reasoning space and captures pathological mode collapse and confident hallucinations. We find that GRCS is the only metric that is consistently negatively correlated with reasoning faithfulness across both more capable and smaller models. Additionally, we introduce Graph Self-Consistency (GSC), a medoid-based decoding strategy that trades nominal accuracy for reasoning fidelity, exposing the degree to which SC is inflated by unfaithful lucky guesses in smaller models, while preserving or improving accuracy in more capable ones. Finally, through adversarial medoid ablation, we demonstrate that the GSC-selected path acts as a "load-bearing path" and forcing models away from it degrades reasoning faithfulness and, in targeted cases, causes drops in accuracy.

Agents have attracted considerably increasing attention due to the power of executing both Reasoning and Acting (ReAct) in open and dynamic environments. The ReAct process typically exhibits a multi-turn trajectory in which one drives Large Language Models (LLMs) to generate both reasoning chains and task-specific actions in an interleaved manner. However, agents often suffer from significant uncertainty, where identical tasks yield divergent trajectories; trajectories with higher uncertainty often produce incomprehensible behaviors, severely undermining agent credibility. This work conjectures that such trajectory-level uncertainty frequently stems from cumulative turn-level reasoning uncertainty induced by LLMs; the latter often exhibits a collection of branches of divergent reasoning chains and their resulting actions. Built upon this, we present the Graph-based Reasoning UncErtainty in Trajectories (GRUET) method for the uncertainty quantification of ReAct, comprising turn-level reasoning uncertainty quantification and trajectory-level uncertainty aggregation; the former precisely quantifies reasoning uncertainty via modeling the reasoning space spanned by potential reasoning branches as a graph and then approximating the reasoning space complexity with graph complexity, while the latter employs simple aggregation strategies for quantifying the overall trajectory credibility. Empirical evaluations across nine LLMs and five benchmarks validate the effectiveness of our proposed GRUET in terms of selective generation performance, measured by AUROC, AUPRC, and AUARC.

Large Language Models (LLMs) have achieved significant breakthroughs across various domains, but they can still produce unreliable or misleading outputs. For responsible LLM applications, uncertainty quantification techniques are used to estimate a model's uncertainty about its outputs, indicating the likelihood that those outputs may be problematic. For LLM reasoning tasks, it is essential to estimate uncertainty not only in the final answer but also in the intermediate reasoning process, particularly to identify where uncertainty arises. Such information may enable more fine-grained and targeted interventions during inference. In this study, we investigate which metrics can effectively localize uncertain places within an LLM reasoning trajectory. Our study reveals that uncertain intermediate continuations are more likely to occur at tokens that are highly sensitive to perturbations in the embeddings of preceding tokens. In our experiments, we show that such perturbation-based metrics achieve stronger performance in localizing uncertain intermediate steps than baseline methods, including probability-based, sampling-based, and Bayesian-based approaches. Meanwhile, our proposed metrics also enjoy good simplicity and efficiency.