LLM Uncertainty Estimation

LLM: Large Language Model

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38 papers in the last four weeks, up 111% on the four weeks before. 0.4% of all new papers.

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Latest papers 298

Mar 27, 2026cs.CL

Ask or Assume? Uncertainty-Aware Clarification-Seeking in Coding Agents

As Large Language Model (LLM) agents are increasingly deployed in open-ended domains like software engineering, they frequently encounter underspecified instructions that lack crucial context. While human developers naturally resolve underspecification by asking clarifying questions, current agents are largely optimized for autonomous execution. In this work, we systematically evaluate the clarification-seeking abilities of LLM agents on an underspecified variant of SWE-bench Verified. We propose an uncertainty-aware multi-agent scaffold that decouples underspecification detection from code execution. Across both proprietary and open-weight frontier LLMs, our scaffold achieves a 69.40% task resolve rate, significantly outperforming a standard single-agent setup and closing the performance gap with agents operating on fully specified instructions. Furthermore, we find that the multi-agent system exhibits well-calibrated information-seeking behavior, conserving queries on simple tasks while proactively seeking information on more complex issues. These findings indicate that current models can be turned into proactive collaborators, where agents independently recognize when to ask questions to elicit missing information in real-world, underspecified tasks.

Nicholas Edwards, Sebastian Schuster

Faculty of Computer Science, University of Vienna, Vienna, Austria · UniVie Doctoral School Computer Science, University of Vienna, Vienna, Austria

Multi-Agent LLM Systems AI Coding Agents LLM Agents LLM Uncertainty Estimation

Mar 26, 2026cs.CL

Do LLMs Know What They Know? Measuring Metacognitive Efficiency with Signal Detection Theory

Standard evaluation of LLM confidence relies on calibration metrics (ECE, Brier score) that conflate how much a model knows (Type-1 accuracy) with how well its confidence signal tracks that knowledge (Type-2 metacognitive sensitivity). We apply Signal Detection Theory (SDT) to decompose these capacities, treating token-level normalised log-probability as a graded confidence variable and answer correctness as the state to be discriminated. We characterise the Type-2 ROC of this signal, including its unequal-variance structure via z-ROC analysis, and -- because the meta-d' efficiency ratio is not well defined for open-ended QA, which lacks a two-alternative Type-1 decision -- quantify metacognitive efficiency with a model-free information measure, normalised metacognitive information (meta-I_2r). Applied to four LLMs (Llama-3-8B-Instruct, Mistral-7B-Instruct-v0.3, Llama-3-8B-Base, Gemma-2-9B-Instruct) across 224,000 factual QA trials, we find: (1) metacognitive information varies more than two-fold across models and co-varies inversely with accuracy -- the least accurate model has the most informative confidence -- though with four models this ordering cannot be separated from an error-difficulty confound, so we report it as coupling, not decoupling; (2) the confidence signal has model-specific unequal-variance structure (z-ROC slopes 0.81 to 1.18) invisible to calibration metrics; (3) metacognitive information is domain-specific, strongest in Arts & Literature for every model; (4) temperature dissociates Type-1 accuracy from metacognitive information, which stays stable while accuracy shifts. All estimates carry permutation nulls and bootstrap confidence intervals. Pre-registered; code and data public.

Jon-Paul Cacioli

Independent Researcher Melbourne, Australia

Confidence Estimation in Language Models Language Model Calibration LLM Uncertainty Estimation Metacognition in Language Models

Mar 26, 2026cs.AI

The Anatomy of Uncertainty in LLMs

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.

Aditya Taparia, Ransalu Senanayake, Kowshik Thopalli +1

School of Computing and Augmented Intelligence, Arizona State University · Lawrence Livermore National Laboratory

LLM Auditing LLM Reliability LLM Uncertainty Estimation Uncertainty Decomposition Epistemic Uncertainty

Mar 23, 2026cs.AI

INTRYGUE: Induction-Aware Entropy Gating for Reliable RAG Uncertainty Estimation

While retrieval-augmented generation (RAG) enhances LLM performance, it does not eliminate hallucinations, making accurate detection essential. Uncertainty-based methods are attractive for this purpose because they can be integrated into real-world pipelines with little overhead. One of the most widely used uncertainty signals is predictive entropy. We show, however, that entropy can be unreliable in RAG settings and trace this limitation to two opposing internal effects. Induction heads, which copy patterns from earlier context, causally support correct responses and lower predictive entropy, but they also appear to co-activate entropy neurons that push it back up. As a result, correct, context-grounded responses can still receive high uncertainty scores. To address this, we propose INTRYGUE (Induction-Aware Entropy Gating for Uncertainty Estimation), a training-free, mechanistically grounded method that gates predictive entropy by an attention-based estimate of induction-head activity. Evaluated across four RAG-style benchmarks and six open-source LLMs (4B to 13B parameters), INTRYGUE performs competitively against a wide range of baselines, matching or exceeding the strongest of them in most settings. Our findings suggest that hallucination detection in RAG benefits from combining predictive uncertainty with interpretable internal signals of context utilization.

Alexandra Kuleshova, Andrei Volodichev, Daria Kotova +1

Applied AI Institute

Hallucination Detection LLM Interpretability LLM Uncertainty Estimation Induction Heads

Mar 9, 2026cs.CL

Learning When to Sample: Confidence-Aware Selective Sampling for Efficient Chain-of-Thought Reasoning

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.

Juming Xiong, Kevin Guo, Congning Ni +7

1Vanderbilt University · 2Vanderbilt University Medical Center · 3Intuit AI Research

CoT Reasoning Efficient Language Model Reasoning LLM Inference Acceleration Adaptive Sampling LLM Uncertainty Estimation LLM Reasoning+1

Feb 19, 2026cs.CL

Fine-Grained Uncertainty Quantification for Long-Form Language Model Outputs: A Comparative Study

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.

Dylan Bouchard, Mohit Singh Chauhan, Viren Bajaj +1

CVS Health, Wellesley, MA

LLM Hallucination Mitigation Hallucination in Language Models Factual Consistency Evaluation LLM Reliability LLM Hallucination Detection LLM Uncertainty Estimation

Feb 14, 2026cs.CL

On Calibration of Large Language Models: From Response To Capability

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.

Sin-Han Yang, Cheng-Kuang Wu, Chieh-Yen Lin +3

Appier AI Research · National Taiwan University

LLM Evaluation Confidence Estimation in Language Models Language Model Calibration LLM Reliability LLM Uncertainty Estimation

Feb 12, 2026cs.AI

When Agents Disagree With Themselves: Behavioral Consistency as an Uncertainty Signal for LLM Agents

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.

Aman Mehta

Snowflake AI Research

AI Agent Reliability Selective Prediction LLM Agent Evaluation Reasoning Consistency in Language Models Language Model Calibration LLM Reliability+2

Feb 4, 2026cs.CL

Decomposed Prompting Does Not Fix Knowledge Gaps, But Helps Models Say "I Don't Know"

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.

Dhruv Madhwal, Lyuxin David Zhang, Dan Roth +2

Arizona State University · University of Pennsylvania · Oracle AI

LLM Prompting Question Decomposition LLM Reliability LLM Hallucination Detection LLM Uncertainty Estimation LLM Abstention

Feb 4, 2026cs.CL

Semantic Self-Distillation for Language Model Uncertainty

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.

Edward Phillips, Sean Wu, Fredrik K. Gustafsson +2

Department of Engineering Science, University of Oxford · Oxford Suzhou Centre for Advanced Research, University of Oxford, Suzhou

Uncertainty Quantification Confidence Estimation in Language Models LLM Reliability Language Model Distillation LLM Uncertainty Estimation

Feb 2, 2026cs.LG

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.

Qihao Wen, Jiahao Wang, Yang Nan +3

University of Arizona · Michigan State University

LLM Reliability LLM Uncertainty Estimation LLM Reasoning

Jan 12, 2026cs.CL

Calibration Is Not Enough: Evaluating Confidence Estimation Under Language Variations

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: \textbf{robustness} to prompt perturbations, \textbf{stability} across semantically equivalent answers, and \textbf{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.

Yuxi Xia, Dennis Ulmer, Terra Blevins +3

Faculty of Computer Science, UniVie Doctoral School Computer Science · Faculty of Philological and Cultural Studies, University of Vienna, Austria · ILLC, University of Amsterdam, Netherlands +2

LLM Evaluation Confidence Estimation in Language Models Language Model Self-Assessment Language Model Calibration LLM Reliability LLM Uncertainty Estimation

Nov 26, 2025cs.LG

Aligning LLMs with Biomedical Knowledge using Balanced Fine-Tuning

Engineering LLMs to accelerate life sciences research requires a robust alignment with biomedical knowledge. We observe that biomedical text exhibits a fundamentally different uncertainty structure from general text: dense low-confidence runs encode epistemic knowledge gaps (dense causal chains, rare entities) rather than the sparse aleatoric stylistic variation typical of general text. Based on this discovery, we propose Balanced Fine-Tuning (BFT), a dual-scale post-training method that combines group-normalized token reweighting with sequence-level reallocation toward knowledge-dense samples exhibiting dense epistemic uncertainty. Across medical evaluation, biological reasoning, sparse-reward RL, and biological representation tasks, BFT provides more consistent gains than SFT and DFT under a shared training setup. When replacing the default closed-source backbones in GeneAgent (GPT-4o) and VCWorld (Gemini-2.5-Flash), the BFT-aligned 70B model delivers stronger performance across biological process reasoning and chemical perturbation prediction. Critically, all BFT variants further improve after subsequent GRPO with sparse rewards, while SFT and DFT degrade, suggesting that epistemic-aware post-training provides a more robust policy initialization. Beyond text generation, BFT-aligned LLMs produce more accurate and professional biomedical profile texts; after encoding these profiles with a text embedding model, the resulting representations support gene-level, cell-level, and perturbation-response tasks, suggesting that BFT-enhanced generation can facilitate biological representation and, in turn, broader biomedical downstream tasks.

Zhenchao Tang, Fang Wang, Haohuai He +13

Tencent AI for Life Sciences Lab, Shenzhen, China. · Sun Yat-sen University, Shenzhen, China. · The Hong Kong Polytechnic University, Hong Kong SAR, China. +2

LLM Alignment LLM Fine-Tuning LLM Uncertainty Estimation LLM Post-Training Medical LLMs

Nov 20, 2025cs.AI

MedBayes-Lite: A Clinical Uncertainty Governance Layer for Risk-Aware Medical Decision Support

Clinical language models often assign high confidence to incorrect predictions, particularly in high-severity and out-of-distribution cases. We present MedBayes-Lite, a retraining-free uncertainty governance layer for transformer-based clinical predictors. It combines Monte Carlo dropout, predictive calibration, and confidence-guided abstention to defer low-confidence predictions for human review, adding no trainable parameters. Evaluated on MedMCQA and MedQA-USMLE, MedBayes-Lite reduces expected calibration error by 0.23 to 0.33 and drives harmful overconfident errors (confident, incorrect, high-severity predictions) toward zero. Under domain shift from MedMCQA to MedQA-USMLE, it reduces confident high-severity errors from about 21% to near zero while roughly halving calibration drift. We also introduce the Clinical Uncertainty Score (CUS), which strongly correlates with harmful overconfidence (r approximately 0.88). Although the framework does not improve risk-coverage ranking, and temperature scaling or deep ensembles may provide advantages in calibration cost or risk ranking, MedBayes-Lite offers a practical calibration-and-abstention layer that reduces confident high-severity errors in clinical question-answering benchmarks.

Elias Hossain, Md Mehedi Hasan Nipu, Maleeha Sheikh +5

College of Engineering and Computer Science, University of Central Florida, Orlando, FL 32816, USA · Department of Computer Science and Engineering, North South University, Dhaka 1229, Bangladesh · Department of Electrical and Computer Engineering, Purdue University Fort Wayne, Fort Wayne, IN 46805, USA +4

Selective Prediction Healthcare Clinical Decision Support LLM Uncertainty Estimation Medical LLMs Uncertainty Calibration

Nov 4, 2025cs.CL

Sequential Bayesian Evaluation of Large Language Model Behavior

It is increasingly important to evaluate the characteristics of systems based on large language models (LLMs). Evaluations in this context often rely on a curated benchmark set of input prompts provided to the LLM, where the output for each prompt may be assigned a binary or ordinal score and the aggregation of scores across prompts is then used as a summary evaluation. In this paper, we develop a Bayesian approach for quantifying the uncertainty that arises in such evaluation metrics as a result of the stochasticity of the LLM-based systems; the same prompt may exhibit different outcomes on repeated runs. Our framework leads naturally to a sequential evaluation, in which we leverage the Bayesian model to preferentially select which prompts in the benchmark to use next, enabling more cost-effective LLM evaluations. We demonstrate this approach through four case studies: pairwise LLM preferences in interactive dialogue (MT-Bench), refusal rates on adversarial inputs (JailbreakBench), embodied agentic reasoning (ALFWorld), and agentic web-search Q&A (GAIA). Our results illustrate how a Bayesian approach can provide insightful uncertainty quantification about the behavior of blackbox LLM-based systems in a manner that is not accessible via deterministic or single-run evaluations.

Saatvik Kher, Shang Wu, Rachel Longjohn +2

Department of Computer Science, University of California, Irvine · Department of Statistics, University of California, Irvine

LLM Evaluation Language Model Generation Evaluation LLM Uncertainty Estimation

Oct 5, 2025cs.CL

When Guessing is Rewarded: Rethinking Language Model Evaluation with Distributional Uncertainty Scoring

Standard language model evaluation assigns scores to single predicted answers, rewarding high-confidence responses regardless of how residual probability mass is distributed over alternative options. This creates a systematic pressure toward overconfident guessing: under accuracy-based schemes, a model maximises its expected score by always committing to an answer rather than abstaining, even when its uncertainty is high. While penalty-based approaches partially address this by raising the confidence threshold for strategic guessing, they still treat all sub-threshold responses identically, ignoring a fundamental distinction in how models can express uncertainty - for example between hedging toward incorrect answers versus hedging toward "I don't know" responses. This paper introduces a novel evaluation metric to solve this problem of not considering a model's entire probability distribution over answer choices. The metric naturally distinguishes between harmful overconfidence in wrong answers and uncertainty expressed through abstention, providing scores in an interpretable default range. Through theoretical analysis and illustrative examples, the metric is shown to offer a more nuanced and aligned evaluation paradigm that incentivises models to express genuine uncertainty rather than guessing. Adapting 12 existing evaluation benchmarks to the metric's variants and measuring performance on six language models shows that for half of the tested benchmarks scores are negative across all tested models, indicating significant tendencies towards hallucination.

Thomas F Burns

Aleph Alpha Research

LLM Evaluation Language Model Generation Evaluation LLM Reliability LLM Hallucination Detection LLM Uncertainty Estimation LLM Abstention

Sep 17, 2025cs.CL

Geometric Uncertainty for Detecting and Correcting Hallucinations in LLMs

Large language models are known to hallucinate, generating linguistically plausible but incorrect answers to questions. Uncertainty quantification has been proposed as a strategy to detect such behaviour, but existing methods lack a unified framework to assess reliability at both the prompt and answer level. We introduce a geometric framework which quantifies language model uncertainty at both levels by explicitly modelling a prompt-conditioned semantic distribution in answer embedding space. Our approach is black-box and sampling-based; we generate multiple answers per prompt, and use archetypal analysis to estimate a geometric support for the answer distribution. At the prompt level, we approximate the distribution entropy to quantify uncertainty; for each individual answer, we then use notions of atypicality to assess its reliability relative to the batch. We employ our framework to not only detect hallucinations but correct them, by selecting the batch example deemed most reliable. Experiments show that our framework performs comparably to or better than prior methods on short form question-answering datasets, and achieves superior results on medical datasets where hallucinations carry particularly critical risks. Beyond pure performance, we suggest the theoretical grounding of our work provides support for semantic distributions as useful objects of study for language model uncertainty.

Edward Phillips, Sean Wu, Soheila Molaei +3

Department of Engineering Science, University of Oxford · GlaxoSmithKline · Oxford Suzhou Centre for Advanced Research

Uncertainty Quantification LLM Hallucination Mitigation Hallucination in Language Models LLM Reliability LLM Hallucination Detection LLM Uncertainty Estimation

Aug 29, 2025cs.CL

PiCSAR: Probabilistic Confidence Selection And Ranking for Reasoning Chains

Best-of-n sampling improves the accuracy of large language models (LLMs) and large reasoning models (LRMs) by generating multiple candidate solutions and selecting the one with the highest reward. The key challenge for reasoning tasks is designing a scoring function that can identify correct reasoning chains without access to ground-truth answers. We propose Probabilistic Confidence Selection And Ranking (PiCSAR): a simple, training-free method that scores each candidate generation using the joint log-likelihood of the reasoning and final answer. The joint log-likelihood of the reasoning and final answer naturally decomposes into reasoning confidence and answer confidence. PiCSAR achieves substantial gains across diverse benchmarks (+10.18 on MATH500, +9.81 on AIME2025), outperforming baselines with at least 2x fewer samples in 16 out of 20 comparisons. Our analysis reveals that correct reasoning chains exhibit significantly higher reasoning and answer confidence, justifying the effectiveness of PiCSAR.

Joshua Ong Jun Leang, Zheng Zhao, Aryo Pradipta Gema +7

Imperial College London · University of Edinburgh · UCL

Confidence Estimation in Language Models Best-of-N Sampling LLM Reranking LLM Uncertainty Estimation Algorithmic Reasoning LLM Reasoning

Jul 24, 2025cs.LG

Toward Efficient Uncertainty in LLMs through Evidential Knowledge Distillation

Accurate uncertainty quantification remains a key challenge for standard LLMs, prompting the adoption of Bayesian and ensemble-based methods. However, such methods typically necessitate computationally expensive sampling, involving multiple forward passes to effectively estimate predictive uncertainty. In this paper, we introduce an approach enabling uncertainty estimation in LLMs without incurring the heavy inference latency typically associated with sampling methods. Specifically, we distill uncertainty-aware teachers - originally requiring multiple forward passes - into single-pass students, fine-tuned using LoRA. We compare two distinct distillation strategies: one in which the student employs traditional softmax-based outputs, and another in which the student leverages Dirichlet-distributed outputs to explicitly model epistemic uncertainty via evidential learning. Empirical evaluation on classification tasks demonstrate that such students can achieve comparable predictive and uncertainty quantification performance relative to their teachers, while requiring only a single forward pass.

Lakshmana Sri Harsha Nemani, P. K. Srijith, Tomasz Kuśmierczyk

Department of Computer Science and Engineering, Indian Institute of Technology Hyderabad, India · Jagiellonian University, Faculty of Mathematics and Computer Science, Kraków, Poland

LLM Uncertainty Estimation Uncertainty-Aware Knowledge Distillation Efficient Language Model Inference Knowledge Distillation Epistemic Uncertainty

Jul 9, 2025cs.CL

On the Effect of Uncertainty on Layer-wise Inference Dynamics

Understanding how large language models (LLMs) internally represent and process their predictions is central to detecting uncertainty and preventing hallucinations. While several studies have shown that models encode uncertainty in their hidden states, it is underexplored how this affects the way they process such hidden states. In this work, we demonstrate that the dynamics of output token probabilities across layers for certain and uncertain outputs are largely aligned, revealing that uncertainty does not seem to affect inference dynamics. Specifically, we use the Tuned Lens, a variant of the Logit Lens, to analyze the layer-wise probability trajectories of final prediction tokens across 11 datasets and 5 models. Using incorrect predictions as those with higher epistemic uncertainty, our results show aligned trajectories for certain and uncertain predictions that both observe abrupt increases in confidence at similar layers. We balance this finding by showing evidence that more competent models may learn to process uncertainty differently. Our findings challenge the feasibility of leveraging simplistic methods for detecting uncertainty at inference. More broadly, our work demonstrates how interpretability methods may be used to investigate the way uncertainty affects inference.

Sunwoo Kim, Haneul Yoo, Alice Oh

School of Computing, KAIST, Daejeon, South Korea.

LLM Inference LLM Interpretability LLM Uncertainty Estimation

May 23, 2025cs.CL

Popular but Wrong: Understanding and Mitigating LLM Overconfidence through Knowledge Popularity

Large language models (LLMs) often produce incorrect answers with high confidence, yet the factors associated with such overconfidence remain insufficiently understood. We study this problem through the lens of knowledge popularity. Using entity-centric factual QA derived from Wikidata triplets, we characterize popularity through question entity popularity, answer popularity, and question-answer co-occurrence. We find two consistent patterns. First, hallucinated answers are far from random: compared with ground-truth answers, they tend to be more popular or more frequently associated with the question entity. Second, confidence is strongly tied to the popularity of generated answers: even among incorrect predictions, more popular answers or those with higher question-answer co-occurrence receive higher confidence. Together, these findings suggest that popular but wrong alternatives may contribute to overconfidence. We further show that popularity-related signals can mitigate overconfidence and improve overall confidence estimation. Across six models and three datasets, incorporating knowledge popularity reduces average confidence on incorrect answers from 0.765 to 0.254 and overall ECE from 0.356 to 0.050, while improving Alignment from 77.08% to 83.72%.

Shiyu Ni, Keping Bi, Jiafeng Guo +1

CAS Key Lab of Network Data Science and Technology, ICT, CAS · State Key Laboratory of AI Safety · University of Chinese Academy of Sciences

LLM Hallucination Mitigation Confidence Estimation in Language Models Hallucination in Language Models Question Answering LLM Reliability LLM Safety+1

Dec 10, 2024cs.CL

Label-Confidence-Aware Uncertainty Estimation in Natural Language Generation

Large Language Models (LLMs) demonstrate remarkable capabilities in generative tasks but pose potential risks due to their tendency to generate hallucinatory responses. Therefore, Uncertainty Quantification (UQ), which aims to distinguish the validity of answers, is crucial for ensuring the safety and robustness of AI systems. However, existing methods primarily rely on measuring the entropy of multiple stochastic samples to represent uncertainty, often overlooking the specific uncertainty information associated with the candidate answer under evaluation. This oversight can lead to biased classification outcomes. In this paper, we investigate the discrepancy between global entropy from multiple samples and local confidence of candidate answer, and propose a Label-Confidence-Aware Uncertainty Quantification (LCA-UQ) method based on Pointwise Kullback-Leibler (PKL) divergence. Our method effectively bridges the gap between the consistency of sampled outputs and the calibration of the candidate answer, thereby enhancing the reliability and stability of uncertainty assessments. Empirical evaluations across a range of popular LLMs and NLP datasets reveal that label sources significantly impact classification. Furthermore, our approach effectively captures the nuances between sampling results and label sources, demonstrating superior performance in uncertainty estimation.

Qinhong Lin, Yinglun Feng, Yuhao Zhang +2

School of Cyberspace Security, Beijing University of Posts and Telecommunications, Beijing, China · QuanCheng Laboratory, Jinan, China

Uncertainty Quantification LLM Uncertainty Estimation Uncertainty Calibration

Jul 20, 2024cs.LG

Prompting the Unknown: Understanding Response Uncertainty in Large Language Models

Large language models (LLMs) are widely used in decision-making across diverse domains. Ensuring the generation of safe and reliable responses is critical for the effective deployment of LLM-based applications, particularly in high-stakes domains such as healthcare and finance. Most of these applications typically use carefully crafted prompts to guide response generation; however, the relationship between prompts and the reliability of LLM-generated responses is not yet fully understood. To address this gap, we propose a novel prompt-response concept model that explains the relationship between the amount of task-relevant information (informativeness) provided in the prompt and the LLM-generated response uncertainty by identifying four sources of response uncertainty: prompt underspecification, model quality, task variability, and semantic redundancy. We prove that response uncertainty decreases as prompt informativeness or model quality increases, mirroring the behavior of epistemic uncertainty in probabilistic models. Our experimental results on real-world datasets further validate our proposed model and corroborate the theoretical results.

Ze Yu Zhang, Arun Verma, Finale Doshi-Velez +1

Department of Computer Science, National University of Singapore, Republic of Singapore · Singapore-MIT Alliance for Research and Technology Centre · Harvard University

LLM Prompting LLM Reliability LLM Uncertainty Estimation Epistemic Uncertainty

Date pendingcs.LG

Evidence for Limited Metacognition in LLMs

The possibility of LLM self-awareness and even sentience is gaining increasing public attention and has major safety and policy implications, but the science of measuring them is still in a nascent state. Here we introduce a novel methodology for quantitatively evaluating metacognitive abilities in LLMs. Taking inspiration from research on metacognition in nonhuman animals, our approach eschews model self-reports and instead tests to what degree models can strategically deploy knowledge of internal states. Using two experimental paradigms, we demonstrate that frontier LLMs introduced since early 2024 show increasingly strong evidence of certain metacognitive abilities, specifically the ability to assess and utilize their own confidence in their ability to answer factual and reasoning questions correctly and the ability to anticipate what answers they would give and utilize that information appropriately. We buttress these behavioral findings with an analysis of the token probabilities returned by the models, which suggests the presence of an upstream internal signal that could provide the basis for metacognition. We further find that these abilities 1) are limited in resolution, 2) emerge in context-dependent manners, and 3) seem to be qualitatively different from those of humans. We also report intriguing differences across models of similar capabilities, suggesting that LLM post-training may have a role in developing metacognitive abilities.

Christopher Ackerman

LLM Evaluation LLM Uncertainty Estimation Metacognition in Language Models

Date pendingcs.CL

Towards Reliable Medical LLMs: Benchmarking and Enhancing Confidence Estimation of Large Language Models in Medical Consultation

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.

Zhiyao Ren, Yibing Zhan, Siyuan Liang +3

Nanyang Technological University, Singapore, Singapore. · Wuhan University, Wuhan, China.

Healthcare Clinical Reasoning LLM Uncertainty Estimation Clinical Language Model Evaluation Medical LLMs

Date pendingcs.AI

Rescaling Confidence: What Scale Design Reveals About LLM Metacognition

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.

Yuyang Dai, Yuxia Wang

INSAIT

Confidence Estimation in Language Models Language Model Calibration LLM Uncertainty Estimation Metacognition in Language Models

Date pendingcs.CL

Decomposing LLM-Judge Uncertainty to Target Expert Labels

An LLM judge evaluates outputs at scale. Experts should label only where it is least sure. Its natural escalation signal conflates two uncertainties: aleatoric, real disagreement in the expert pool, which labels cannot reduce, and epistemic, the judge's ignorance, which labels do reduce. A small Bayesian model separates them: a regression on labels already collected learns how far to trust a black-box judge's prediction. Both components follow as simple formulas, with no sampling or further judge calls. The components isolate on a real LLM judge against exactly known truth, and stated confidence is no guide to its actual error. On real human disagreement (ChaosNLI) the epistemic ranking removes 83% more error than total uncertainty for the same expert labels, though simply escalating the least-labelled items does as well there. We demonstrate we can estimate where a judge is ignorant rather than where experts genuinely disagree, and propose using this to direct expert labelling. Code and data are available at https://github.com/composo-ai/judge-uncertainty-decomposition.

Ryan Lail

Composo AI

Annotator Disagreement LLM-as-a-Judge Uncertainty Quantification Human-in-the-Loop Annotation LLM Uncertainty Estimation Aleatoric Uncertainty+2

Date pendingcs.AI

ActMap: Single-Pass Uncertainty Quantification from Generation-Time Activation Maps

Practical uncertainty quantification (UQ) for large language models must decide, from a single generation, whether a specific answer should be trusted. Existing methods either sample multiple generations, read only output-token probabilities, or reduce the model's internal computation to a single hidden state. We introduce ActMap, a white-box representation that compresses the generation-time hidden-state trajectory (every layer, every generated token) into a fixed

12\times32\times128

tensor of temporal-statistic channels that preserves structure across transformer depth and pooled hidden coordinates. The map is captured during the generation pass with no measurable overhead, has a fixed shape across model depths and hidden sizes, and occupies 96 KiB: a compact artifact that can be retained for audit-relevant generations and probed directly, with occlusion analysis localizing the classifier's signal to mid-depth regions of the map. A lightweight classifier, instantiated as a compact Vision Transformer, reads an estimated correctness probability from each map in a fraction of a millisecond; capacity-matched MLPs perform comparably, indicating the representation itself carries the result. Trained and evaluated in-domain on short-answer QA, direct-answer math, and summarization factuality with three instruction-tuned 7-8B models, ActMap consistently outperforms sampling, token-probability, attention, and embedding baselines, and matches ACT-ViT, a detector trained on dense activation tensors

67\times

larger, at essentially the same mean AUROC with lower calibration error on ten of twelve pairs. The resulting score supports abstention, routing, and selective verification from a single generation, making it a practical primitive for scalable oversight of deployed models.

Jacopo Dardini (University of Bologna), Roberta Calegari (University of Bologna)

University of Bologna, Italy

Uncertainty Quantification Confidence Estimation in Language Models LLM Auditing Language Model Calibration LLM Reliability LLM Uncertainty Estimation