Uncertainty Localization in LLM Reasoning via Embedding Perturbations

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.