LLM Uncertainty Estimation

Hallucinations in large language models (LLMs) remain a central obstacle to trustworthy deployment, motivating detectors that are accurate, lightweight, and broadly applicable. Since an LLM with a prompt defines a conditional distribution, we argue that the complexity of the distribution is an indicator of hallucination. However, the density of the distribution is unknown and the samples (i.e., responses generated for the prompt) are discrete distributions, which leads to a significant challenge in quantifying the complexity of the distribution. We propose to compute the optimal-transport distances between the sets of token embeddings of pairwise samples, which yields a Wasserstein distance matrix measuring the costs of transforming between the samples. This Wasserstein distance matrix provides a means to quantify the complexity of the distribution defined by the LLM with the prompt. Based on the Wasserstein distance matrix, we derive two complementary signals: AvgWD, measuring the average cost, and EigenWD, measuring the cost complexity. This leads to a training-free detector for hallucinations in LLMs. We further extend the framework to black-box LLMs via teacher forcing with an accessible teacher model. Experiments show that AvgWD and EigenWD are competitive with strong uncertainty baselines and provide complementary behavior across models and datasets, highlighting distribution complexity as an effective signal for LLM truthfulness.

Diffusion large language models (D-LLMs) have emerged as a promising alternative to auto-regressive models due to their iterative refinement capabilities. However, hallucinations remain a critical issue that hinders their reliability. To detect hallucination responses from model outputs, token-level uncertainty, such as entropy, has been widely used to indicate potential factual errors. Nevertheless, unlike auto-regressive models that generate tokens sequentially, D-LLMs generate fixed-length sequences simultaneously, where only a small subset of tokens is informative for hallucination detection. Thus, aggregating uncertainty over all tokens can be suboptimal. Moreover, the evolution trend of uncertainty throughout the diffusion process can also provide valuable signals, highlighting the necessity of modeling its denoising dynamics for hallucination detection. In this paper, we propose DynHD, which bridges these gaps from both spatial (token sequence) and temporal (denoising dynamics) perspectives. To handle the information density imbalance across tokens, we propose a semantic-aware evidence construction module that extracts hallucination-indicative signals by removing task-invariant structural tokens and emphasizing the uncertainty of the remaining informative tokens. To model denoising dynamics for hallucination detection, we introduce a reference evidence generator that learns the expected evolution trajectory of uncertainty evidence, along with a deviation-based hallucination detector that makes predictions by measuring the discrepancy between the observed and reference trajectories. Extensive experiments demonstrate that DynHD consistently outperforms state-of-the-art baselines while achieving higher efficiency across multiple benchmarks and backbone models. The code is available at: https://github.com/qyy11-com/DynHD.

Large language models (LLMs) are often confidently wrong, making reliable uncertainty estimation (UE) essential. Output-based heuristics are cheap but brittle, while probing internal representations is effective yet high-dimensional and hard to transfer. We propose a compact, per-instance UE method that scores cross-layer agreement patterns in internal representations using a single forward pass. Across three models, our method matches probing in-distribution, with mean diagonal differences of at most $-1.8$ AUPRC percentage points and $+4.9$ Brier score points. Under cross-dataset transfer, it consistently outperforms probing, achieving off-diagonal gains up to $+2.86$ AUPRC and $+21.02$ Brier points. Under 4-bit weight-only quantization, it remains robust, improving over probing by $+1.94$ AUPRC points and $+5.33$ Brier points on average. Beyond performance, examining specific layer--layer interactions reveals differences in how disparate models encode uncertainty. Altogether, our UE method offers a lightweight, compact means to capture transferable uncertainty in LLMs.

Despite the growing demand for eliciting uncertainty from large language models (LLMs), empirical evidence suggests that LLM behavior is not always adequately captured by the elicitation techniques developed under the classical probabilistic uncertainty framework. This mismatch leads to systematic failure modes, particularly in settings that involve ambiguous question-answering, in-context learning, and self-reflection. To address this, we propose novel prompt-based uncertainty elicitation techniques grounded in imprecise probabilities, a principled framework for repesenting and eliciting higher-order uncertainty. Here, first-order uncertainty captures uncertainty over possible responses to a prompt, while second-order uncertainty (uncertainty about uncertainty) quantifies indeterminacy in the underlying probability model itself. We introduce general-purpose prompting and post-processing procedures to directly elicit and quantify both orders of uncertainty, and demonstrate their effectiveness across diverse settings. Our approach enables more faithful uncertainty reporting from LLMs, improving credibility and supporting downstream decision-making.

Verbalized confidence, in which LLMs report a numerical certainty score, is widely used to estimate uncertainty in black-box settings, yet the confidence scale itself (typically 0--100) is rarely examined. We show that this design choice is not neutral. Across six LLMs and three datasets, verbalized confidence is heavily discretized, with more than 78% of responses concentrating on just three round-number values. To investigate this phenomenon, we systematically manipulate confidence scales along three dimensions: granularity, boundary placement, and range regularity, and evaluate metacognitive sensitivity using $meta\text{-}d'$. We find that a 0--20 scale consistently improves metacognitive efficiency over the standard 0--100 format, while boundary compression degrades performance and round-number preferences persist even under irregular ranges. These results demonstrate that confidence scale design directly affects the quality of verbalized uncertainty and should be treated as a first-class experimental variable in LLM evaluation.

Leyva-Vázquez and Smarandache (2025) demonstrated that neutrosophic T/I/F evaluation, where Truth, Indeterminacy, and Falsity are independent dimensions not constrained to sum to 1.0, which reveals "hyper-truth"' (T+I+F > 1.0) in 35% of complex epistemic cases evaluated by LLMs. We extend their work in two directions. First, we replicate and extend their experiment across five model families from five vendors (Anthropic, Meta, DeepSeek, Alibaba, Mistral), finding hyper-truth in 84% of unconstrained evaluations, which confirms the phenomenon is cross-vendor under our prompt protocol. Second, and more significantly, we identify a limitation of scalar T/I/F that their framework cannot address: models adopting an `"Absorption" position (T=0, I=1, F=0) produce identical scalar outputs for fundamentally different epistemic situations (paradox, ignorance, contingency), collapsing the very distinctions neutrosophic logic was designed to preserve. We demonstrate that extending the evaluation to include declared losses (structured descriptions of what the model cannot evaluate and why) substantially recovers these distinctions. Models producing identical scalars for paradox and ignorance produce nearly disjoint loss vocabularies (Jaccard similarity < 0.10 on loss description keywords), with domain-specific, severity-rated loss declarations that differentiate the nature of their uncertainty. This suggests that scalar T/I/F is a necessary but insufficient representation of epistemic state, and that tensor-structured output (scalars + losses) provides a more faithful model of LLM epistemic capabilities.

Large language models (LLMs) can achieve strong reasoning performance through chain-of-thought (CoT) reasoning, yet they often generate unnecessarily long reasoning paths that incur high inference cost. Self-consistency-based approaches push accuracy higher still, but they require sampling and aggregating multiple reasoning trajectories, leading to substantial computational overhead. In this paper, we introduce a confidence-aware selective sampling framework that, at inference time, analyzes a single reasoning trajectory to adaptively determine whether to rely on that trajectory alone or trigger multi-path sampling. The framework uses trajectory-level numeric features and sentence-level linguistic features extracted from reasoning states to guide selective multi-path reasoning. We train it on MedQA and evaluate it in-domain on MedQA and under calibration-only transfer on MathQA, MedMCQA, and MMLU, without further fine-tuning. Experimental results show that the proposed framework maintains comparable performance to full and efficient multi-path reasoning baselines, with accuracy changes of $-0.41 \pm 0.58$ and $-0.31 \pm 0.58$ percentage points, respectively, while reducing token usage by $71.7 \pm 5.0$ and $36.6 \pm 9.1$. These findings demonstrate that reasoning trajectories contain rich signals for uncertainty estimation, enabling a simple, transferable mechanism to balance accuracy and efficiency in LLM reasoning.

Table reasoning requires models to jointly perform semantic understanding and precise numerical operations. Most existing methods rely on a single-turn reasoning paradigm over tables which suffers from context overflow and weak numerical sensitivity. To address these limitations, we previously proposed TableMind as a tuning-based autonomous programmatic agent that simulates human-like interaction within a lightweight large language model (LLM). TableMind internalizes planning, action, and reflection through a two-stage training strategy involving supervised fine-tuning (SFT) on filtered high-quality data and reinforcement learning (RL) via a multi-perspective reward and the Rank-Aware Policy Optimization (RAPO) algorithm. While TableMind establishes a solid foundation for programmatic agents, the inherent stochasticity of LLMs remains a critical challenge that leads to hallucinations. In this paper, we extend this foundation to TableMind++ by introducing a novel uncertainty-aware inference framework to mitigate hallucinations. Specifically, we propose memory-guided plan pruning to retrieve historical trajectories for validating and filtering out logically flawed plans to address epistemic uncertainty. To ensure execution precision, we introduce confidence-based action refinement which monitors token-level probabilities to detect and self-correct syntactic noise for aleatoric uncertainty mitigation. Finally, we employ dual-weighted trajectory aggregation to synthesize a robust consensus from multiple reasoning paths. Extensive experiments on diverse benchmarks demonstrate that TableMind++ consistently outperforms previous baselines and proprietary models to validate the effectiveness of integrating autonomous training with uncertainty quantification. Our code is available.

Large Language Models (LLMs) that can express interpretable and calibrated uncertainty are crucial in high-stakes domains. While methods to compute uncertainty post-hoc exist, they are often sampling-based and therefore computationally expensive or lack calibration. We propose a three-stage pipeline to post-train LLMs to efficiently infer calibrated uncertainty estimates for their responses. First, we compute fine-grained entropy-based uncertainty scores on the training data, capturing the distributional variability of model outputs in embedding space. Second, these scores are calibrated via Platt scaling, producing reliable and human-interpretable uncertainty signals. Finally, the target LLM is post-trained via reinforcement learning to align its policy with these calibrated signals through a verifiable reward function. Unlike post-hoc uncertainty estimation methods, our approach provides interpretable and computationally efficient uncertainty estimates at test time. Experiments show that models trained with our pipeline achieve better calibration than baselines and generalize to unseen tasks without further processing, suggesting that they learn a robust uncertainty reasoning behavior.

LLMs are increasingly deployed in high-stakes domains such as medical triage and legal assistance, often as document-grounded QA systems in which a user provides a description, relevant sources are retrieved, and an LLM generates a prediction. In practice, initial user queries are often underspecified, and a single retrieval pass is insufficient for reliable decision-making, leading to incorrect and overly confident answers. While follow-up questioning can elicit missing information, existing methods typically depend on implicit, unstructured confidence signals from the LLM, making it difficult to determine what remains unknown, what information matters most, and when to stop asking questions. We propose InfoGatherer, a framework that gathers missing information from two complementary sources: retrieved domain documents and targeted follow-up questions to the user. InfoGatherer models uncertainty using Dempster-Shafer belief assignments over a structured evidential network, enabling principled fusion of incomplete and potentially contradictory evidence from both sources without prematurely collapsing to a definitive answer. Across legal and medical tasks, InfoGatherer outperforms strong baselines while requiring fewer turns. By grounding uncertainty in formal evidential theory rather than heuristic LLM signals, InfoGatherer moves towards trustworthy, interpretable decision support in domains where reliability is critical.

Reliable deployment of large language models (LLMs) requires accurate uncertainty estimation. Existing methods are predominantly answer-first, producing confidence only after generating an answer, which measure the correctness of a specific response and limits practical usability. We study a confidence-first paradigm, where the model outputs its confidence before answering, interpreting this score as the model's probability of answering the question correctly under its current policy. We propose CoCA(Co-optimized Confidence and Answers), a GRPO reinforcement learning framework that jointly optimizes confidence calibration and answer accuracy via segmented credit assignment. By assigning separate rewards and group-relative advantages to confidence and answer segments, CoCA enables stable joint optimization and avoids reward hacking. Experiments across math, code, and factual QA benchmarks show improved calibration and uncertainty discrimination while preserving answer quality, thereby enabling a broader range of downstream applications.

Qualitative analysis of open-ended interviews plays a central role in ethnographic and economic research by uncovering individuals' values, motivations, and culturally embedded financial behaviors. While large language models (LLMs) offer promising support for automating and enriching such interpretive work, their ability to produce nuanced, reliable interpretations under inherent task ambiguity remains unclear. In our work we evaluate LLMs on the task of identifying the top three human values expressed in long-form interviews based on the Schwartz Theory of Basic Values framework. We compare their outputs to expert annotations, analyzing both performance and uncertainty patterns relative to the experts. Results show that LLMs approach the human ceiling on set-based metrics (F1, Jaccard) but struggle to recover exact value rankings, as reflected in lower RBO scores. While the average Schwartz value distributions of most models closely match those of human analysts, their uncertainty structures across the Schwartz values diverge from expert uncertainty patterns. Among the evaluated models, Qwen performs closest to expert-level agreement and exhibits the strongest alignment with expert Schwartz value distributions. LLM ensemble methods yield consistent gains across metrics, with Majority Vote and Borda Count performing best. Notably, systematic overemphasis on certain Schwartz values, like Security, suggests both the potential of LLMs to provide complementary perspectives and the need to further investigate model-induced value biases. Overall, our findings highlight both the promise and the limitations of LLMs as collaborators in inherently ambiguous qualitative value analysis.

Large Language Models (LLMs) have recently been successfully applied to regression tasks -- such as time series forecasting and tabular prediction -- by leveraging their in-context learning abilities. However, their autoregressive decoding process may be ill-suited to continuous-valued outputs, where obtaining predictive distributions over numerical targets requires repeated sampling, leading to high computational cost and inference time. In this work, we investigate whether distributional properties of LLM predictions can be recovered without explicit autoregressive generation. To this end, we study a set of regression probes trained to predict statistical functionals (e.g., mean, median, quantiles) of the LLM's numerical output distribution directly from its internal representations. Our results suggest that LLM embeddings carry informative signals about summary statistics of their predictive distributions, including the numerical uncertainty. This investigation opens up new questions about how LLMs internally encode uncertainty in numerical tasks, and about the feasibility of lightweight alternatives to sampling-based approaches for uncertainty-aware numerical predictions.

Autonomous agents are increasingly entrusted with complex, long-horizon tasks, ranging from mathematical reasoning to software generation. While agentic workflows facilitate these tasks by decomposing them into multi-step reasoning chains, reliability degrades significantly as the sequence lengthens. Specifically, minor interpretation errors in natural-language instructions tend to compound silently across steps. We term this failure mode accumulated semantic ambiguity. Existing approaches to mitigate this often lack runtime adaptivity, relying instead on static exploration budgets, reactive error recovery, or single-path execution that ignores uncertainty entirely. We formalize the multi-step reasoning process as a Noisy MDP and propose DenoiseFlow, a closed-loop framework that performs progressive denoising through three coordinated stages: (1)Sensing estimates per-step semantic uncertainty; (2)Regulating adaptively allocates computation by routing between fast single-path execution and parallel exploration based on estimated risk; and (3)Correcting performs targeted recovery via influence-based root-cause localization. Online self-calibration continuously aligns decision boundaries with verifier feedback, requiring no ground-truth labels. Experiments on six benchmarks spanning mathematical reasoning, code generation, and multi-hop QA show that DenoiseFlow achieves the highest accuracy on every benchmark (83.3% average, +1.3% over the strongest baseline) while reducing cost by 40--56% through adaptive branching. Detailed ablation studies further confirm framework-level's robustness and generality. Code is available at https://anonymous.4open.science/r/DenoiseFlow-21D3/.

Despite their capabilities, Multimodal Large Language Models (MLLMs) may produce plausible but erroneous outputs, hindering reliable deployment. Accurate uncertainty metrics could enable escalation of unreliable queries to human experts or larger models for improved performance. However, existing uncertainty metrics have practical constraints, such as being designed only for specific modalities, reliant on external tools, or computationally expensive. We introduce UMPIRE, a training-free uncertainty quantification framework for MLLMs that works efficiently across various input and output modalities without external tools, relying only on the models' own internal modality features. UMPIRE computes the incoherence-adjusted semantic volume of sampled MLLM responses for a given task instance, effectively capturing both the global semantic diversity of samples and the local incoherence of responses based on internal model confidence. We propose uncertainty desiderata for MLLMs and provide theoretical analysis motivating UMPIRE's design. Extensive experiments show that UMPIRE consistently outperforms baseline metrics in error detection and uncertainty calibration across image, audio, and video-text benchmarks, including adversarial and out-of-distribution settings. We also demonstrate UMPIRE's generalization to non-text output tasks, including image and audio generation.

Concept Bottleneck Models (CBMs) provide inherent interpretability by first mapping input samples to high-level semantic concepts, followed by a combination of these concepts for the final classification. However, the annotation of human-understandable concepts requires extensive expert knowledge and labor, constraining the broad adoption of CBMs. On the other hand, there are a few works that leverage the knowledge of large language models (LLMs) to construct concept bottlenecks. Nevertheless, they face two essential limitations: First, they overlook the uncertainty associated with the concepts annotated by LLMs and lack a valid mechanism to quantify uncertainty about the annotated concepts, increasing the risk of errors due to hallucinations from LLMs. Additionally, they fail to incorporate the uncertainty associated with these annotations into the learning process for concept bottleneck models. To address these limitations, we propose a novel uncertainty-aware CBM method, which not only rigorously quantifies the uncertainty of LLM-annotated concept labels with valid and distribution-free guarantees, but also incorporates quantified concept uncertainty into the CBM training procedure to account for varying levels of reliability across LLM-annotated concepts. We also provide the theoretical analysis for our proposed method. Extensive experiments on the real-world datasets validate the desired properties of our proposed methods.

Given a black-box AI system and a task, at what confidence level can a practitioner trust the system's output? We answer with a reliability level -- a single number per system-task pair, derived from self-consistency sampling and conformal calibration, that serves as a black-box deployment gate with exact, finite-sample, distribution-free guarantees. Self-consistency sampling reduces uncertainty exponentially; conformal calibration guarantees correctness within 1/(n+1) of the target level, regardless of the system's errors -- made transparently visible through larger answer sets for harder questions. Weaker models earn lower reliability levels (not accuracy -- see Definition 2.4): GPT-4.1 earns 94.6% on GSM8K and 96.8% on TruthfulQA, while GPT-4.1-nano earns 89.8% on GSM8K and 66.5% on MMLU. We validate across five benchmarks, five models from three families, and both synthetic and real data. Conditional coverage on solvable items exceeds 0.93 across all configurations; sequential stopping reduces API costs by around 50%.

Structured Outputs from current LLMs exhibit sporadic errors, hindering enterprise AI deployment. We present CONSTRUCT, a real-time uncertainty estimator that scores the trustworthiness of LLM Structured Outputs. Lower-scoring outputs are more likely to contain errors, enabling automatic prioritization of limited human review bandwidth. CONSTRUCT additionally scores the trustworthiness of each field within a Structured Output, helping reviewers quickly identify which parts of the output are incorrect. Our method is suitable for any LLM (including black-box LLM APIs without logprobs), does not require labeled training data or custom model deployment, and supports complex Structured Outputs with heterogeneous fields and nested JSON schemas. We also introduce one of the first public LLM Structured Output benchmarks with reliable ground-truth values. Over this four-dataset benchmark, CONSTRUCT detects errors in outputs from various LLMs (including Gemini 3 and GPT-5) with significantly higher precision/recall than existing techniques.

With the widespread adoption of large language models (LLMs) in natural language processing, prompt engineering and retrieval-augmented generation (RAG) have become mainstream to enhance LLMs' performance on complex tasks. However, LLMs generate outputs autoregressively, leading to inevitable output uncertainty. Since model performance is highly sensitive to prompt design, precise uncertainty measurement is crucial for reliable prompt optimization. For multi-class multiple-choice (understanding) tasks, conventional uncertainty measures (e.g., entropy) based on output probabilities treat all classes equally and ignore class prior differences in pretraining corpora. This failure to distinguish spurious confidence (from priors) from true certainty (from contextual understanding) results in poor confidence calibration. To address this, we propose Log-Scale Focal Uncertainty (LSFU), a first-token-based metric inspired by focal loss. LSFU incorporates label prior probabilities as a risk-modulation factor to suppress noise from high-frequency classes and emphasize risk for low-frequency long-tail classes, with a dynamic weighting mechanism unifying the measurement scale. Based on LSFU, we further propose the uncertainty-calibrated prompt optimization framework (UCPOF), which leverages the first token of model outputs to select high-quality exemplars and dynamically optimize prompts. Comprehensive evaluations show UCPOF improves average accuracy by 6.03% over few-shot baselines, surpasses always-on full RAG by 5.75% in overall average accuracy, and reduces the average retrieval trigger rate by 50.66%. By adaptively triggering RAG only for high-uncertainty samples, our framework significantly lowers computational costs while maintaining state-of-the-art performance.

Uncertainty quantification has emerged as an effective approach to closed-book hallucination detection for LLMs, but existing methods are largely designed for short-form outputs and do not generalize well to long-form generation. We introduce a taxonomy for fine-grained uncertainty quantification in long-form LLM outputs that distinguishes methods by design choices at three stages: response decomposition, unit-level scoring, and response-level aggregation. We formalize several families of consistency-based black-box scorers, providing generalizations and extensions of existing methods. We also introduce FactScore-STEM-Geo, a new 400-question long-form QA dataset spanning four categories across STEM and Geography. In our experiments across multiple LLMs and datasets, we find 1) claim-response entailment consistently performs better or on par with more complex claim-level scorers, 2) claim-level scoring generally yields better results than sentence-level scoring, and 3) uncertainty-aware decoding is highly effective for improving the factuality of long-form outputs. Our framework clarifies relationships between prior methods, enables apples-to-apples comparisons, and provides practical guidance for selecting components for fine-grained UQ.

We argue that uncertainty is a key and understudied limitation of LLMs' performance in creative writing, which is often characterized as trite and cliché-ridden. Literary theory identifies uncertainty as a necessary condition for creative expression, while current alignment strategies steer models away from uncertain outputs to ensure factuality and reduce hallucination. We formalize this tension by quantifying the ``uncertainty gap'' between human-authored stories and model-generated continuations. Through a controlled information-theoretic analysis of 28 LLMs on high-quality storytelling datasets, we demonstrate that human writing consistently exhibits significantly higher uncertainty than model outputs. We find that instruction-tuned and reasoning models exacerbate this trend compared to their base counterparts; furthermore, the gap is more pronounced in creative writing than in functional domains, and shows a consistent correlation with writing quality. Achieving human-level creativity requires new uncertainty-aware alignment paradigms that can distinguish between destructive hallucinations and the constructive ambiguity required for literary richness.

The rapid rise of large language models (LLMs) is reshaping the landscape of automatic assessment in education. While these systems demonstrate substantial advantages in adaptability to diverse question types and flexibility in output formats, they also introduce new challenges related to output uncertainty, stemming from the inherently probabilistic nature of LLMs. Output uncertainty is an inescapable challenge in automatic assessment, as assessment results often play a critical role in informing subsequent pedagogical actions, such as providing feedback to students or guiding instructional decisions. Unreliable or poorly calibrated uncertainty estimates can lead to unstable downstream interventions, potentially disrupting students' learning processes and resulting in unintended negative consequences. To systematically understand this challenge and inform future research, we benchmark a broad range of uncertainty quantification methods in the context of LLM-based automatic assessment. Although the effectiveness of these methods has been demonstrated in many tasks across other domains, their applicability and reliability in educational settings, particularly for automatic grading, remain underexplored. Through comprehensive analyses of uncertainty behaviors across multiple assessment datasets, LLM families, and generation control settings, we characterize the uncertainty patterns exhibited by LLMs in grading scenarios. Based on these findings, we evaluate the strengths and limitations of different uncertainty metrics and analyze the influence of key factors, including model families, assessment tasks, and decoding strategies, on uncertainty estimates. Our study provides actionable insights into the characteristics of uncertainty in LLM-based automatic assessment and lays the groundwork for developing more reliable and effective uncertainty-aware grading systems in the future.

Temperature scaling is a simple method that allows to control the uncertainty of probabilistic models. It is mostly used in two contexts: improving the calibration of classifiers and tuning the stochasticity of large language models (LLMs). In both cases, temperature scaling is the most popular method for the job. Despite its popularity, a rigorous theoretical analysis of the properties of temperature scaling has remained elusive. We investigate here some of these properties. For classification, we show that increasing the temperature increases the uncertainty in the model in a very general sense (and in particular increases its entropy). However, for LLMs, we challenge the common claim that increasing temperature increases diversity. Furthermore, we introduce two new characterisations of temperature scaling. The first one is geometric: the tempered model is shown to be the information projection of the original model onto the set of models with a given entropy. The second characterisation clarifies the role of temperature scaling as a submodel of more general linear scalers such as matrix scaling and Dirichlet calibration: we show that temperature scaling is the only linear scaler that does not change the hard predictions of the model.

Accurate confidence estimation is critical for reliable use of large language models (LLMs). Prior work on LLM calibration largely focuses on response-level confidence, which estimates the correctness of a single generated output. However, this formulation is misaligned with many practical settings where the central question is how likely a model is to solve a query overall. We show that this mismatch results from the stochastic nature of modern LLM decoding, under which single-response correctness fails to reflect underlying model capability. To address this issue, we introduce capability calibration, a new evaluation framework for measuring how well query-level confidence aligns with a model's expected accuracy on individual queries. We formally distinguish capability calibration (CC) from response calibration (RC) and show that the two differ both theoretically and empirically. We further show that CC is better suited than RC to applications like pass@k prediction and inference budget allocation. Finally, we evaluate common confidence estimation methods to understand the practical feasibility of CC.

Running the same LLM agent on identical inputs yields 2.3-4.2 distinct action sequences per 10 runs; this behavioral variance constitutes a training-free, black-box uncertainty signal that instantiates selective classification and distribution-free calibration for agentic systems. Across 8,000 runs of four models on 200 HotpotQA questions, consistent tasks (at most 2 unique paths) achieve 82-87% accuracy while inconsistent tasks (4 or more paths) achieve 41-65%, a gap that survives controls for task difficulty. Divergence concentrates at step 2 (50.5% of Llama tasks), and consistency metrics detect failures with AUROC 0.62-0.78. Exploiting this signal, selective prediction (answering only when k=3 runs agree) achieves 87-88% accuracy at 54-62% coverage, a 6-14pp gain over single-run baselines, and matches a split-conformal baseline without a held-out calibration set. A cross-benchmark validation on SWE-bench (50 tasks, 1,000 runs) preserves the consistency hierarchy while revealing an ~8x spread in mean trajectory length across models, and bootstrap analysis shows single-run evaluations misrank models 29.3% of the time.

Large language models often struggle to recognize their knowledge limits in closed-book question answering, leading to confident hallucinations. While decomposed prompting is typically used to improve accuracy, we investigate its impact on reliability. We evaluate three task-equivalent prompting regimes: Direct, Assistive, and Incremental, across different model scales and multi-hop QA benchmarks. We find that although accuracy gains from decomposition diminish in frontier models, disagreements between prompting regimes remain highly indicative of potential errors. Because factual knowledge is typically stable while hallucinations are stochastic, cross-regime agreement provides a precise signal of internal uncertainty. We leverage this signal to implement a training-free abstention policy that requires no retrieval or fine-tuning. Our results show that disagreement-based abstention outperforms standard uncertainty baselines as an error detector, improving both F1 and AUROC across settings. This demonstrates that decomposition-based prompting can serve as a practical diagnostic probe for model reliability in closed-book QA.

Large language models present challenges for principled uncertainty quantification, in part due to their complexity and the diversity of their outputs. Semantic dispersion, or the variance in the meaning of sampled answers, has been proposed as a useful proxy for model uncertainty, but the associated computational cost prohibits its use in latency-critical applications. We show that sampled semantic distributions can be distilled into lightweight student models which estimate a prompt-conditioned density before the language model generates an answer token. The student model predicts a semantic distribution over possible answers; the entropy of this distribution provides a prompt-level uncertainty signal, and the probability density allows answer-level reliability evaluation. Across experiments on TriviaQA and MMLU, we find our student models perform competitively relative to the teacher's sampled semantic dispersion on a hallucination prediction task, whilst offering additional uncertainty primitives for out-of-domain detection and multiple-choice answer selection. We term this technique Semantic Self-Distillation (SSD), which can serve as a general framework for distilling predictive uncertainty in complex output spaces beyond language.

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.

Large-scale language models (LLMs) often offer clinical judgments based on incomplete information, increasing the risk of misdiagnosis. Existing studies have primarily evaluated confidence in single-turn, static settings, overlooking the coupling between confidence and correctness as clinical evidence accumulates during real consultations, which limits their support for reliable decision-making. We propose the first benchmark for assessing confidence in multi-turn interaction during realistic medical consultations. Our benchmark unifies three types of medical data for open-ended diagnostic generation and introduces an information sufficiency gradient to characterize the confidence-correctness dynamics as evidence increases. We implement and compare 27 representative methods on this benchmark; two key insights emerge: (1) medical data amplifies the inherent limitations of token-level and consistency-level confidence methods, and (2) medical reasoning must be evaluated for both diagnostic accuracy and information completeness. Based on these insights, we present MedConf, an evidence-grounded linguistic self-assessment framework that constructs symptom profiles via retrieval-augmented generation, aligns patient information with supporting, missing, and contradictory relations, and aggregates them into an interpretable confidence estimate through weighted integration. Across two LLMs and three medical datasets, MedConf consistently outperforms state-of-the-art methods on both AUROC and Pearson correlation coefficient metrics, maintaining stable performance under conditions of information insufficiency and multimorbidity. These results demonstrate that information adequacy is a key determinant of credible medical confidence modeling, providing a new pathway toward building more reliable and interpretable large medical models.

Confidence estimation (CE) indicates how reliable the answers of large language models are and impacts user trust and decision-making. Existing evaluations mainly concern the alignment between confidence and correctness, but ignore the variability of language: confidence estimates should remain consistent under semantically equivalent prompts or answer variations, while changing when answer meaning differs, as this may indicate a change in correctness. Therefore, we introduce a novel evaluation framework based on three complementary properties: robustness to prompt perturbations, stability across semantically equivalent answers, and sensitivity to semantically different answers. We show that these metrics are largely independent from existing CE metrics, and that common CE methods often fail on them: while most methods achieve high robustness and stability, they struggle to distinguish semantically different answers, potentially because they do not effectively leverage generation-side information. Overall, our framework exposes overlooked limitations of current CE evaluations and provides guidance for selecting confidence estimators for real-world applications.