A Survey of Uncertainty Estimation Methods on Large Language Models (2025)

Abstract: Large language models (LLMs) have demonstrated remarkable capabilities across various tasks. However, these models could offer biased, hallucinated, or non-factual responses camouflaged by their fluency and realistic appearance. Uncertainty estimation is the key method to address this challenge. While research efforts in uncertainty estimation are ramping up, there is a lack of comprehensive and dedicated surveys on LLM uncertainty estimation. This survey presents four major avenues of LLM uncertainty estimation. Furthermore, we perform extensive experimental evaluations across multiple methods and datasets. At last, we provide critical and promising future directions for LLM uncertainty estimation.

## introduction large language models (llms) have emerged as state-of-the-art solutions for a wide range of problems, mainly due to their unparalleled ability to generate coherent and contextually appropriate responses to diverse user prompts @xcite . however, with the increasing adoption of llms, concerns have grown regarding their tendency to produce biased, hallucinated, non-factual, and misaligned outputs @xcite . these issues are further exacerbated by the fact that such flawed responses often appear highly fluent and convincingly realistic, making them difficult to detect. a promising approach to addressing the challenge of misleading yet plausible responses is uncertainty estimation, which assigns an uncertainty or confidence score to the model's output. figure 1 provides an overview of this process. first, the llm generates an initial response based on the input. next, a confidence score is computed for this response. the score is then evaluated against a predefined threshold to determine the final output. if i have a headache. can i take some tylenol? yes, you can take tylenol for your headache. ## uncertainty sources in llm there are two primary sources of uncertainty: aleatoric and epistemic uncertainties @xcite . in the context of llms @xcite @xcite , these sources manifest in the following ways: how to estimate uncertainty and confidence? following the conceptualization by @xcite , we illustrate the process as shown in figure 2. for each input x, an llm model has an underlying response distribution for it ( 1 ). for ease of illustration, we assume the distribution is a normal distribution n (µ, σ 2 ). uncertainty estimation is to estimate the underlying variance σ 2 . for example, the sample variance of m different responses r 1 , • • • , r m ( 2 ) can be an estimator for the variance, which indicates the variations of responses (u in figure 2 ). there are generally two types of confidence, i.e., overall confidence c and the confidence c i associated with each response candidate r i . the overall confidence c is complementary to u , i.e., the precision 1/σ 2 of the distribution is a confidence c to the input. the associated confidence is related to x and the tokens in a specific response r i . to provide the final response to answer the input x given sampled responses, some literature resort to majority voting to select the most-voted response r * ( 3 ) @xcite , while others choose to generate one extra response r m +1 with lowtemperature settings ( 4 ) @xcite . ## conclusion this survey paints a comprehensive landscape for uncertainty estimation methods on llms during the inference stage, classifying them into four classes: verbalizing, latent information, consistency-based, and semantic clustering methods. we further enrich our survey with extensive evaluations and promising future directions.