The generation of texts using Large Language Models (LLMs) is inherently uncertain, with sources of uncertainty being not only the generation of texts, but also the prompt used and the downstream interpretation. Within this work, we provide a formal framework for the measurement of uncertainty that takes these different aspects into account. Our framework models prompting, generation, and interpretation as interconnected autoregressive processes that can be combined into a single sampling tree. We introduce filters and objective functions to describe how different aspects of uncertainty can be expressed over the sampling tree and demonstrate how to express existing approaches towards uncertainty through these functions. With our framework we show not only how different methods are formally related and can be reduced to a common core, but also point out additional aspects of uncertainty that have not yet been studied.
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Figure 1: Structured view of generating an LLM response with corresponding uncertainties. In our formal framework, the random variables Xi,Yi, and Zi are corresponding to modeling the uncertainty of the different phases of the generative process.
LLM reasoning is stochastic, and so understanding a model requires grappling with the distribution of reasoning chains that it might produce for a given question, i.e., its uncertainty. Resampling-based analyses characterize this distribution, revealing which steps of a rollout determine how the model arrives at its answer. However, a major limitation of these approaches is that resampling text sequences at every token or sentence in a reasoning chain is very costly. Our work strives to make resampling analysis more computationally efficient, while also shedding light on an important scientific question: what is the right statistical model for explaining uncertainty dynamics in text generation? We show that when resampling many reasoning chains, uncertainty dynamics converge to stable patterns, and noise is largely an artifact of sampling rather than an LLM's sensitivity to each individual token or reasoning step. We develop a statistical model for smoothing noisy low-sample rollout data to better approximate high-sample data, allowing us to significantly cut sampling costs.
Understanding why a large language model (LLM) is uncertain about the response is important for their reliable deployment. Current approaches, which either provide a single uncertainty score or rely on the classical aleatoric-epistemic dichotomy, fail to offer actionable insights for improving the generative model. Recent studies have also shown that such methods are not enough for understanding uncertainty in LLMs. In this work, we advocate for an uncertainty decomposition framework that dissects LLM uncertainty into three distinct semantic components: (i) input ambiguity, arising from ambiguous prompts; (ii) knowledge gaps, caused by insufficient parametric evidence; and (iii) decoding randomness, stemming from stochastic sampling. Through a series of experiments we demonstrate that the dominance of these components can shift across model size and task. Our framework provides a better understanding to audit LLM reliability and detect hallucinations, paving the way for targeted interventions and more trustworthy systems.
Uncertainty estimation is important for deploying LLMs in high-stakes applications such as healthcare and finance, where hallucinations can appear fluent and plausible while being factually incorrect, making it difficult for users to judge whether an output should be trusted. Existing methods require one or more full autoregressive generations to estimate uncertainty, which introduces substantial inference cost and often delays uncertainty assessment. In this paper, we investigate whether effective uncertainty estimation can be achieved with partial generation or even input-only information. Specifically, we first develop a unified framework that formulates uncertainty estimation as an early estimation problem over the autoregressive generation process of LLMs. This framework organises existing and proposed estimators by the information they observe, ranging from multi-generation to input-only prediction, and clarifies the performance-cost trade-off underlying different uncertainty estimation methods. Building on this view, we study two largely underexplored low-cost settings: estimating uncertainty with part of the generation, and predicting uncertainty from the input prompt. We propose Logit Magnitude, which uses top-M logit evidence to estimate uncertainty from an early-stopped generation prefix, and MetaUE, which distils generation-based uncertainty into a lightweight input-only estimator trained with uncertainty scores. Extensive experiments on general and domain-specific benchmarks show that Logit Magnitude achieves strong performance, and partial generations of LLMs are often sufficient for effective uncertainty estimation. MetaUE further provides a competitive input-only approximation in several settings. These findings suggest that effective uncertainty estimation requires less generation than commonly assumed, enabling unreliable responses to be identified earlier.