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

Jul 9, 2026cs.AI

When LLMs Agree, Are They Right? Auditing Self-Consistency and Cross-Model Agreement as Confidence Signals

LLM-as-judge (Zheng et al., 2023) is increasingly the default for evaluating AI systems in enterprise pipelines, often scaled to ensembles (Verga et al., 2024) or "mixture-of-experts" (Shazeer et al., 2017) panels of judges. These systems share a key assumption: that consistency -- agreement among judges, or among a model's own samples -- indicates correctness. We show this assumption is unreliable. Agreement is not accuracy: a model can agree with itself, and different models can agree with each other, out of shared bias, a memorized heuristic, or an option-position prior rather than truth. We ask when agreement is nonetheless a usable proxy, in a large-scale cross-runner study: 53 runners drew K=50 samples for assigned overlapping cases across comparisons of model tier, prompting, and scale on GPQA Diamond and AIME -- 265,000 samples. Using majority-correctness as the deployment label and a hierarchical runner-clustered bootstrap, agreement is a positive but weak predictor (rho 0.20-0.59, all positive under item-clustered resampling) whose usefulness is regime-dependent: best for unsaturated mid-tier models and for allocating compute, and worst -- over-confident yet no more accurate -- for the most consistent frontier model (agreement >=0.8 on 77% of GPQA case-result entries, 48% of those wrong). An exploratory cross-family check on three Claude tiers shows the same frontier over-confidence, with confident errors recurring across providers above a marginal-preserving null. Self-consistency is thus a conditional proxy for correctness, not a standalone confidence score. We publicly release the de-identified per-run rows and answer distributions.

Kaihua Ding

University of Pennsylvania

LLM-as-a-Judge LLM Reliability LLM Uncertainty Estimation Self-Consistency in Language Models

Jul 9, 2026cs.CL

Can We Trust LLM's Logic? Quantifying Uncertainty, Coherence, and Robustness via a Graph-Based Framework

Large-Language Models (LLMs) can be prone to flawed and unfaithful reasoning that decoding strategies like Self-Consistency (SC) fail to detect as they evaluate only final-answer agreement while ignoring the logical validity of intermediate steps. This raises three fundamental questions: How can we reliably quantify uncertainty in LLM reasoning? Can semantic, structural, and causal awareness select more faithful reasoning compared to naïve majority voting? and How robust is reasoning topology under adversarial conditions? To address these questions, we introduce GRAPHEVAL, a graph-based reasoning framework that re-frames uncertainty quantification (UQ) as a holistic reasoning fidelity problem. We propose a novel UQ metric, Graph Reasoning Coherence Score (GRCS), that quantifies semantic-structural consensus of the reasoning space and captures pathological mode collapse and confident hallucinations. We find that GRCS is the only metric that is consistently negatively correlated with reasoning faithfulness across both more capable and smaller models. Additionally, we introduce Graph Self-Consistency (GSC), a medoid-based decoding strategy that trades nominal accuracy for reasoning fidelity, exposing the degree to which SC is inflated by unfaithful lucky guesses in smaller models, while preserving or improving accuracy in more capable ones. Finally, through adversarial medoid ablation, we demonstrate that the GSC-selected path acts as a "load-bearing path" and forcing models away from it degrades reasoning faithfulness and, in targeted cases, causes drops in accuracy.

Riccardo Revalor, Jalees Rehman, Debjit Pal

¶Department of Electrical and Computer Engineering · ‡Department of Biochemistry and Molecular Genetics

CoT Faithfulness LLM Reasoning with Graphs Reasoning Evaluation Reasoning Consistency in Language Models Adversarial Robustness of Language Models LLM Uncertainty Estimation+1

Jul 8, 2026cs.CL

Future Confidence Distillation in Large Language Models

Reliable confidence estimation is essential for deploying large language models (LLMs) in confidence-aware systems, where downstream decisions such as retrieval, tool use, and adaptive computation depend on accurately estimating answer reliability. Existing approaches, however, largely treat confidence as a property of completed responses, overlooking how confidence-related information evolves throughout the answering process. In this work, we investigate confidence from a temporal perspective by comparing pre-solution Feeling-of-Knowing (FOK) and post-solution Judgement-of-Learning (JOL) confidence estimates across frontier and open-source LLMs. We show that post-solution confidence is consistently better calibrated and more discriminative than pre-solution confidence, while linear probes trained on hidden representations recover substantially richer confidence-related information than models explicitly verbalise. Building on this observation, we introduce future confidence distillation, which trains predictors operating on pre-solution hidden representations using teacher confidence estimates produced by post-solution correctness probes. Despite requiring only pre-solution representations for inference, distilled predictors recover much of the calibration improvement achieved by post-solution confidence, remain highly sample efficient, and transfer across datasets within the same domain. Together, our findings demonstrate that confidence-related information evolves throughout the answering process and can be anticipated before answer generation is complete, enabling significantly more reliable yet low-cost confidence estimation.

Sahil Kale

University of California, Los Angeles Los Angeles, USA

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

Jul 7, 2026cs.LG

What Predicts Correctness in Text-to-SQL? A Selective-Prediction Study

Evaluating uncertainty in AI-generated SQL queries requires estimating whether a query is correct, where correct means it executes to the same result as a human-written reference. We study which signals predict correctness on hard multi-table text-to-SQL, using AUROC to measure how well each ranks correct queries above incorrect ones. On BIRD and Spider, black-box signals such as string, structural, and execution self-consistency, a schema-relevance score, and query executability all fall between about 0.61 and 0.68 AUROC, with string self-consistency strongest at 0.675; white-box log-probability is similar (0.67). The signals that move past this ceiling are verification-based: an LLM judge scores from 0.72 (GPT-4o-mini) to 0.78 (Claude). Judges from different providers make different errors, so a two-provider ensemble reaches 0.82 AUROC with a well-calibrated probability (expected calibration error 0.03) and supports useful abstention frontiers (for example, answering 27% of questions at 24% selective risk) where self-consistency offers no valid low-risk subset. The pattern holds across two benchmarks, two generators, and two judge providers. We also ask whether a verifier can be trained. Fine-tuned verifiers, both encoder and generative, reach about 0.77 to 0.79 AUROC in-distribution but fall to about 0.66 on unseen schemas; scaling to 7B, adding schema diversity, distilling a strong judge's rationales, and cross-benchmark training all fail to close that gap. Cross-schema transfer appears to track model scale and reasoning rather than fine-tuning. In practice, correctness uncertainty for text-to-SQL lives in reasoning-based signals: a fine-tuned verifier is a good in-domain tool, but a verifier that generalizes across schemas currently means a large frozen reasoning model.

Robert Richardson

Affiliation

LLM Answer Verification Selective Prediction Text-to-SQL LLM Uncertainty Estimation

Jul 7, 2026cs.CL

Estimating Uncertainty from Reasoning: A Large-Scale Study of Multi- and Crosslingual MCQA Performance in LLMs

Uncertainty estimation (UE) enables LLM-powered systems to recognize when to abstain, yet existing research has predominantly focused on English. We present the first large-scale evaluation of UE methods across 22 languages, spanning high-, mid-, and low-resource settings. Using two human-curated Q&A datasets, we compare open and closed box UE methods (nine in total) across different model sizes and architectures while eliciting long-form reasoning, avoiding LLM-as-a-judge and embedding-based scoring, which can introduce evaluation noise. We report three main actionable findings. First, we find that prompting models to reason in English while keeping questions in low-resource languages substantially improves UE performance, suggesting that comprehension of low-resource languages is largely intact, and that the reliability bottleneck lies in generation rather than understanding. Second, prompting models to reason in English closes the UE performance gap between low and high-resource languages, demonstrating that generation language matters more than the question language. Third, the choice of UE method should depend on model scale: at smaller scales, open-box probability-based methods outperform alternatives; at larger scales, closed-box self-verbalized uncertainty becomes superior. Finally, we provide an analysis of threshold selection for selective prediction, offering guidance on calibrating abstention in multilingual settings.

Andrea Bacciu, Andrea Alfarano, Saab Mansour +2

Amazon · INSAIT, Sofia

Multilingual Language Model Evaluation Selective Prediction Confidence Estimation in Language Models Multilingual QA LLM Uncertainty Estimation

Jul 7, 2026cs.CV

Propose and Attend: Training-free MLLM Grounding Confidence via Multi-Token Localized Attention

Multimodal large language models can emit localized predictions, bounding boxes for objects and temporal windows for video and audio events, but they hallucinate these regions prolifically. The model's own token log-probabilities are nearly uninformative: they conflate grounding quality with input ambiguity, and coordinate tokens become near-deterministic once the model commits. We propose Multi-Token Localized Attention (MTLA): a training-free, post-hoc score that measures how strongly a prediction's tokens attend to the region they claim. Prior attention-based detectors, which sum attention over the entire input modality and read a single response token, are weaker special cases; we show that summing only within the claimed region and aggregating across all prediction tokens recovers a stronger grounding signal. The same recipe applies almost trivially to other modalities and tasks: object detection in images and temporal localization in video and audio. Across multiple MLLM families and three modalities, MTLA improves hallucination AUROC by +7 to +38 over the best prior training-free baseline. Used as a confidence score for re-ranking, it nearly doubles the zero-shot COCO detection AP of an open-source 8B generalist (from 20.4 to 37.0), narrowing the gap to supervised detectors without any task-specific training.

Daniel Shalam, Emanuel Ben Baruch, Avi Ben Cohen +1

Amazon

Multimodal Grounding LLM Uncertainty Estimation Multimodal Model Evaluation VLM Hallucination Mitigation

Jul 7, 2026cs.CL

SpanUQ: Span-Level Uncertainty Quantification for Large Language Model Generation

Uncertainty estimation is essential not only for the trustworthy deployment of large language models (LLMs) but also as a foundation for self-refinement in LLM generation. However, existing approaches operate at suboptimal granularities: token-level scores lack semantic coherence, while sequence-level scores fail to localize errors. We formalize Span-Level Uncertainty Estimation (SLUE), a new task that targets the natural granularity for uncertainty: semantically coherent text spans, each conveying a single assessable unit of meaning. To address this task, we introduce SPANUQ, a lightweight probe that distills the uncertainty knowledge from expensive multi-sample inference into a single forward pass over LLM hidden states. SPANUQ employs a DETR-style span decoder to simultaneously detect spans and estimate their uncertainty via a Mixture of Beta distribution, trained with a principled combination of Beta NLL regression and contrastive ranking objectives. We construct SPANUQ-BENCH, the first span-level uncertainty benchmark comprising 20K prompts, 293K annotated spans, and continuous soft labels derived from multi-sample claim verification. Experiments on five LLM backbones show that SPANUQ consistently achieves the best span-level uncertainty quality, outperforming the strongest probe baseline and all sampling-based methods while being 10-20x faster. Its DETR-based span detector attains 0.910 F1, surpassing the best heuristic by 39.4%, enabling precise error localization that sequence-level methods cannot provide. The framework generalizes across five LLMs spanning two model families.

Yimeng Zhang, Yingying Zhuang, Ziyi Wang +12

Amazon · Northeastern University

LLM Evaluation Confidence Estimation in Language Models LLM Uncertainty Estimation Language Model Probing

Jul 5, 2026cs.CL

Uncertainty-Aware Abstention in Large Language Models with Provable Alignment Guarantees

Large language models (LLMs) are increasingly deployed in question answering (QA) systems, yet they may generate hallucinated or misaligned responses without reliable confidence estimates. Uncertainty quantification (UQ) offers a natural basis for selective answering, where a system answers only when its prediction is deemed reliable and abstains otherwise. However, existing uncertainty scores for LLMs are often heuristic: a threshold chosen on such scores does not, by itself, provide statistical guarantees on the error rate among accepted answers. We propose CIC, a confidence-interval-based calibration framework that converts arbitrary uncertainty scores into risk-controlled selective answering rules. Given a held-out calibration set, CIC evaluates each generated response using an application-specific alignment criterion and associates it with an uncertainty score and a binary error label. For each candidate uncertainty threshold, CIC estimates the acceptance-conditioned error rate and constructs a high-probability upper confidence bound using either Hoeffding-style or Clopper-Pearson confidence intervals. It then selects the largest threshold whose upper bound is below a user-specified risk level

α

, thereby maximizing the answering rate subject to a finite-sample reliability constraint. Under exchangeability, CIC guarantees with probability at least

1-δ

that the selected threshold, if non-null, controls the error rate among accepted answers at level

α

. We evaluate CIC on both closed-ended and open-ended QA benchmarks across seven LLMs and multiple uncertainty estimators. Experimental results show that CIC consistently achieves valid risk control while retaining strong answering efficiency, providing a practical and statistically grounded mechanism for deploying LLMs in reliability-sensitive QA workflows.

Sijin Dong, Hiroyuki Shinnou

1Ibaraki University, Japan.

Selective Prediction Confidence Estimation in Language Models Question Answering LLM Reliability LLM Uncertainty Estimation Uncertainty Calibration

Jul 4, 2026cs.SE

The "I Don't Know" Filter: Enhancing Agentic Reliability in Function Calling

The language models that underpin agents have seen a rapid rise in performance on function calling benchmarks. However, the metrics used in the training and evaluation of these models often encourage models to make positive claims even when the answer is uncertain, leading to hallucinations. Such hallucinations can be disastrous when language models are trusted to use function calls to make decisions in high stakes applications. To that end, we propose an agent evaluation metric that takes into account the negative outcomes associated with incorrect function calls. Further, to catch hallucinations before they can cause harm, we propose a lightweight trainable filter that can quantify a language model's uncertainty and remove potentially harmful function calls. By training that filter to detect and suppress uncertain function calls without modifying the underlying model, we demonstrate a practical path toward agents that know when to say "I don't know," a property we argue is essential to production reliability.

Stefan Broecker, Mason del Rosario, Boris Selitser +1

University of California, Davis, Department of Computer Science · Okareo, Inc. · University of California, Davis, Department of Mathematics

AI Agent Reliability LLM Agent Evaluation LLM Uncertainty Estimation LLM Abstention LLM Agent Reliability

Jul 4, 2026cs.AI

Evaluating LLM Uncertainty in Long-Form Generation Using Deterministic Ground Truth

As LLMs generate increasingly long outputs, effective uncertainty estimation must identify errors at fine-grained levels rather than discard entire responses. While such methods exist, evaluating uncertainty at any resolution (token to an entire generation) is challenging and highly sensitive to label imperfections, making zero-noise benchmarks essential; yet, long-form generation benchmarks tend to rely on fallible labels rather than deterministic ground truth. We introduce Single-answer Atomic Long-form Target (SALT), a benchmark of six procedurally generated tasks with single deterministic long textual ground truths, enabling unit-level evaluation of correctness, calibration, and ranking without external judges. Equipped with SALT, our analysis of 50+ LLMs reveals key insights: We identify which confidence functions dominate each uncertainty aspect and show that confidence ranking largely breaks at atomic resolution, even when clearer separability emerges at coarser line-level units. SALT further enables controlled atom-level interventions throughout generation, revealing two separable drivers of future errors: propagation from corrupted prefixes, dominated by global context correctness, and bounded degradation from increasing answer-context length. Finally, we demonstrate that reasoning, via Chain-of-Thought prompting or internalized through training, introduces a trade-off, improving accuracy while degrading confidence ranking. These findings directly impact risk-critical applications requiring reliable error identification and mitigation.

Ido Amit, Ido Galil, Ran El-Yaniv

1Technion · 2Nvidia

LLM Evaluation LLM Uncertainty Estimation Uncertainty Calibration

Jul 2, 2026cs.LG

Bayesian Sparse Low-Rank Adaptation for Large Language Model Uncertainty Estimation

Large language models (LLMs) exhibit remarkable reasoning capabilities, but their task-specific fine-tuning is notoriously plagued by overconfidence, severely hindering trustworthy deployment. We propose Data-Adaptive Lower-Rank Adaptation (DALorRA), a simple and effective variational Bayesian sparse framework that shifts the paradigm of uncertainty quantification from the dense parameter space to the lightweight rank level of low-rank adaptation (LoRA). With the insight that LoRA essentially aggregates multiple rank-one components that may provide superfluous model capacity, DALorRA imposes stochastic masking on rank dimensions, enabling Bayesian regularization of model capacity during training and ensemble-like calibration during inference. Extensive experiments demonstrate DALorRA's excellent calibration of LLMs without compromising reasoning accuracy.

Jijie Zhang, Zhe Ren, Quan Zhang +1

School of Artificial Intelligence, Jilin University · Michigan State University

Low-Rank Adaptation Language Model Calibration LLM Uncertainty Estimation Bayesian LoRA

Jul 1, 2026cs.AI

Bayesian Uncertainty Propagation for Agentic RAG Pipelines: A Proof-of-Concept Study on Multi-Hop Question Answering

Trustworthy deployment of Agentic Retrieval-Augmented Generation (RAG) systems requires mechanisms for estimating when multi-stage reasoning pipelines may fail. This paper presents an uncertainty-aware Agentic Retrieval-Augmented Generation (RAG) framework in which planner, evaluator and generator stages produce uncertainty signals derived from semantic divergence and generator self-evaluation. These signals are propagated through a Bayesian Network (BN) to estimate system-level uncertainty and provide node-level indicators of potential failure points across the workflow. The approach is evaluated on StrategyQA and HotpotQA using GPT-3.5-Turbo and GPT-4.1-Nano, with Area Under the Receiver Operating Characteristic Curve (AUROC), Area Under the Accuracy-Rejection Curve (AUARC), Expected Calibration Error (ECE), and Brier Score used to assess discrimination, selective prediction and calibration. Results show that Bayesian propagation is more effective on HotpotQA, where uncertainty accumulates across multi-hop reasoning stages, while StrategyQA exposes limitations caused by miscalibration and unreliable upstream signals. The study positions Bayesian uncertainty propagation as a promising but preliminary mechanism for monitoring Agentic RAG systems, with future validation required in industrial domains such as Offshore Wind (OSW) maintenance decision support.

Louis Donaldson, Connor Walker, Koorosh Aslansefat +1

University of Hull, Hull HU6 7RX, UK

Uncertainty Quantification Agentic RAG LLM Uncertainty Estimation Uncertainty Propagation Uncertainty Calibration

Jun 30, 2026cs.CL

Reinforcement Learning with Metacognitive Feedback Elicits Faithful Uncertainty Expression in LLMs

Metacognition is a critical component of intelligence that describes the ability to monitor and regulate one's own cognitive processes. Yet LLMs exhibit systemic deficiencies in key metacognitive faculties: they hallucinate with high confidence, fail to recognize knowledge boundaries, and misrepresent their internal uncertainty--undermining trustworthiness and reliability. Since monitoring task performance and adapting behavior accordingly are central to metacognition, we posit that models capable of accurately judging their own performance are better positioned to improve it. We operationalize this idea via two novel mechanisms: reinforcement learning with metacognitive feedback (RLMF), a paradigm to refine completion rankings during preference optimization based on the quality of a model's self-judgments of performance, and metacognitive data selection, which uses similar self-judgments to identify high-value training examples, outperforming naive active learning. We apply these innovations to the problem of faithful calibration (FC), a task that is itself fundamentally metacognitive: the goal is to align expressed with intrinsic uncertainty, difficult even for frontier LLMs. We adopt a two-stage, decoupled approach, first using these methods to calibrate the faithfulness of models' self-reported confidence scores, then mapping to natural, context-adaptable linguistic uncertainty via targeted output editing. Extensive experiments show RLMF achieves generalizable, state-of-the-art FC on diverse tasks while preserving accuracy. Further, RLMF surpasses standard RL by up to 63% while enhancing models' ability to assess and express their own capability limits. This positions RLMF as a promising paradigm to enhance LLM metacognition toward improved abilities and alignment, and suggests metacognitive performance as an effective RL signal to overcome limits of prior intrinsic feedback methods.

Gabrielle Kaili-May Liu, Avi Caciularu, Gal Yona +2

Yale University · Google Research

RL for Language Models Reinforcement Learning Language Model Calibration LLM Uncertainty Estimation Metacognition in Language Models

Jun 30, 2026cs.LG

CoMet: Context and Multiplicity Decomposition for Multimodal Uncertainty Estimation

Uncertainty estimation has been a long-standing challenge in AI models; it amounts to "knowing what you don't know," and metacognition is notoriously difficult even for humans (cf. the Dunning-Kruger effect). Although it is still far from solved even in simpler classification systems, tackling it in multimodal large language models (MLLMs) is becoming increasingly important. Within MLLMs, uncertainty can stem from any of the diverse sources as well as from their relationships, and further can stem from the unbounded answers in the open-ended setting. To tackle the issues, we propose CoMet, an MLLM uncertainty estimation method by decomposing uncertainty into a context-specific term and a multiplicity-specific term. The former captures ambiguity induced by the given context (e.g., task or prompt), while the latter captures how many plausible answers determined by the context remain compatible with the given input. We train a lightweight post-hoc uncertainty module to estimate these quantities, which enables efficient uncertainty estimation without autoregressive answer generation or repeated sampling. Experiments on various open-ended multimodal benchmarks, hallucination detection, and multiple-choice visual question answering benchmarks show that CoMet consistently improves uncertainty estimation over existing baselines while remaining efficient in practice. Code is available at https://github.com/princetonvisualai/comet_uncertainty

Sanghyuk Chun, William Yang, Amaya Dharmasiri +1

Princeton University

Uncertainty Quantification Multimodal Large Language Models LLM Uncertainty Estimation Uncertainty Decomposition

Jun 30, 2026cs.AI

Wisdom Of The (AI) Crowd: Investigating Artificial Swarm Intelligence In Large Language Models

Human swarm intelligence demonstrates remarkable collective accuracy but faces scalability constraints in cost, coordination, and time. We investigate whether large language models (LLMs) can approximate swarm intelligence effects through artificial swarms, addressing a critical gap in understanding AI-based aggregation mechanisms. We conducted a controlled experiment with 960 manually executed prompts across three proprietary models (GPT-5, Gemini 2.5 Pro, Claude Sonnet 4.5), testing intra-model sampling and inter-model aggregation on eight estimation tasks. Results reveal consistent error reduction through intra- and inter-model aggregation, with significant error reductions up to 37 percentage points in MAPE across different aggregation strategies. We observed small to large effect sizes for positive correlations (Spearman's

ρ=0.242-0.568

, all

p<0.001

) between relative confidence interval widths and relative estimation errors, suggesting LLMs possess metacognitive awareness when assessing uncertainty. We discuss implications for research and practice, providing actionable insights for deploying LLM swarms in organizational decision-making.

Justin Brenne, Christian Meske

Ruhr-University Bochum, Bochum, Germany · Ruhr-Universitaet Bochum, Bochum, Germany

LLM Uncertainty Estimation Language Model Ensembles

Jun 29, 2026cs.CL

Uncertainty-Aware Generation and Decision-Making Under Ambiguity

With rapidly improving capabilities, Large Language Models (LLMs) are increasingly used in many complex real-world tasks. Beyond requiring in-depth knowledge and reasoning skills, many of these tasks exhibit a high degree of subjectivity and require that the outputs of the model can be trusted. While a lot of progress has been made to train better models, decision-making algorithms have received less attention. In this work, we present and evaluate various uncertainty-aware decision-making algorithms based on Bayesian decision theory and risk-averse decision making on the tasks of tutoring and automatic peer reviewing. Concretely, we take uncertainty over tutoring strategies and review scores into account when generating a tutor response or review and use conformal prediction to provide guarantees over strategy and score. We find empirically that these algorithms can improve the utility of the generations but need to be carefully implemented when ambiguity is high. For example, risk-averse rules can degrade performance by optimizing for generic outputs, while Bayesian methods tend to perform better. Our work uses techniques from decision theory to improve LLM-based decision-making and outlines open challenges for the community.

Nico Daheim, Iryna Gurevych

Ubiquitous Knowledge Processing Lab (UKP Lab), Department of Computer Science, Technical University of Darmstadt · National Research Center for Applied Cybersecurity ATHENE, Germany

Intelligent Tutoring Systems LLM Decision-Making Bayesian Decision Theory LLM Uncertainty Estimation Automated Peer Review Decision-Making under Uncertainty

Jun 28, 2026cs.LG

Reported Confidence in LLMs Tracks Commitment More Than Correctness

Confidence is an estimate of the probability that a chosen answer is correct. Verbal confidence reports are widely used as uncertainty measures in large language models, but whether they are best understood as estimates of correctness is unclear. We test this with a two-stage abstention paradigm from the neuroscience of perceptual decision making: a model first answers and reports its confidence, then decides whether to commit it to a user or abstain. Across four non-reasoning models, prompt framings, and confidence formats, verbal confidence predicted the commit/abstain decision substantially better than whether the answer was correct. Calibrated token log-probabilities showed the opposite profile, with abstention-prediction coupled to correctness discrimination, the signature of an answer-evidence signal. After removing the variance verbal confidence shared with log-probabilities, the residual stayed aligned with commitment while its link to correctness fell to near chance. The dissociation generalised to four reasoning models across four benchmarks of varying difficulty, from hard multiple-choice to frontier-level freeform questions. Mechanistic analyses in Gemma 3 and 4 were convergent: a post-answer state known to causally support verbal-confidence generation already encoded the future abstention decision before the abstention prompt, organised mainly by that decision rather than by correctness, the two lying in approximately orthogonal directions in activation space. Steering along a verbal-confidence-specific direction causally shifted abstention. Verbal and log-probability confidence are thus not interchangeable: log-probabilities track answer evidence and correctness, whereas verbal confidence is better understood as a behaviour-facing readout of an internal commit-readiness state, challenging the practice of treating verbal reports as proxies for reliability.

Dharshan Kumaran

Google DeepMind

Confidence Estimation in Language Models LLM Interpretability LLM Uncertainty Estimation Metacognition in Language Models LLM Abstention

Jun 27, 2026cs.CL

AB-RAG: Adaptive Budgeted Retrieval-Augmented Generation for Reliable Question Answering

Retrieval-Augmented Generation (RAG) has become the standard way to ground large language models in external knowledge, yet most systems retrieve a fixed number of passages for every question regardless of its difficulty. This wastes computation on easy questions, starves hard ones, and gives no signal for when a generated answer can be trusted. With a growing share of question answering systems built on top of commercial language model APIs, a method that can decide how much to retrieve, and how far to trust its own answers, without retraining the underlying model, is of clear practical value. This paper presents AB-RAG (Adaptive Budgeted Retrieval-Augmented Generation), a training-free and backbone-agnostic framework that generates an answer, estimates its confidence from a combination of three signals, and then decides whether to stop or to retrieve more evidence, subject to a fixed retrieval budget. The estimator combines the model's own certainty, the agreement between the answer and the evidence, and the variance of the retrieval scores. For models that expose token probabilities the certainty signal is read directly; for closed APIs it is approximated by self-consistency, so the method works without access to model internals. Across three backbones and two datasets, the central result is that the confidence estimate reliably separates correct from incorrect answers on every backbone, reaching a clean split of 57.6% against 0% Exact Match between high- and low-confidence answers on a factoid dataset. The adaptive policy improves accuracy on capable backbones, and the study reports its negative and nuanced findings honestly, including a confidence signal that proved unsuitable for short answers and a retrieval signal whose sign was found and corrected through measurement. The entire study was carried out on a single consumer laptop with only a few dollars of API spend.

Ansh Kamthan

Department of Artificial Intelligence and Machine Learning Manipal University Jaipur Jaipur, India

Retrieval-Augmented Generation LLM Answer Verification Confidence Estimation in Language Models Adaptive RAG LLM Reliability LLM Uncertainty Estimation

Jun 26, 2026cs.CL

From Signals to Transfer: A Factorised Study of Probe-Based Uncertainty Estimation in Large Language Models

Probe-based uncertainty estimation (UE) has emerged as a prominent approach to detect hallucinations in Large Language Models (LLMs) by learning uncertainty from internal model signals. Yet, recent methods vary simultaneously across feature design, training data construction, and evaluation setting, obscuring what actually drives performance. To address this issue, we propose a factorised study of probe-based UE under matched conditions. Our results show that raw hidden states and attention features are difficult to outperform in-domain. However, under distribution shift, structured and compressed features are more robust, suggesting that in-domain performance alone is insufficient to measure progress. Furthermore, prompting and label construction significantly affect probe behaviour. Building on these best-practice findings, we train benchmark-based pretrained probes that transfer reasonably well to open-ended factual generation, providing a stable off-the-shelf baseline. Our work encourages more deployment-oriented evaluation of probe-based uncertainty estimators. The code repository is available at https://github.com/ponhvoan/ProbeUE.

Ponhvoan Srey, Xiaobao Wu, Cong-Duy Nguyen +3

Nanyang Technological University · Shanghai Jiao Tong University · VinUniversity +1

Uncertainty Quantification Hallucination in Language Models LLM Uncertainty Estimation Language Model Robustness Language Model Probing

Jun 23, 2026cs.AI

Bayesian control for coding agents

Modern coding agents pair LLM generators with various tools, including cheap diagnostics and expensive verifiers. The tool-use decisions are typically governed by orchestrators that often use fixed rules and ignore uncertainty. We formulate orchestration as cost-sensitive sequential hypothesis testing: a Bayesian controller maintains a belief over candidate correctness and dynamically decides whether to gather more evidence, refine the candidate, verify it, or stop. Across six generators and nine coding benchmarks, Bayesian control proves to be most valuable when verification is costly and critics are informative but imperfect. Beyond control, the belief state yields an interpretable correctness score that outperforms token-probability and raw tool-success baselines for uncertainty quantification.

Theodore Papamarkou, Vladislav Smirnov, Viktor Mazanov +4

1PolyShape · 3MBZUAI

Language Model-Based Control Coding Agents Bayesian Decision Theory LLM Uncertainty Estimation Sequential Hypothesis Testing

Jun 23, 2026cs.CL

Beyond Logprobs: A Multi-Signal Confidence Engine for LLM-Based Document Field Extraction

In high-stakes document processing pipelines, including financial reconciliation, compliance verification, and procurement automation, an LLM extraction that is silently wrong is more dangerous than one that is visibly absent. The central challenge is not extraction accuracy alone but reliable confidence estimation: knowing, field by field, whether an extraction can be trusted for automation or deferred to human review. Token-level log-probabilities, verbalized confidence, and multi-sample self-consistency all collapse toward all-positive behaviour at practical thresholds, offering no reliable separation between trustworthy and untrustworthy extractions. We present ExtractConf, a cross-domain, field-agnostic confidence engine that grounds confidence estimation in two structurally different readings of the same document. A field-guided Hunter call extracts each field under schema-slot completion pressure; a document-guided Mapper call scans holistically and surfaces values grounded in document content. This asymmetry yields different failure modes: Hunter hallucinates values for absent fields, while Mapper misses visually non-salient ones. Their disagreement is independently informative. ExtractConf fuses cross-call disagreement, LLM-internal uncertainty, OCR, image quality, and spatial layout into a classifier requiring no domain-specific rules or retraining. On DocILE (55-field invoices, 26% failure rate), it achieves 0.928 ROC AUC and reduces selective prediction risk by 70% over logprob-mean. At 80% coverage, accuracy reaches 99.1%, enabling a practical human-in-the-loop workflow. Zero-shot transfer to CORD receipts achieves 0.858 AUC; lightweight Lasso recalibration reduces ECE by 89% and Brier by 43%, confirming the signals generalise across document domains.

Nitesh Kumar

1Perfios Software Solutions Pvt. Ltd.

Selective Prediction Document Information Extraction LLM Reliability LLM Uncertainty Estimation

Jun 23, 2026cs.CL

CALIBER: Calibrating Confidence Before and After Reasoning in Language Models

Reasoning language models are increasingly asked not only to answer difficult questions, but also to estimate their likelihood of success. Existing methods typically elicit confidence only once: either before thinking or after answering. We argue that confidence in reasoning models is state-dependent: before thinking, confidence should estimate the chance of the model correctly solving the prompt, while after thinking it should predict whether the realized answer is likely to be correct. This distinction determines the appropriate supervision target: prompt-level success should supervise confidence estimates made after seeing the prompt, while individual answer-level correctness should supervise confidence estimates made after answering. We introduce CALIBER (Calibration Before and After Reasoning), which elicits both estimates and supervises each with the target matched to its information state. Under this unified protocol, CALIBER reduces Expected Calibration Error (ECE) by 52.5% over the strongest single-confidence baseline on BigMathDigits for the 7B model, while achieving the best Brier score and AUROC, and remains within 2.1 points of the best accuracy. Further, on a larger 30B model, CALIBER achieves the best ECE on BigMathDigits while remaining competitive in Brier score and AUROC. Out of distribution, it achieves the best ECE and Brier score on GPQA and TriviaQA, and remains competitive on SimpleQA. Ablations further show that this position-target alignment is most beneficial under distribution shift where it consistently reduces calibration error across all out-of-distribution benchmarks.

Conor Finlay, Joshua Kurien, Saurabh Dash +2

1Cohere Labs

Confidence Estimation in Language Models Language Model Calibration LLM Uncertainty Estimation Large Reasoning Models

Jun 22, 2026cs.AI

The Origins of Stochasticity: Comprehensive Investigations on Uncertainty Quantification for Large Language Models

Recent advancements in Large Language Models (LLMs) have enabled sophisticated reasoning and content generation, yet their inherent stochasticity poses significant challenges for ensuring predictive credibility. While traditional uncertainty taxonomy paradigms, such as the dichotomy of aleatoric and epistemic uncertainties, provide conceptual foundations, they often fail to capture the multi-component and multi-stage nature of LLM generation and struggle to evaluate the effectiveness of various Uncertainty Quantification (UQ) methods. In this paper, we propose a granular uncertainty taxonomy that systematically attributes LLM uncertainty into input-level, parameter-level, token-level, and decoding-process sources. Correspondingly, we categorize existing UQ methods into Bayesian, ensemble, consensus-based, and single-pass approaches. Furthermore, we introduce a comprehensive evaluation framework covering diverse generation settings and metrics. We empirically evaluate 21 typical UQ methods across three prominent LLM families, including Qwen3, Llama 3.2, and DeepSeek-V3, on benchmarks such as TriviaQA, GSM8K, and HumanEval. Our experimental results demonstrate that (i) the effectiveness of UQ methods is sensitive to task types and generation settings; (ii) consensus-based methods, typed Deg and EigV, consistently outperform other UQ approaches; and (iii) larger model scales correlate with lower uncertainty estimates, suggesting an empirical scaling law for LLM uncertainty. This work bridges the gap between theoretical origins and practical deployment, providing a versatile diagnostic tool for systematically quantifying uncertainty in LLM applications.

Xiang-Jun Ou, Shuang Liang, Xin-Yu Hu +3

National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing 210063, China. · School of Intelligent Science and Technology, Nanjing University, Suzhou 215163, China.

LLM Evaluation Uncertainty Quantification LLM Uncertainty Estimation

Jun 20, 2026cs.CL

The Score Granularity Gap in Black-Box LLM Classification: A Comparative Study of Confidence Constructions

Large language models (LLMs) are increasingly deployed as black-box classifiers in pipelines that automate confident decisions and route uncertain ones to human review. Such selective prediction needs a confidence score that an operator can threshold at a chosen risk level. Prior work asks whether LLM confidence is well calibrated or well ranked; we ask a complementary, deployment-oriented question that has been largely overlooked: at what resolution can the score be thresholded? We call the answer the score granularity gap. Through a controlled comparison of seven ways to build a confidence score, from a single verbalized number, to token probabilities, to querying the model many times and combining the answers, across 25 model-dataset pairs (9 LLMs, 3 benchmarks), we find that single-shot verbalized confidence, once correctly converted to a class probability, ranks cases surprisingly well, yet takes only a handful of distinct values. It therefore offers an operator only a few coarse thresholds, no matter how well it ranks. We show which constructions widen this gap, at what inference cost, and with what effect on ranking, notably that multi-query aggregation helps weak models but can degrade already-strong ones. We translate these trade-offs into concrete deployment guidance.

Ao Sun, Tian Sun, Jiaxing Geng

LLM Evaluation Selective Prediction Confidence Estimation in Language Models Language Model Calibration LLM Uncertainty Estimation

Jun 18, 2026cs.AI

A Systematic Evaluation of Black-Box Uncertainty Estimation Methods for Large Language Models

Although large language models (LLMs) have shown strong capabilities across a wide range of tasks, their outputs often remain unreliable and may contain hallucinations, making uncertainty estimation (UE) essential for building trustworthy LLMs. In practice, many mainstream LLMs are only accessible through restricted APIs, where internal signals such as logits and hidden states are unavailable, making black-box UE especially important. However, existing work on black-box UE for LLMs remains fragmented in methodology and lacks a unified empirical comparison. To address this gap, we present a systematic review of black-box UE methods and organize them into five categories: verbalization-based, sampling-based, explanation-based, multi-agent, and hybrid methods. We further build a unified evaluation framework and benchmark 24 representative methods across 4 models and 4 dataset settings. Our results show that no single method consistently dominates across all settings. Nevertheless, methods that reason over and compare candidates in the answer space are generally effective, and hybrid methods that combine multiple uncertainty signals perform well under most conditions. By releasing the benchmark data and a unified evaluation framework, we aim to facilitate reproducible comparisons and support future research, while our empirical findings provide practical guidance for developing future black-box UE methods for LLMs.

Jiayi Wang, Xu-Yao Zhang

School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China · State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China

LLM Evaluation Uncertainty Quantification LLM Reliability LLM Uncertainty Estimation

Jun 18, 2026stat.ML

AURA: Adaptive Uncertainty-aware Refinement for LLM-as-a-Judge Auditing

Large language models (LLMs) are increasingly used as judges for open-ended generation, as large-scale human evaluation is often expensive and difficult to scale, yet their preferences remain imperfect proxies for human judgment. Existing auditing pipelines often assume that a reliable subset of examples or clean supervision signals are available beforehand, for example from human annotation, heuristic filtering, or the outputs of strong judges. In LLM evaluation, this assumption is fragile: the initial split may inherit judge bias, while human verification is typically too scarce to define stable groups at scale. We propose AURA, an adaptive uncertainty--aware refinement framework for auditing pairwise LLM--as--a--judge decisions under selected human verification. AURA iteratively learns a human-consistency signal, propagates reliable evidence, and prioritizes uncertain comparisons for human review. The key idea is to treat trust in a judge as a latent quantity that is progressively refined as evidence accumulates. We provide a compact formulation, a stable refinement procedure, and a comprehensive evaluation on both synthetic and real pairwise LLM-answer data.

Zilong Zhang, Yi-Ting Hung, Weiyi He +3

Department of Mathematics and Statistics Georgia State University · Department of Probability and Statistics Department of Computer Science and Engineering Michigan State University · Department of Mathematics and Statistics Concordia University +1

LLM-as-a-Judge LLM Auditing Active Learning Human-in-the-Loop Evaluation LLM Uncertainty Estimation

Jun 17, 2026cs.AI

Uncertainty Decomposition for Clarification Seeking in LLM Agents

Recent position papers argue that the classical aleatoric/epistemic uncertainty framework is insufficient for interactive large language model (LLM) agents and call for underspecification-aware, decomposed, and communicable uncertainty representations that can unlock new agent capabilities such as proactive clarification seeking and shared mental-model building. Practical deployment constraints -- black-box APIs, interactive latency budgets, and the absence of labeled trajectories -- rule out logprob-based, multi-sampling, and training-based methods, leaving prompt-based estimation as the most viable family for surfacing such signals at deployment time. We answer this call with a simple prompt-based decomposition that separates action confidence from request uncertainty (u), enabling the agent to ask for clarification when the task specification is ambiguous. To evaluate it, we introduce two clarification-augmented benchmarks (WebShop-Clarification and ALFWorld-Clarification) in which 50% of tasks are deliberately underspecified, and systematically compare the proposed decomposition against ReAct+UE and Uncertainty-Aware Memory (UAM) across five LLM backbones (GPT-5.1, DeepSeek-v3.2-exp, GLM-4.7, Qwen3.5-35B, GPT-OSS-120B) on these variants together with the standard WebShop, ALFWorld, and REAL benchmarks for fault detection. Averaged across the five backbones, the proposed decomposition improves clarification F1 on ALFWorld-Clarification by 73% over ReAct+UE and by 36% over UAM, and leads clarification F1 on every backbone on WebShop-Clarification and on four of five backbones on ALFWorld-Clarification, indicating that the gains generalize beyond a single LLM.

Gregory Matsnev

AI Talent Hub, ITMO University Saint Petersburg 197101, Russia

LLM Agents LLM Uncertainty Estimation Uncertainty Decomposition LLM Agent Reliability

Jun 17, 2026cs.AI

LLM Doesn't Know What It Doesn't Know: Detecting Epistemic Blind Spots via Cross-Model Attribution Divergence on Clinical Tabular Data

Large language models (LLMs) are increasingly applied to structured clinical data, yet whether they can recognize the limits of their own knowledge on such tasks remains unexplored. We study this question through the lens of cross-model attribution divergence with the goal of reducing epistemic uncertainty for structured tasks, comparing Qwen 2.5 7B and XGBoost on a prediction task via attribution divergence analysis. We report four findings. First, LLM verbalized confidence is epistemically vacuous, it outputs a near-constant (0.856-0.937) regardless of whether accuracy is 49% or 75.3%, tracking prompt format rather than prediction quality. Second, the LLM exhibits an inverse difficulty effect: accuracy drops to 64.8% when XGBoost is 99% correct, but matches XGBoost (73.8% vs. 73.1%) when it is moderately uncertain. Third, few-shot examples and SHAP-derived feature evidence are orthogonal, super-additive interventions: they reduce the Attribution Disagreement Score (ADS) from 1.54 to 0.38 and improve accuracy from 49% to 75.3% without training. Fourth, a cross-model calibrator that determined LLM reliability using attribution divergence signals reduces expected calibration error from 0.254 to 0.080, replacing uninformative verbalized confidence with patient-specific reliability estimates, without accessing model internals or requiring repeated inference. We frame these findings as a cold start problem for LLMs on structured data and outline a path toward genuine epistemic self-awareness.

Akshat Dasula, Prasanna Desikan, Jaideep Srivastava

Centific AI Research · Department of Computer Science & Engineering, University of Minnesota-Twin Cities, Minneapolis, USA.

Language Model Calibration LLM Uncertainty Estimation Clinical Language Model Evaluation Epistemic Uncertainty

Jun 16, 2026cs.LG

A Risk Decomposition Framework for Pre-Hoc Fine-Tuning Prediction

The high cost of fine-tuning LLMs poses a significant economic barrier; pre-hoc performance prediction offers a critical solution to substantially reduce this expense. However, the theoretical limits of pre-hoc performance prediction remain unexplored. We formulate it as a stochastic estimation problem under information constraints, decomposing prediction risk into two components: an intrinsic limit (static data-model compatibility) and a reducible optimization variance. We prove that optimization variance admits a necessary lower bound on its decay rate, implying fundamental constraints on how quickly uncertainty dissipates, regardless of the predictor used. Based on these dynamics, we derive a budget-optimal probing principle and introduce a predictability phase diagram that organizes tasks into three distinct regimes: Static-Sufficient, Dynamic-Critical, and Noise-Dominant. Extensive experiments on synthetic and real-world benchmarks validate these theoretical regimes and demonstrate the efficiency of our probing strategy.

Yuxiang Luo, Chen Wang, Nan Tang

The Hong Kong University of Science and Technology (Guangzhou).

Fine-Tuning LLM Fine-Tuning LLM Uncertainty Estimation

Jun 15, 2026cs.AI

Quantifying Consistency in LLM Logical Reasoning via Structural Uncertainty

Large language models can arrive at the same answer through reasoning paths that are unstable, contradictory, or difficult to rank consistently -- a failure mode especially prevalent in multi-step deductive reasoning. Existing methods assess reliability primarily through output dispersion -- measuring how much sampled answers differ -- but this discards a complementary signal: whether the model can consistently rank competing reasoning candidates. We propose structural uncertainty, a consistency-aware framework derived from the stability of self-preference-induced rankings over sampled reasoning solutions. Given a query, we generate multiple candidate solutions and ask the model to judge pairwise preferences among its own outputs. We aggregate self-preferences into ranking distributions via Bradley-Terry modeling with PageRank, and decompose the signal into two entropy-based components: across-trial ranking instability and within-trial candidate ambiguity. Across five LLMs and eight benchmarks, structural signals provide information complementary to answer dispersion: on logical and mathematical reasoning tasks, the combination improves identification of unreliable instances, while on factual retrieval the structural signal collapses toward uniformity, diagnosing a regime boundary where reasoning-level consistency evaluation is uninformative. The two components relate differently to accuracy: within-trial ambiguity correlates positively with correctness -- consistent with settings where multiple plausible solution paths remain competitive -- while across-trial instability correlates negatively, signaling unreliable reasoning. Structural uncertainty is best understood not as a universal confidence estimator, but as a regime-sensitive evaluator of logical reasoning consistency.

Baishali Chaudhury, Mengdie Flora Wang, Hyunji Hayley Park +3

AWS Generative AI Innovation Center

Reasoning Consistency in Language Models LLM Reliability LLM Uncertainty Estimation LLM Mathematical Reasoning Uncertainty Decomposition LLM Reasoning