Confidence Estimation in Language Models

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Overview

The field studies whether language models can tell when their answers are likely to be wrong, which matters for deciding when to answer, abstain, retrieve evidence, or spend more computation. Methods include verbalized confidence, token probabilities and sampling-based agreement, as well as hidden-state probes, activation signals, post-hoc calibration, and conformal prediction. These approaches are tested across settings such as factual question answering, mathematical reasoning, code generation, multilingual tasks, and tool-using agents. A central challenge is that confidence signals can disagree or shift with prompts, training, and distribution changes; good calibration or error ranking alone does not guarantee useful decisions or reliable risk guarantees.

Latest papers

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249 papers45 papers in the last four weeks, up 96% on the four weeks before. 0.3% of all new papers.

May 26, 2026

Same Answer, Different Confidence: Protocol Sensitivity in LLM Confidence Calibration

Large language models (LLM) can state their confidence in an answer (verbalized confidence), or the confidence can be read from the probability of the answer's tokens (token confidence). Comparisons of the two ask which is better calibrated, but the token probability of an answer depends on the text that precedes it. Across five open LLMs and four question-answering datasets, we fix each answer, its verbalized confidence, and its correctness label, and vary how each score is measured. The scores themselves change with the protocol, and so does the comparison between them. Changing the context in which the token probability is read shifts the gap between the two scores by about the size of the gap itself (.287 vs. .304 in expected calibration error, ECE; .189 vs. .145 in AUROC). The 95% interval of the shift excludes zero in 19 and 17 of the 20 settings, and under AUROC the shift has the same sign in all of them, so the context changes how answers are ranked. The better score flips in 8 settings under each metric, counting only flips that the intervals support, and the shift also appears in four larger models of up to 72B parameters. Most of the shift appears with changes to the instruction, not to the position of the answer. Other measurement choices also matter, and stated confidence depends on how a supplied answer is written. We turn these results into a reporting checklist for LLM confidence and its comparisons.

Hankyeol Kim, Pilsung Kang

Seoul National University

LLM EvaluationConfidence Estimation in Language ModelsLanguage Model CalibrationLLM ReliabilityLLM Uncertainty EstimationVerbalized Confidence Estimation
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May 25, 2026

Confidence and Calibration of Activation Oracles for Reliable Interpretation of Language Model Internals

An activation oracle is a language model trained to convert the activations of another model into natural language. However, it is so far unclear to what extent these verbalizations are calibrated. Crucially, the oracle's verbalization come without any measure of confidence. Here, we compare five methods for estimating the confidence of an activation oracle. Our experiments cover four oracles from two model families (Qwen and Gemma, from 8B to 27B parameters), tested on the secret word task, whereby the oracle is supposed to recover a secret word, that has been fine-tuned into a model but does not appear in the model outputs. Our results with 6,0006{,}000 samples per method/oracle combination show that the best calibration depends on the availability of a hypothesis space or a calibration set: When an assumed auditor can list the possible answers in advance, the oracle should score each candidate answer directly. Scoring the candidates gives a higher accuracy on every oracle and a confidence that separates correct from incorrect answers better than any other method. When the oracle has to write its answer as free text, the agreement over twenty sampled answers gives the best calibrated confidence, which needs only five labeled secret words to be tuned. When a calibration set is available, a rescaled probability of the answer is as good as re-sampling, at the cost of one generation instead of twenty. Asking the oracle to write a number for its confidence, on the other side, gives no useful signal on any oracle. Code and the patched trainer are available at https://github.com/federicotorrielli/probabilistic_activation_oracles.

Federico Torrielli, Peter Schneider-Kamp, Lukas Galke Poech

University of Turin · University of Southern Denmark

Confidence Estimation in Language ModelsLLM InterpretabilityLanguage Model CalibrationLLM Uncertainty Estimation
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May 25, 2026

Second Guess: Detecting Uncertainty Through Abstention and Answer Stability in Small Language Models

Large language models often generate confident but incorrect answers rather than abstaining when uncertain. This problem is particularly acute for small language models (SLMs), where computational constraints and autonomous operation amplify the need for reliable uncertainty detection. We propose Second Guess, a lightweight, parameter-free prompting technique for abstention in multiple-choice question answering (MCQA) that is well-suited for SLMs. Our key empirical insight is that models which truly know an answer will select it consistently, while uncertain models exhibit unstable behavior when an ``I don't know'' option is added. Evaluated on four open models (2B-8B parameters) and four benchmarks, Second Guess achieves the highest composite risk improvement of 10.81%. Notably, it maintains an 8% composite risk improvement on fine-tuned models where entropy-based methods degrade, and improves most for lower-performing models. All code and results required to reproduce this work is available in https://github.com/Mystic-Slice/second-guess

Ashwath Vaithinathan Aravindan, Mayank Kejriwal

University of Southern California Los Angeles, 90007, California, United States of America · Information Sciences Institute 4676 Admiralty Way #1001, Los Angeles, 90292, California, United States of America

Confidence Estimation in Language ModelsMultiple-Choice Question AnsweringSmall Language ModelsLLM Uncertainty EstimationLLM Abstention
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May 25, 2026

Decision-Making with Lightweight Confidence-Aware Language Model for Autonomous Driving

Large Language Models (LLMs) and Multimodal LLMs (MLLMs) have demonstrated immense potential in autonomous driving (AD) by offering human-like reasoning and open-world generalization. However, the excessive computational overhead and high inference latency of these massive models severely hinder their deployment in resource-constrained AD systems. To address this challenge, we propose a novel decision-making framework utilizing a lightweight confidence-aware language model, which bridges the gap between complex multimodal intention reasoning and efficient inference. Specifically, we design a multi-agent collaborative workflow, comprising action voting, confidence assessment, and summarization agents, to generate high-quality, confidence-annotated decision demonstrations via explicit Chain-of-Thought (CoT) reasoning. These demonstrations are then distilled into a lightweight language model featuring a dual-head architecture, enabling the joint prediction of decision probabilities and the generation of textual rationales. The distillation is realized via a confidence-aware fine-tuning strategy coupled with Retrieval Augmented Generation (RAG) to enhance the model's adaptability and data efficiency. Comprehensive closed-loop experiments on the nuPlan benchmark demonstrate that our approach achieves state-of-the-art (SOTA) success rates in both regular and long-tail scenarios while maintaining low inference latency.

Ruoyu Yao, Ruiguo Zhong, Pei Liu +3

The Hong Kong University of Science and Technology (Guangzhou), Guangzhou 511453, China

Confidence Estimation in Language ModelsLanguage Model DistillationLLM Uncertainty EstimationAutonomous Driving PlanningEfficient Language Model Inference
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May 24, 2026

Inference Time Optimization with Confidence Dynamics

Inference time optimization techniques, such as repeated sampling, have significantly advanced the reasoning capabilities of Large Language Models (LLMs). However, the critical role of model uncertainty remains largely underexplored in these optimization strategies. In this paper, we investigate the dynamics of confidence along reasoning trajectories and for first time reveal a surprising and unique pattern: correct answer traces tend to exhibit confidence improvement over time (positive confidence gain), while incorrect traces show attenuated or declining confidence as reasoning proceeds. Based on this observation, we propose Confidence Dynamic Gain (CDG) based voting, which incorporates how the confidence trajectory of the response evolves along the reasoning chain. Experiments across four open-source architectures (DeepSeek-R1, gpt-oss, Gemma-3, Qwen-QwQ) on the AIME24/25, HMMT25, and BRUMO25 benchmarks demonstrate that CDG yields a significant performance boost over baselines. These results demonstrate that our method provides a robust discriminative signal for improving answer selection in LLM reasoning. We also provide theoretical insights for this phenomenon. Code will be released at https://github.com/Accenture/CDG.git.

Yu Wang, Minghao Liu, Jiayun Wang +3

Center for Advanced AI, Accenture.

Inference-Time OptimizationConfidence Estimation in Language ModelsQuestion AnsweringLLM Uncertainty EstimationLLM Reasoning
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May 24, 2026

Trust but Verify: Prover-Verifier Deliberation for Selective LLM Prediction

Reliably knowing when a language model is correct is almost as important as being correct. We introduce prover-verifier deliberation (PVD), an inference-time protocol grounded in interactive proof theory, as a mechanism for selective prediction: the protocol produces both an answer and a structured confidence verdict, allowing a system to report high-confidence answers while abstaining on uncertain cases. In each dialogue, a prover defends a candidate answer through checkable sub-claims while a verifier issues targeted challenges and returns Accept, Challenge, or Reject. Because frozen language models are imperfect provers and verifiers operating over a noisy channel, formal soundness and completeness guarantees do not transfer; instead, we characterize the protocol empirically through its coverage-precision behavior. Our main experiment uses Claude Sonnet 4.6 as prover and Claude Haiku 4.5 as verifier on GPQA Diamond. Questions accepted with no answer revision, which we call Accept + No Change (ANC), are reported as the high-confidence subset; we evaluate this subset by its precision and coverage. ANC separates reliable from unreliable answers, yielding a ∼\sim30pp HC-Prec gap over the non-ANC complement. Robustness experiments with GPT and Gemini pairings show that high HC-Prec can transfer across model families, while verifier strictness and domain competence largely determine the size of the selection gap. On Humanity's Last Exam, weaker prover-verifier pairings can collapse or invert the ANC signal, illustrating a practical failure mode when the verifier operates outside its effective region. Comparisons with self-consistency, universal self-consistency, multi-agent debate, and Reflexion suggest that prover-verifier deliberation supplies a distinct argument-defensibility signal for selective prediction.

João Sedoc, Baotong Zhang, Dean Foster

New York University

LLM Answer VerificationSelective PredictionConfidence Estimation in Language ModelsSelective InferenceLLM ReliabilityLLM Uncertainty Estimation+1
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May 23, 2026

Understanding and Mitigating Premature Confidence for Better LLM Reasoning

Long chains of thought (CoT) from current language models frequently contain logical gaps and unjustified leaps, limiting the gains from additional test-time compute. Improving reasoning quality directly would require process reward models, but the step-level annotations needed to train them are expensive and scarce. We find such a signal in how the model's confidence evolves during reasoning: premature confidence, the tendency to commit to an answer early and use the remaining tokens to rationalize it, strongly predicts flawed reasoning across tasks and model scales. We exploit this in progressive confidence shaping, a reinforcement learning objective that trains models to update their confidence as they reason rather than commit early -- rewarding gradual confidence growth and penalizing early commitment, with no external labels or reward models. The method improves accuracy and reasoning quality from 1.5B to 8B parameters across arithmetic (Countdown), math (DAPO, AIME), and science (ScienceQA): on Countdown, accuracy improves 3.2x (+42.0pp) and flawed reasoning drops 48pp; on AIME, Pass@64 improves 6.6pp. Consistent with this mechanism, the method also improves faithfulness: on a safety benchmark, our models more transparently surface misleading content in their reasoning traces rather than concealing it. Controlled experiments reveal that the problem and its remedy scale together: premature confidence grows with model size and task difficulty, and so do the gains from addressing it.

Jingchu Gai, Guanning Zeng, Christina Baek +4

1Carnegie Mellon University · 2Tsinghua University

Confidence Estimation in Language ModelsRL for Language Model ReasoningLLM Uncertainty EstimationLLM Reasoning
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May 22, 2026

LLMs Show No Signs Of Individuated Metacognition

Confidence-weighted routing, selective abstention, and ensemble weighting all assume that a model's stated confidence is informative about its capability on the question being asked. They presume functional metacognition, the capacity to assess one's own capabilities, without exercising them. Aggregate calibration is well studied, with mixed results, but the underlying structure of elicited confidence is less well understood. We decompose binary confidence judgements from 20 frontier Large Language Models (LLMs) across six benchmarks using tetrachoric factor analysis paired with pairwise calibration, asking whether two models that differ in confidence also differ in performance. On factual recall and information retrieval benchmarks the cross-model confidence matrix is approximately rank-one and a single dominant factor captures most of the latent variance. Models retrieving facts share an item-level difficulty axis and differ mainly in their decision thresholds along it. Across all benchmarks the relationship between confidence and performance collapses once items that all models agree on are removed. Inter-model pairwise calibration is small even where statistically significant, and what remains shrinks to nothing once base-rate differences along the shared factor are controlled for. Mathematical reasoning is the apparent exception, but this turns out to be a confound where reasoning models answer questions about their confidence by trying to solve them in their chain of thought, bypassing the sub-symbolic self-knowledge we seek to measure. We find no evidence for significant verbalised individuated metacognition in any tested domain.

M. Moran, Mark Whiting

Pareto AI

LLM EvaluationConfidence Estimation in Language ModelsLanguage Model CalibrationLLM Uncertainty EstimationMetacognition in Language Models
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May 20, 2026

Calibration vs Decision Making: Revisiting the Reliability Paradox in Unlearned Language Models

Machine unlearning aims to remove the influence of specific training data from a model while preserving reliable behavior on the remaining data, making reliable prediction and uncertainty estimation essential for evaluation. Calibration is commonly used as a proxy for reliability in language models, but low calibration error does not necessarily imply reliable decision rules, as models may rely on spurious correlations while remaining well calibrated. We investigate this gap in generative language models using the multiple-choice question-answering evaluation protocol on the TOFU benchmark, measuring probabilistic reliability with calibration metrics (ECE, MCE, Brier) and decision-rule reliability via attribution-based shortcut detection with Integrated Gradients and Local Mutual Information. We find that fine-tuned models achieve low calibration error (ECE ~ 0.04) compared to pretrained models (ECE > 0.5), and models after unlearning retain similarly low calibration despite reduced accuracy on the forget split, while attribution analysis shows increased reliance on correlation-based tokens. These results demonstrate that good calibration can coexist with shortcut-based decision rules after unlearning, extending the reliability paradox to the machine unlearning setting.

Divyaksh Shukla, Ashutosh Modi

Indian Institute of Technology Kanpur (IIT Kanpur)

Shortcut Learning in Language ModelsConfidence Estimation in Language ModelsLanguage Model CalibrationLLM ReliabilityLLM UnlearningMachine Unlearning Evaluation
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May 19, 2026

Reading Calibrated Uncertainty from Language Model Trajectories

The maximum softmax probability (MSP) represents a default approach when evaluating uncertainty quantification for language model generation with structured output. Although cheap, it is often miscalibrated. Methods that probe the model's internal activations feed raw hidden states into opaque classifiers, reading activations as static snapshots and leaving implicit the layer-wise trajectory by which a representation is formed. Yet, similar endpoints can arise from very different paths, and how evidence accumulates, reinforces, or reverses across depth might reveal uncertainty that final probabilities obscure. We extract eleven scale-invariant geometric features, tracing the cumulative path of per-layer MLP updates, and feed them to a sparse linear probe. The probe outperforms MSP under selective abstention, with gains scaling with baseline miscalibration up to 21 AURC points. Because every feature has a closed-form geometric meaning, the probe's coefficients trace how and where along depth errors take shape -- which layers commit prematurely, which contradict the running state, where trajectories drift away from their endpoint.

Aliai Eusebi, Alexander Herzog, Xiaoyu Liang +3

University College London, London, United Kingdom · Core46, London, United Kingdom

Confidence Estimation in Language ModelsLLM ReliabilityLLM Uncertainty EstimationRepresentation Geometry in Language ModelsUncertainty CalibrationLanguage Model Probing
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May 19, 2026

Retrieval-Augmented Linguistic Calibration

Linguistic cues such as "I believe" and "probably" offer an intuitive interface for communicating confidence, yet a generalisable, principled calibration framework for linguistic confidence expressions remains underexplored. In particular, co-occurring linguistic cues, contextual variation, and subjective audience interpretation pose unique challenges. We therefore model linguistic confidence as a distribution over plausible perceived probability values that a statement is correct, capturing interpretation variability that scalar representations discard. Within this distributional framework, we introduce faithfulness as a complementary evaluation dimension and present Faithfulness Divergence (FD), an information-theoretic metric quantifying the surprise induced in audience beliefs upon truth revelation. Building on these foundations, we present Retrieval-Augmented Linguistic Calibration (RALC), a lightweight post-hoc pipeline that propagates calibrated confidence signals back into natural language via retrieval-augmented rewriting. Across three QA benchmarks and five LLM families, RALC improves in-domain faithfulness and calibration up to 66% and 58%, respectively, outperforming black-box and grey-box calibration baselines.

Yi-Fan Yeh, Linwei Tao, Minjing Dong +4

School of Computer Science University of Sydney Sydney, Australia · City University of Hong Kong Hong Kong · Shanghai Jiao Tong University Shanghai, China +1

Confidence Estimation in Language ModelsFaithfulness of Language Model ReasoningLanguage Model CalibrationLLM Uncertainty EstimationVerbalized Confidence EstimationConfidence Estimation
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May 19, 2026

Diagnosing Multi-step Reasoning Failures in Black-box LLMs via Stepwise Confidence Attribution

Large Language Models have achieved strong performance on reasoning tasks with objective answers by generating step-by-step solutions, but diagnosing where a multi-step reasoning trace might fail remains difficult. Confidence estimation offers a diagnostic signal, yet existing methods are restricted to final answers or require internal model access. In this paper, we introduce Stepwise Confidence Attribution (SCA), a framework for closed-source LLMs that assigns step-level confidence based only on generated reasoning traces. SCA applies the Information Bottleneck principle: steps aligning with consensus structures across correct solutions receive high confidence, while deviations are flagged as potentially erroneous. We propose two complementary methods: (1) NIBS, a non-parametric IB approach measuring consistency without graph structures, and (2) GIBS, a graph-based IB model that learns subgraphs through a differentiable mask to capture logical variability. Extensive experiments on mathematical reasoning and multi-hop question answering show that SCA reliably identifies low-confidence steps strongly correlated with reasoning errors. Moreover, using step-level confidence to guide self-correction improves the correction success rate by up to 13.5% over answer-level feedback.

Xiaoou Liu, Tiejin Chen, Dengjia Zhang +3

1Arizona State University · 2Johns Hopkins University · 3Purdue +1

Uncertainty QuantificationConfidence Estimation in Language ModelsLLM ReliabilityLLM Uncertainty EstimationLLM Reasoning
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May 19, 2026

Position: Uncertainty Quantification in LLMs is Just Unsupervised Clustering

Uncertainty Quantification (UQ) is widely regarded as the primary safeguard for deploying Large Language Models (LLMs) in high-stakes domains. However, we argue that the field suffers from a category error: mainstream UQ methods for LLMs are just unsupervised clustering algorithms. We demonstrate that most current approaches inherently quantify the internal consistency of the model's generations rather than their external correctness. Consequently, current methods are fundamentally blind to factual reality and fail to detect ``confident hallucinations,'' where models exhibit high confidence in stable but incorrect answers. Therefore, the current UQ methods may create a deceptive sense of safety when deploying the models with uncertainty. In detail, we identify three critical pathologies resulting from this dependence on internal state: a hyperparameter sensitivity crisis that renders deployment unsafe, an internal evaluation cycle that conflates stability with truth, and a fundamental lack of ground truth that forces reliance on unstable proxy metrics to evaluate uncertainty. To resolve this impasse, we advocate for a paradigm shift to UQ and outline a roadmap for the research community to adopt better evaluation metrics and settings, implement mechanism changes for native uncertainty, and anchor verification in objective truth, ensuring that model confidence serves as a reliable proxy for reality.

Tiejin Chen, Longchao Da, Xiaoou Liu +1

School of Computing and Augmented Intelligence, Arizona State University

LLM EvaluationUncertainty QuantificationConfidence Estimation in Language ModelsLLM ReliabilityLLM Hallucination DetectionLLM Uncertainty Estimation
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May 16, 2026

Confidence Geometry Reveals Trace-Level Correctness in Large Language Model Reasoning

Large language models (LLMs) generate not only reasoning text, but also token-level confidence trajectories that record how uncertainty evolves during inference. Whether these trajectories are relevant to reasoning correctness remains unclear. Here we show that confidence trajectories encode a content-agnostic confidence geometry associated with trace-level final-answer correctness. Using only token-level confidence values, without access to the input question, reasoning text, hidden states, or external verifiers, we find that low-dimensional representations of confidence trajectories separate correct from incorrect reasoning traces. Across GSM8K, MATH, and MMLU, this geometric separation is quantitatively linked to downstream predictability: stronger clustering of correct and incorrect traces, measured by the Davies--Bouldin index, consistently corresponds to higher correctness-discrimination AUC. We further show that correctness-related information is enriched in the tail of reasoning, suggesting that late-stage confidence dynamics carry key correctness signals. We propose NeuralConf, a lightweight estimator that learns from confidence trajectories for correctness evaluation. Under a fixed trace budget, NeuralConf-derived scores improve confidence-weighted answer aggregation over majority voting, tail confidence, and other static baselines. These results reveal that LLMs expose trace-intrinsic statistical signals of correctness through their own confidence dynamics, offering a route to improve inference using information already present within generation.

Shuo Liu, Ding Liu, Shi-Ju Ran

School of Computer Science and Technology, Tiangong University, Tianjin, China. · Center for Quantum Physics and Intelligent Sciences, Department of Physics, Capital Normal University, Beijing, China.

Confidence Estimation in Language ModelsLLM ReliabilityLLM Uncertainty EstimationLLM Reasoning
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May 14, 2026

Margin-Adaptive Confidence Ranking for Reliable LLM Judgement

Jung et al. (2025) introduce a hypothesis testing framework for guaranteeing agreement between large language models (LLMs) and human judgments, relying on the assumption that the model's estimated confidence is monotonic with respect to human-disagreement risk. In practice, however, this assumption may be violated, and the generalization behavior of the confidence estimator is not explicitly analyzed. We mitigate these issues by learning a dedicated confidence estimator instead of relying on heuristic confidence signals. Our approach leverages simulated annotator diversity and a margin-based ranking formulation to explicitly model how confidently an LLM distinguishes between human-agreement and human-disagreement cases. We further derive generalization guarantees for this estimator, revealing a margin-dependent trade-off that informs the design of an adaptive estimator training procedure. When integrated into fixed-sequence testing, the learned confidence estimator yields improved ranking accuracy and empirically strengthens the monotonic relationship between confidence and disagreement risk, leading to higher success rates in satisfying target agreement levels across multiple datasets and judge models.

Gaojie Jin, Yong Tao, Lijia Yu +1

Department of Computer Science, University of Exeter · Institute of AI for Industries, Chinese Academy of Sciences · Department of Mathematics and Computer Science, Eindhoven University of Technology

LLM EvaluationLLM-as-a-JudgeLearning to RankConfidence Estimation in Language ModelsHuman-AI AgreementLLM Uncertainty Estimation
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May 13, 2026

Inducing Artificial Uncertainty in Language Models

In safety-critical applications, language models should be able to characterize their uncertainty with meaningful probabilities. Many uncertainty quantification approaches require supervised data; however, finding suitable unseen challenging data is increasingly difficult for large language models trained on vast amounts of scraped data. If the model is consistently (and correctly) confident in its predictions, the uncertainty quantification method may consistently overestimate confidence on new and unfamiliar data. Finding data which exhibits enough uncertainty to train supervised uncertainty quantification methods for high-performance models may therefore be challenging, and will increase in difficulty as LLMs saturate datasets. To address this issue, we first introduce the problem of inducing artificial uncertainty in language models, then investigate methods of inducing artificial uncertainty on trivially easy data in the absence of challenging data at training time. We use probes trained to recognize artificial uncertainty on the original model, and find that these probes trained on artificial uncertainty outperform probes trained without artificial uncertainty in recognizing real uncertainty, achieving notably higher calibration on hard data with minimal loss of performance on easy data.

Sophia Hager, Simon Zeng, Nicholas Andrews

Johns Hopkins University · Microsoft

Confidence Estimation in Language ModelsLanguage Model CalibrationLLM Uncertainty Estimation
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May 13, 2026

LLMs as Implicit Imputers: Uncertainty Should Scale with Missing Information

Large language models (LLMs) are increasingly deployed in settings where the available context is incomplete or degraded. We argue that an LLM generating answers under incomplete context can be viewed as an implicit imputer, and evaluated against a criterion from the multiple imputation (MI) literature: uncertainty should scale with the amount of missing information. We assess this criterion on SQuAD, using a controlled framework in which context availability is varied across five levels. We evaluate two answer-level uncertainty measures that can be estimated from repeated sampling: sampling-based confidence (empirical mode frequency) and response entropy. Confidence fails to reflect increasing missingness: it remains high even as accuracy collapses. Entropy, by contrast, increases with context removal, consistent with the MI analogy, and explains substantially more variance in accuracy than confidence across all evidence levels (quadratic R2R^2 gap up to 0.057). We further introduce a black-box diagnostic ρR(α)ρ_R(α) that estimates the proportion of baseline uncertainty resolved by context level αα, requiring only repeated sampling with and without context. These results suggest that entropy is a more responsive black-box uncertainty measure than confidence under incomplete context.

Stef van Buuren

1. TNO - Netherlands Organization for Applied Scientific Research, Leiden · 2. Dept. of Methodology and Statistics, University of Utrecht

LLM EvaluationConfidence Estimation in Language ModelsLLM ReliabilityLLM Uncertainty Estimation
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May 12, 2026

ORCE: Order-Aware Alignment of Verbalized Confidence in Large Language Models

Large language models (LLMs) often produce answers with high certainty even when they are incorrect, making reliable confidence estimation essential for deployment in real-world scenarios. Verbalized confidence, where models explicitly state their confidence in natural language, provides a flexible and user-facing uncertainty signal that can be applied even when token logits are unavailable. However, existing verbalized-confidence methods often optimize answer generation and confidence generation jointly, which can cause confidence-alignment objectives to interfere with answer accuracy. In this work, we propose a decoupled and order-aware framework for verbalized confidence calibration. Our method first generates an answer and then estimates confidence conditioned on the fixed question--answer pair, allowing confidence optimization without directly perturbing the answer-generation process. To align confidence with correctness likelihood, we construct a sampling-based surrogate from multiple model completions and optimize rank-based reinforcement learning objectives that encourage responses with higher estimated correctness likelihood to receive higher verbalized confidence. Experiments on reasoning and knowledge-intensive benchmarks show that our method improves calibration and failure prediction performance while largely preserving answer accuracy. These results demonstrate that verbalized confidence can be more reliably aligned by decoupling confidence estimation from answer generation and optimizing the relative ordering of confidence across responses.

Chen Li, Xiaoling Hu, Songzhu Zheng +2

Stony Brook University, NY, USA · Massachusetts General Hospital and Harvard Medical School, MA, USA · Morgan Stanley, NY, USA

Confidence Estimation in Language ModelsLanguage Model CalibrationLLM ReliabilityLLM Uncertainty EstimationVerbalized Confidence Estimation
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May 12, 2026

Confidently Deceptive: On the Relationship Between Confidence and Deception in LLMs

The increasing capabilities of large language models (LLMs) are being accompanied by deep-rooted risks of deceptive behaviours that cause models to produce misleading outputs in service of a contextually or experimentally induced goal. The harm posed by such behaviours depends not only on the content of deceptive outputs but also how confidently models deliver them, since confidence has a major impact on how persuasive the communication is to end users. In this paper, we provide a comprehensive study on the crucial relationship between confidence and deception across existing deception benchmarks and different model families, while covering both verbalized numerical and logit-based aggregated confidence. Through this, we reveal how confidently models behave when being deceptive. We demonstrate that when producing deceptive rather than honest responses, models exhibit a gap between their belief (how likely they think a claim is to be true) and their commitment (how firmly they assert and would defend that claim). LLMs produce persuasive deceptive claims while reporting low belief in their factual correctness. Their reported commitment to deceptive responses can easily be increased through further prompting and preference fine-tuning, with smaller and condition-dependent changes in reported belief. However, we show that low reported belief remains comparatively invariant and provides a strong signal for detecting deception in the evaluated settings. Using only an API call, our approach achieves detection scores of up to 0.99 for induced deception and 0.89 for emergent deception. This ultimately shows how confidence can be a practical tool for detecting and diagnosing deceptive behaviour in LLMs.

Ali Asad, Stephen Obadinma, Anshul Pattoo +2

Department of Electrical and Computer Engineering & Ingenuity Labs Research Institute Queen’s University, Kingston, Canada

Language Model Safety EvaluationConfidence Estimation in Language ModelsDeception in Language ModelsLLM Safety EvaluationLLM Honesty
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May 11, 2026

VERDI: Single-Call Confidence Estimation for Verification-Based LLM Judges via Decomposed Inference

LLM-as-Judge systems are widely deployed for automated evaluation, yet practitioners lack reliable methods to know when a judge's verdict should be trusted. Token log-probabilities, the standard post-hoc confidence signal, are unavailable for many commercial LLMs and, even when accessible, saturate above 0.999 with structured JSON output. We introduce VERDI (VERification-Decomposed Inference), a method that extracts confidence from the reasoning trace a structured judge already produces, with no additional inference calls. VERDI decomposes each verification-style evaluation into sub-checks and derives three structural signals: Step-Verdict Alignment, Claim-Level Margin, and Evidence Grounding Score. We combine them with Platt-scaled logistic regression. On three public benchmarks, VERDI achieves AUROC 0.72-0.91 on GPT-4.1-mini and 0.66-0.80 on GPT-5.4-mini. On Qwen3.5-4B/9B/27B, where answer-token logprobs are anti-calibrated (higher confidence on errors, AUROC 0.32-0.49), VERDI achieves 0.56-0.70. We additionally validate on a production system with eight rubrics (AUROC 0.73-0.88 on factual rubrics), demonstrate cross-model transfer (AUROC 0.66-0.69), and show that a 33M-parameter NLI (Natural Language Inference) model provides a scalable alternative to regex extraction.

Jasmine Qi, Danylo Dantsev, Muyang Sun

Indeed Inc.

Post-Hoc CalibrationLLM-as-a-JudgeLLM Answer VerificationLanguage Model Generation EvaluationConfidence Estimation in Language ModelsLLM Reliability+1
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May 11, 2026

Grounded or Guessing? LVLM Confidence Estimation via Blind-Image Contrastive Ranking

Large vision-language models suffer from visual ungroundedness: they can produce a fluent, confident, and even correct response driven entirely by language priors, with the image contributing nothing to the prediction. Existing confidence estimation methods cannot detect this, as they observe model behavior under normal inference with no mechanism to determine whether a prediction was shaped by the image or by text alone. We introduce BICR (Blind-Image Contrastive Ranking), a model-agnostic confidence estimation framework that makes this contrast explicit during training by extracting hidden states from a frozen LVLM twice: once with the real image-question pair, and once with the image blacked out while the question is held fixed. A lightweight probe is trained on the real-image hidden state and regularized by a ranking loss that penalizes higher confidence on the blacked-out view, teaching it to treat visual grounding as a signal of reliability at zero additional inference cost. Evaluated across five modern LVLMs and seven baselines on a benchmark covering visual question answering, object hallucination detection, medical imaging, and financial document understanding, BICR achieves the best cross-LVLM average on both calibration and discrimination simultaneously, with statistically significant discrimination gains robust to cluster-aware analysis at 4-18x fewer parameters than the strongest probing baseline.

Reza Khanmohammadi, Erfan Miahi, Simerjot Kaur +4

Michigan State University · Independent AI Researcher · JPMorgan AI Research +1

VLM EvaluationConfidence Estimation for VLMsVision-Language ModelsConfidence Estimation in Language ModelsVision-Language GroundingVisually Grounded Reasoning+1
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May 8, 2026

A Semantic-Sampling Framework for Evaluating Calibration in Open-Ended Question Answering

Calibration measures whether a model's predicted confidence aligns with its empirical accuracy, and is central to the reliable deployment of large language models (LLMs) in high-stakes domains such as medicine and law. While much recent work focuses on improving LLM calibration, the equally important question of how to evaluate it in realistic settings remains underdeveloped. Open-ended question answering (QA), the most common deployment setting for modern LLMs, is where existing evaluation methods fall short: logit-based metrics need restricted output formats and internal probabilities; verbalized confidence is self-reported and often overconfident; and sampling-based methods rely on task-specific extraction rules without a clear finite-sample target. We introduce Sem-ECE (Semantic-Sampling Expected Calibration Error), a calibration evaluation framework for open-ended QA that samples answers from the model, groups them into semantic classes, and uses the resulting frequencies as confidence. We study two estimators within this framework: Sem1_1-ECE, the same-sample self-consistency score, and Sem2_2-ECE, a held-out variant that separates answer selection from confidence evaluation. We prove both are asymptotically unbiased, and further show that they agree on easy questions but diverge on hard ones with Sem2_2 achieving strictly smaller calibration error, so their gap also serves as a diagnostic for question difficulty. Experiments on three open-ended QA benchmarks across five leading commercial LLMs match our theoretical predictions and show that Sem-ECE outperforms verbalized confidence and existing sampling-based methods, while complementing logit-based evaluation when internal probabilities are unavailable.

Zhanliang Wang, Jiancong Xiao, Ruochen Jin +3

University of Pennsylvania, Philadelphia, PA · Dartmouth College, Hanover, NH

LLM EvaluationConfidence Estimation in Language ModelsLanguage Model CalibrationModel CalibrationLLM ReliabilityLLM Uncertainty Estimation
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May 8, 2026

Beyond Confidence: Rethinking Self-Assessments for Performance Prediction in LLMs

Large Language Models (LLMs) are increasingly used in settings where reliable self-assessment is critical. Assessing model reliability has evolved from using probabilistic correctness estimates to, more recently, eliciting verbalized confidence. Confidence, however, has been shown to be an inconsistent and overoptimistic predictor of model correctness. Drawing on cognitive appraisal theory, a framework from human psychology that decomposes self-evaluation into multiple components, we propose a multidimensional perspective on model self-assessment. We elicit six appraisal-based dimensions of self-assessment, alongside confidence, and evaluate their utility for predicting model failure across 12 LLMs and 38 tasks spanning eight domains. We find that competence-related appraisal dimensions, particularly effort and ability, consistently match or outperform confidence across most settings. Effort additionally yields less overoptimistic estimates that remain stable across model sizes. In contrast, affective dimensions provide marginally predictive signals. Furthermore, the most informative dimension varies systematically with task characteristics: effort is most predictive for reasoning-intensive tasks, while ability and confidence dominate on retrieval-oriented tasks. Broadly, our findings indicate that structured multidimensional self-assessment is a promising approach to improving the reliability and safety of language model deployment across diverse real-world settings.

Sree Bhattacharyya, Samarth Khanna, Leona Chen +3

Department of Informatics and Intelligent Systems, College of Information Sciences, The Pennsylvania State University. · Department of Computer Science and Engineering, College of Engineering, The Pennsylvania State University.

LLM EvaluationConfidence Estimation in Language ModelsLanguage Model Self-AssessmentLanguage Model CalibrationLLM ReliabilityLLM Uncertainty Estimation
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May 7, 2026

Measuring Black-Box Confidence via Reasoning Trajectories: Geometry, Coverage, and Verbalization

Reliable confidence estimation enables safe deployment of chain-of-thought (CoT) reasoning through text-only APIs. Yet the dominant black-box baseline, self-consistency over K samples, is linearly expensive and ignores the geometry of the trace. We propose a black-box trajectory-confidence score: we embed a CoT as a sliding-window trajectory and measure its convergence to external answer anchors with a one-parameter softmax. The method needs no logits, hidden states, or supervised calibrators. Across six (benchmark, reasoner) settings on MedQA-USMLE, GPQA Diamond, and MMLU-Pro with Gemini 3.1 Pro and Claude Sonnet 4.6, fusing this score with coverage and verbalized-confidence channels at K=4 yields Pareto improvements over self-consistency at K=8 in 6/6 settings (median AUC 0.78 vs 0.71, deltaAUC=+0.075). A fixed-pick control (+0.060) and E5 cross-embedder replication rule out answer switching and single-vendor artifacts. Geometry peaks in the penultimate window across benchmarks and reasoners, and inverts at the terminal window on GPQA Diamond. Three unscaffolded regimes separate black-box confidence into a judge-mediated Coverage prior (C), within-trace Geometry (G), and a conditional Verbalization channel (V). Across 18 benchmark x reasoner x proposer settings, C and G provide independent signal in 18/18 and 16/18, while V contributes residual signal in 6/18. Swapping the judge from GPT-5-mini to Claude Sonnet 4.6 leaves G-only AUC unchanged (|delta|<=0.013) and shifts C-only AUC by at most +/-0.02 (kappa=0.82). Fusion beats the best single channel in 17/18 settings (median AUC 0.78, max 0.92).

Marc Boubnovski Martell, Josefa Lia Stoisser, Kaspar Märtens +4

1Novo Nordisk · University of Oxford

LLM Uncertainty EstimationCoT ReasoningReasoning Trace AnalysisConfidence Estimation in Language ModelsVerbalized Confidence EstimationLLM Reasoning+1
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May 7, 2026

Towards Generation-Efficient Uncertainty Estimation in Large Language Models

Uncertainty estimation is important for deploying LLMs in high-stakes applications such as healthcare and finance, where hallucinations can appear fluent and plausible while being factually incorrect, making it difficult for users to judge whether an output should be trusted. Existing methods require one or more full autoregressive generations to estimate uncertainty, which introduces substantial inference cost and often delays uncertainty assessment. In this paper, we investigate whether effective uncertainty estimation can be achieved with partial generation or even input-only information. Specifically, we first develop a unified framework that formulates uncertainty estimation as an early estimation problem over the autoregressive generation process of LLMs. This framework organises existing and proposed estimators by the information they observe, ranging from multi-generation to input-only prediction, and clarifies the performance-cost trade-off underlying different uncertainty estimation methods. Building on this view, we study two largely underexplored low-cost settings: estimating uncertainty with part of the generation, and predicting uncertainty from the input prompt. We propose Logit Magnitude, which uses top-M logit evidence to estimate uncertainty from an early-stopped generation prefix, and MetaUE, which distils generation-based uncertainty into a lightweight input-only estimator trained with uncertainty scores. Extensive experiments on general and domain-specific benchmarks show that Logit Magnitude achieves strong performance, and partial generations of LLMs are often sufficient for effective uncertainty estimation. MetaUE further provides a competitive input-only approximation in several settings. These findings suggest that effective uncertainty estimation requires less generation than commonly assumed, enabling unreliable responses to be identified earlier.

Mingcheng Zhu, Yu Liu, Tingting Zhu

University of Oxford

LLM Inference EfficiencyUncertainty QuantificationConfidence Estimation in Language ModelsLLM ReliabilityLLM Uncertainty Estimation
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May 7, 2026

HyperLens: Quantifying Cognitive Effort in LLMs with Fine-grained Confidence Trajectory

While Large Language Models (LLMs) achieve strong performance across diverse tasks, their inference dynamics remain poorly understood because of the limited resolution of existing analysis tools. In this work, we identify an intrinsic magnification mechanism in transformer architectures: deeper layers inherently magnify the small changes of layer-wise confidence, providing a fine-grained confidence trajectory. Building on this insight, we introduce HyperLens, a high-resolution probe designed to trace confidence trajectories and quantify the cognitive effort during inference. Across LLMs and datasets, HyperLens reveals a consistent divergence in confidence trajectories that separates complex from simple tasks. We abstract this pattern into a quantitative cognitive effort metric. Our analysis reveals a fundamental principle: complex tasks consistently require higher cognitive effort. Finally, we provide a mechanistic diagnosis of a common side effect of standard Supervised Fine-Tuning (SFT): it can reduce cognitive effort and consequently degrade performance on in-domain tasks.

Chengda Lu, Xiaoyu Fan, Wei Xu

1IIIS, Tsinghua University · 2Shanghai Qi Zhi Institute.

Confidence Estimation in Language ModelsLLM InterpretabilityLLM Fine-TuningLanguage Model Probing
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May 6, 2026

Detecting Hallucinations in Large Language Models via Internal Attention Divergence Signals

We propose a lightweight and single-pass uncertainty quantification method for detecting hallucinations in Large Language Models. The method uses attention matrices to estimate uncertainty without requiring repeated sampling or external models. Specifically, we measure the Kullback-Leibler divergence between each attention head's distribution and a uniform reference distribution, and use these features in a logistic regression probe. Across multiple datasets, task types, and model families, attention divergence is highly predictive of answer correctness and performs competitively with existing uncertainty estimation methods. We find that this signal is concentrated in middle layers and on factual tokens such as named entities and numbers, suggesting that attention dynamics provides an efficient and interpretable white-box signal of model uncertainty.

Gijs van Dijk

Utrecht University

Language Model Error DetectionConfidence Estimation in Language ModelsLLM InterpretabilityHallucination in Language ModelsLLM ReliabilityLLM Hallucination Detection+1
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May 4, 2026

Zero-Shot Confidence Estimation for Small LLMs: When Supervised Baselines Aren't Worth Training

How reliably can a small language model estimate its own correctness? The answer determines whether local-to-cloud routing-escalating queries a cheap local model cannot handle-can work without supervised training data. As inference costs dominate large language model (LLM) deployment budgets, routing most queries to a cheap local model while reserving expensive cloud calls for hard cases is an increasingly common cost-control strategy. We compare zero-shot confidence signals against RouteLLM-style supervised baselines across three 7-8B model families and two datasets (1,000 and 500 queries per model, respectively). Average token log-probability, which requires no training data, matches or exceeds supervised baselines in-distribution (Area Under the Receiver Operating Characteristic curve (AUROC) 0.650-0.714 vs. 0.644-0.676) and substantially outperforms them out-of-distribution (0.717-0.833 vs. 0.512-0.564), because it measures a property of the model's generation rather than the query distribution. This paper further proposes retrieval-conditional self-assessment, a pre-generation signal that selectively injects retrieved knowledge when similarity is high, improving over bare self-assessment by up to +0.069 AUROC at 3-10x lower latency than log-probability. A supervised baseline trained on 1,000 labeled examples never exceeds the zero-shot signal. We release all code, data, and experiment logs.

Luong N. Nguyen

Confidence Estimation in Language ModelsLanguage Model Self-AssessmentLLM ReliabilityLLM Uncertainty EstimationLLM Routing
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Apr 30, 2026

Geometry-Calibrated Conformal Abstention for Language Models

When language models lack relevant knowledge for a given query, they frequently generate plausible responses that can be hallucinations, rather than admitting being agnostic about the answer. Retraining models to reward admitting ignorance can lead to overly conservative behaviors and poor generalization due to scarce evaluation benchmarks. We propose a post hoc framework, Conformal Abstention (CA), adapted from conformal prediction (CP) to determine whether to abstain from answering a query. CA provides finite-sample guarantees on both the probability of participation (i.e., not abstaining) and the probability that the generated response is correct. Importantly, the abstention decision relies on prediction confidence rather than the non-conformity scores used in CP, which are intractable for open-ended generation. To better align prediction confidence with the model's ignorance, we introduce a calibration strategy using representation geometry within the model to measure knowledge involvement in shaping the response. Experiments demonstrate that we improve selective answering significantly with 75 percent conditional correctness.

Rui Xu, Yi Chen, Sihong Xie +1

Information Hub, AI Thrust Hong Kong University of Science and Technology (Guangzhou) Guangzhou, Guangdong, China

Uncertainty QuantificationSelective PredictionConfidence Estimation in Language ModelsHallucination in Language ModelsConformal PredictionLLM Abstention+4
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Apr 27, 2026

Distilling Self-Consistency into Verbal Confidence: A Pre-Registered Negative Result and Post-Hoc Rescue on Gemma 3 4B

Small instruct-tuned LLMs produce degenerate verbal confidence under minimal elicitation: ceiling rates above 95%, near-chance Type-2 AUROC, and Invalid validity profiles. We test whether confidence-conditioned supervised fine-tuning (CSFT) with self-consistency-derived targets can close the gap between internal information and verbal readout. A pre-registered Phase 0 protocol on Gemma 3 4B-it with a modal filter restricting training to items with correct modal answers produced a negative result: AUROC2 dropped from 0.554 to 0.509 due to label-entropy collapse in the training targets. An exploratory rescue removed the filter, training on all 2,000 calibration items. This produced a binary verbal correctness discriminator with AUROC2 = 0.774 on held-out TriviaQA, compressing a 10-sample self-consistency signal (AUROC2 = 0.999) into a single-pass readout exceeding logit entropy (0.701). The shuffled-target control showed no improvement (0.501). On MMLU, accuracy improved from 54.2% to 77.4% with the shuffled model at baseline (56.1%), supporting a target-dependent interpretation. The result is exploratory, binary rather than continuously calibrated, and observed at a single scale. It identifies two design lessons: confidence training requires label entropy, and correct targets regularise output format.

Jon-Paul Cacioli

Independent Researcher, Melbourne, Australia

Supervised Fine-TuningConfidence Estimation in Language ModelsSelf-Consistency DecodingLanguage Model CalibrationLLM ReliabilityLanguage Model Distillation+1
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