Confidence Estimation in Language Models

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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

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

Apr 25, 2026

Process Supervision of Confidence Margin for Calibrated LLM Reasoning

Scaling test-time computation with reinforcement learning (RL) has emerged as a reliable path to improve large language models (LLM) reasoning ability. Yet, outcome-based reward often incentivizes models to be overconfident, leading to hallucinations, unreliable confidence-based control, and unnecessary compute allocation. We introduce Reinforcement Learning with Confidence Margin (RLCM), a calibration-aware RL framework that jointly optimizes correctness and confidence reliability via a margin-enhanced process reward over intermediate-budget completions. Rather than aligning confidence to correctness likelihoods, RLCM encourages to widen the confidence margin between correct and incorrect steps within a single reasoning trajectory. Across mathematical, code, logic and science benchmarks, our method substantially improves calibration while maintaining or improving accuracy. We further show that, with calibrated confidence signals, the resulting models enable more efficient conformal risk control and effective confidence-weighted aggregation.

Liaoyaqi Wang, Chunsheng Zuo, William Jurayj +2

Johns Hopkins University

Confidence Estimation in Language Models RL for Language Model Reasoning Language Model Calibration LLM Reliability Process Supervision LLM Uncertainty Estimation

Apr 24, 2026

How LLMs Detect and Correct Their Own Errors: The Role of Internal Confidence Signals

Large language models can detect their own errors and sometimes correct them without external feedback, but the underlying mechanisms remain unknown. We investigate this through the lens of second-order models of confidence from decision neuroscience. In a first-order system, confidence derives from the generation signal itself and is therefore maximal for the chosen response, precluding error detection. Second-order models posit a partially independent evaluative signal that can disagree with the committed response, providing the basis for error detection. Kumaran et al. (2026) showed that LLMs cache a confidence representation at a token immediately following the answer (i.e. post-answer newline: PANL) -- that causally drives verbal confidence and dissociates from log-probabilities. Here we test whether this PANL signal extends beyond confidence to support error detection and self-correction. Here we test whether this signal supports error detection and self-correction, deriving predictions from the second-order framework. Using a verify-then-correct paradigm, we show that: (i) verbal confidence predicts error detection far beyond token log-probabilities, ruling out a first-order account; (ii) PANL activations predict error detection beyond verbal confidence itself; and (iii) PANL predicts which errors the model can correct -- where all behavioural signals fail. Causal interventions confirm that PANL signals rescue error detection behavior when answer information is corrupted. All findings replicate across models (Gemma 3 27B and Qwen 2.5 7B) and tasks (TriviaQA and MNLI). These results reveal that LLMs naturally implement a second-order confidence architecture whose internal evaluative signal encodes not only whether an answer is likely wrong but whether the model has the knowledge to fix it.

Dharshan Kumaran, Viorica Patraucean, Simon Osindero +2

Google DeepMind · Princeton University

LLM Self-Correction Language Model Error Detection Confidence Estimation in Language Models LLM Interpretability LLM Uncertainty Estimation Metacognition in Language Models

Apr 24, 2026

Calibration Drift Under Reasoning: How Chain-of-Thought Budgets Induce Overconfidence in Large Language Models

The ability of large language models (LLMs) to express calibrated uncertainty is important for safe deployment. Chain-of-thought (CoT) reasoning is widely used to improve accuracy and reliability, but its effect on calibration is not fully understood. We show that this picture is incomplete: in some settings, increasing the reasoning budget beyond a task-specific threshold can cause models to become systematically overconfident, assigning high confidence to incorrect answers. We call this phenomenon Calibration Drift Under Reasoning (CDUR) and study it both theoretically and empirically. We define reasoning budget B and analyze conditions under which Expected Calibration Error ECE(B) follows a non-monotonic pattern: it first decreases as reasoning corrects errors, then increases as longer reasoning produces internally consistent but incorrect explanations. We propose a Hypothesis Lock-In model based on autoregressive generation to explain this behavior. We evaluate Llama-3.1-8B and Llama-3.3-70B on 47 reasoning-trap questions across four reasoning budgets and three seeds (1,368 API calls; 574 valid responses). The 8B model shows non-monotonic calibration behavior, while results for the 70B model are limited to baseline evaluation and are inconclusive for budget-dependent effects. We introduce CABStop, a calibration-aware stopping rule that halts reasoning when confidence diverges from an auxiliary accuracy estimate. These results suggest that increasing reasoning depth does not always improve reliability and should be monitored carefully.

Prakul Sunil Hiremath, Harshit R. Hiremath

Department of Computer Science and Engineering Visvesvaraya Technological University, Belagavi · Department of Computer Science and Business System SG Balekundri Institute of Technology, Belagavi

Confidence Estimation in Language Models CoT Reasoning Language Model Calibration LLM Reliability LLM Uncertainty Estimation LLM Reasoning

Apr 24, 2026

Verbal Confidence Saturation in 3-9B Open-Weight Instruction-Tuned LLMs: A Pre-Registered Psychometric Validity Screen

Verbal confidence elicitation is widely used to extract uncertainty estimates from LLMs. We tested whether seven instruction-tuned open-weight models (3-9B parameters, four families) produce verbalised confidence that meets minimal validity criteria for item-level Type-2 discrimination under minimal numeric elicitation with greedy decoding. In a pre-registered study (OSF: osf.io/azbvx), 524 TriviaQA items were administered under numeric (0-100) and categorical (10-class) elicitation to eight models at Q5_K_M quantisation on consumer hardware, yielding 8,384 deterministic trials. A psychometric validity screen was applied to each model-format cell. All seven instruct models were classified Invalid on numeric confidence (H2 confirmed, 7/7 vs. predicted >=4/7), with a mean ceiling rate of 91.7% (H1 confirmed). Categorical elicitation did not rescue validity. Instead, it disrupted task performance in six of seven models, producing accuracy below 5% (H4 not confirmed). Token-level logprobability did not usefully predict verbalised confidence under the observed variance regime (H5 confirmed, mean cross-validated R^2 < 0.01). Within the reasoning-distilled model, reasoning-trace length showed a strong negative partial correlation with confidence (rho = -0.36, p < .001), consistent with the Reasoning Contamination Effect. These results do not imply that internal uncertainty representations are absent. They show that minimal verbal elicitation fails to preserve internal signals at the output interface in this model-size regime. Psychometric screening should precede any downstream use of such signals.

Jon-Paul Cacioli

Independent Researcher, Melbourne, Australia

LLM Evaluation Confidence Estimation in Language Models Psychometric Validation LLM Reliability LLM Uncertainty Estimation Verbalized Confidence Estimation

Apr 21, 2026

Binary Agreement for Efficient Unsupervised Confidence Calibration of Reasoning LLMs

Reasoning language models often lack the calibrated confidence needed for reliable deployment, particularly when correctness labels are unavailable and sampling budgets are limited. We introduce Binary Agreement for Self-consistency Calibration (BASC), which uses self-consistency as an unlabeled proxy for correctness without constructing costly self-consistency targets for each calibration query. Our key observation is that agreement between an anchor response and a single independent probe is a Bernoulli observation whose conditional mean is the anchor's latent self-consistency. Pooling these observations across unlabeled queries, BASC supports both recalibrating existing confidence scores and learning more discriminative scores before recalibration, using as few as two responses per calibration query and only one at deployment. The use of binary isotonic recalibration provides a distribution-free calibration guarantee with respect to latent self-consistency. Across 5 tasks and 9 reasoning models, BASC substantially improves calibration with respect to correctness.

Thomas Zollo, Jimmy Wang, Richard Zemel

Columbia University

Confidence Estimation in Language Models Language Model Calibration LLM Reliability LLM Uncertainty Estimation Self-Consistency in Language Models Large Reasoning Models

Apr 19, 2026

Beyond "I Don't Know": Evaluating LLM Self-Awareness in Discriminating Data and Model Uncertainty

Reliable Large Language Models (LLMs) should abstain when confidence is insufficient. However, prior studies often treat refusal as a generic "I don't know'', failing to distinguish input-level ambiguity (data uncertainty) from capability limitations (model uncertainty). This lack of distinction limits downstream action decisions like requesting clarification or invoking external tools. In this work, we introduce UA-Bench, a benchmark of over 3,500 questions drawn from six datasets spanning knowledge-intensive and reasoning-intensive tasks, designed to evaluate explicit uncertainty attribution. An evaluation of 18 frontier LLMs shows that even state-of-the-art models struggle to reliably discriminate between data uncertainty and model uncertainty, and that high answer accuracy does not necessarily imply strong uncertainty attribution ability. To narrow this gap, we propose a lightweight data synthesis and reinforcement learning strategy. Experiments on both Qwen3-4B-Instruct-2507 and Qwen3-8B in thinking mode show that the proposed method improves uncertainty attribution while preserving answer accuracy. Our code and data are publicly available now.

Jingyi Ren, Ante Wang, Yunghwei Lai +5

Dept. of Comp. Sci. & Tech., Institute for AI, Tsinghua University, Beijing, China · Institute for AI Industry Research (AIR), Tsinghua University, Beijing, China

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

Apr 19, 2026

Instinct vs. Reflection: Unifying Token and Verbalized Confidence in Multimodal Large Models

Multimodal Large Language Models (MLLMs) have demonstrated exceptional capabilities in various perception and reasoning tasks. Despite this success, ensuring their reliability in practical deployment necessitates robust confidence estimation. Prior works have predominantly focused on text-only LLMs, often relying on computationally expensive self-consistency sampling. In this paper, we extend this to multimodal settings and conduct a comprehensive evaluation of MLLMs' response confidence estimation. Our analysis reveals a significant instinct-reflection misalignment: the model's implicit token-level support frequently diverges from its verbal self-assessment confidence. To address this misalignment, we propose a monotone confidence fusion framework to merge dual-channel signals and cross-channel consistency to estimate correctness. Subsequently, an order-preserving mean alignment step is applied to correct global bias, which improves calibration while preserving the risk-coverage trade-off for selective prediction. Experiments on diverse open-source and closed-source MLLMs show that our method consistently yields more reliable confidence estimates and improves both calibration and failure prediction. Code will be available at https://github.com/Yunkaidang/Instinct-vs.-Reflection.

Yunkai Dang, Yifan Jiang, Yizhu Jiang +3

School of Artificial Intelligence, Nanjing University.

Selective Prediction Confidence Estimation in Language Models Multimodal Large Language Models Language Model Calibration LLM Reliability LLM Uncertainty Estimation+1

Apr 18, 2026

Complementing Self-Consistency with Cross-Model Disagreement for Uncertainty Quantification

Large language models (LLMs) often produce confident yet incorrect responses, and uncertainty quantification is one potential solution to more robust usage. Recent works routinely rely on self-consistency to estimate aleatoric uncertainty (AU), yet this proxy collapses when models are overconfident and produce the same incorrect answer across samples. We analyze this regime and show that cross-model semantic disagreement is higher on incorrect answers precisely when AU is low. Motivated by this, we introduce an epistemic uncertainty (EU) term that operates in the black-box access setting: EU uses only generated text from a small, scale-matched ensemble and is computed as the gap between inter-model and intra-model sequence-semantic similarity. We then define total uncertainty (TU) as the sum of AU and EU. In a comprehensive study across five 7-9B instruction-tuned models and ten long-form tasks, TU improves ranking calibration and selective abstention relative to AU, and EU reliably flags confident failures where AU is low. We further characterize when EU is most useful via agreement and complementarity diagnostics.

Kimia Hamidieh, Veronika Thost, Walter Gerych +2

1MIT · MIT-IBM Watson AI Lab · 3WPI +1

Selective Prediction Confidence Estimation in Language Models LLM Reliability LLM Uncertainty Estimation Aleatoric Uncertainty Uncertainty Calibration+2

Apr 17, 2026

Beyond Surface Statistics: Robust Conformal Prediction for LLMs via Internal Representations

Large language models are increasingly deployed in settings where reliability matters, yet output-level uncertainty signals such as token probabilities, entropy, and self-consistency can become brittle under calibration--deployment mismatch. Conformal prediction provides finite-sample validity under exchangeability, but its practical usefulness depends on the quality of the nonconformity score. We propose a conformal framework for LLM question answering that uses internal representations rather than output-facing statistics: specifically, we introduce Layer-Wise Information (LI) scores, which measure how conditioning on the input reshapes predictive entropy across model depth, and use them as nonconformity scores within a standard split conformal pipeline. Across closed-ended and open-domain QA benchmarks, with the clearest gains under cross-domain shift, our method achieves a better validity--efficiency trade-off than strong text-level baselines while maintaining competitive in-domain reliability at the same nominal risk level. These results suggest that internal representations can provide more informative conformal scores when surface-level uncertainty is unstable under distribution shift.

Yanli Wang, Peng Kuang, Xiaoyu Han +2

Imperial College London · Zhejiang University · University of Illinois Urbana-Champaign +1

Language Model Robustness Conformal Prediction Confidence Estimation in Language Models Language Model Calibration LLM Reliability Conformal Risk Control+2

Apr 15, 2026

Calibrated Selective Fact-Checking via Evidence Chain Evaluation

Large language models (LLMs) can achieve strong fact-checking accuracy, yet forced binary decisions conceal a critical reliability problem: systems may issue confident verdicts even when supporting evidence is weak, sparse, or internally inconsistent. We address this issue through Evidence Chain Evaluation (ECE), a selective fact-checking framework that permits abstention via an uncertain verdict instead of requiring a true/false decision for every claim. The evaluated system is a tool-using verification agent that gathers evidence through web search, scholarly search, and executable checks, and then returns a structured verdict with confidence and source-level metadata. On ECE-Bench, ECE achieves 91.6% standard accuracy, 93.7% coverage, and 97.8% selective accuracy on answered claims. Although ECE does not outperform the strongest retrieval baseline on aggregate calibration metrics such as Expected Calibration Error, Brier score, or AURC, it delivers a clear selective-prediction trade-off: the system maintains very high accuracy on answered claims while deferring 6 of 95 cases. These deferred cases are concentrated in lower-reliability evidence settings (5/6 at source level L4), supporting the view that abstention functions as a safety-oriented mechanism for handling epistemically weak evidence. Code is available at https://github.com/ cheshireyang/ECE.git

Dekun Yang

Zhejiang University

Automated Fact-Checking Selective Prediction Confidence Estimation in Language Models

Apr 14, 2026

Enhancing Confidence Estimation in Telco LLMs via Twin-Pass CoT-Ensembling

Large Language Models (LLMs) are increasingly applied to complex telecommunications tasks, including 3GPP specification analysis and O-RAN network troubleshooting. However, a critical limitation remains: LLM-generated confidence scores are often biased and unreliable, frequently exhibiting systematic overconfidence. This lack of trustworthy self-assessment makes it difficult to verify model outputs and safely rely on them in practice. In this paper, we study confidence calibration in telecom-domain LLMs using the representative Gemma-3 model family (4B, 12B, and 27B parameters), evaluated on TeleQnA, ORANBench, and srsRANBench. We show that standard single-pass, verbalized confidence estimates fail to reflect true correctness, often assigning high confidence to incorrect predictions. To address this, we propose a novel Twin-Pass Chain of Thought (CoT)-Ensembling methodology for improving confidence estimation by leveraging multiple independent reasoning evaluations and aggregating their assessments into a calibrated confidence score. Our approach reduces Expected Calibration Error (ECE) by up to 88% across benchmarks, significantly improving the reliability of model self-assessment. These results highlight the limitations of current confidence estimation practices and demonstrate a practical path toward more trustworthy evaluation of LLM outputs in telecommunications.

Anton Saenko, Pranshav Gajjar, Abiodun Ganiyu +1

NextG Wireless Lab, North Carolina State University, Raleigh, NC, USA

Confidence Estimation in Language Models Language Model Calibration

Apr 14, 2026

Agentic Control in Variational Language Models

We study whether a variational language model can support a minimal and measurable form of agentic control grounded in its own internal evidence. Our model combines local variational hidden computation (EVE), a homeostatic latent regulator, structurally aware checkpoint retention and a calibrated uncertainty-aware controller operating on top of the retained model. Rather than treating uncertainty as a passive diagnostic measured after prediction, we treat it as an operational signal that can regulate training, support checkpoint retention and guide inference-time intervention. The resulting framework is deliberately focused. It studies a closed-loop form of internal control in which structural and predictive signals become actionable. Empirically, the variational backbone improves over a matched deterministic reference on the language-modeling task while also exhibiting a richer and more usable uncertainty profile. On top of this backbone, the calibrated controller remains active, uses multiple actions under a full agentic evaluation and yields a positive quality-cost trade-off. These results support a precise claim: internal uncertainty can serve not only as a descriptive property of a variational language model, but also as a practical control interface for regulation, checkpoint retention and minimal agentic routing.

Yves Ruffenach

Conservatoire National des Arts et Métiers, Strasbourg, France

Language Model-Based Control Language Modeling Language Model Calibration Confidence Estimation in Language Models

Apr 14, 2026

Calibrated Confidence Estimation for Tabular Question Answering

Large language models (LLMs) are increasingly deployed for tabular question answering, yet calibration on structured data is largely unstudied. This paper presents the first systematic comparison of five confidence estimation methods across five frontier LLMs and two tabular QA benchmarks. All models are severely overconfident (smooth ECE 0.35-0.64 versus 0.10-0.15 reported for textual QA). A consistent self-evaluation versus perturbation dichotomy replicates across both benchmarks and all four fully-covered models: self-evaluation methods (verbalized, P(True)) achieve AUROC 0.42-0.76, while perturbation methods (semantic entropy, self-consistency, and our Multi-Format Agreement) achieve AUROC 0.78-0.86. Per-model paired bootstrap tests reject the null at p<0.001 after Holm-Bonferroni correction, and a 3-seed check on GPT-4o-mini gives a per-seed standard deviation of only 0.006. The paper proposes Multi-Format Agreement (MFA), which exploits the lossless and deterministic serialization variation unique to structured data (Markdown, HTML, JSON, CSV) to estimate confidence at 20% lower API cost than sampling baselines. MFA reduces ECE by 44-63%, generalizes across all four models on TableBench (mean AUROC 0.80), and combines complementarily with sampling: an MFA + self-consistency ensemble lifts AUROC from 0.74 to 0.82. A secondary contribution, structure-aware recalibration, improves AUROC by +10 percentage points over standard post-hoc methods.

Lukas Voss

Independent Researcher

Confidence Estimation in Language Models Language Model Calibration LLM Uncertainty Estimation Uncertainty Quantification Table QA

Apr 14, 2026

Masked by Consensus: Disentangling Privileged Knowledge in LLM Correctness

Humans use introspection to evaluate their understanding through private internal states inaccessible to external observers. We investigate whether large language models possess similar privileged knowledge about answer correctness, information unavailable through external observation. We train correctness classifiers on question representations from both a model's own hidden states and external models, testing whether self-representations provide a performance advantage. On standard evaluation, we find no advantage: self-probes perform comparably to peer-model probes. We hypothesize this is due to high inter-model agreement of answer correctness. To isolate genuine privileged knowledge, we evaluate on disagreement subsets, where models produce conflicting predictions. Here, we discover domain-specific privileged knowledge: self-representations consistently outperform peer representations in factual knowledge tasks, but show no advantage in math reasoning. We further localize this domain asymmetry across model layers, finding that the factual advantage emerges progressively from early-to-mid layers onward, consistent with model-specific memory retrieval, while math reasoning shows no consistent advantage at any depth.

Tomer Ashuach, Shai Gretz, Yoav Katz +2

Technion – Israel Institute of Technology · IBM Research · Kempner Institute, Harvard University

Language Model Introspection Language Model Self-Assessment LLM Reasoning Factual Knowledge in Language Models Confidence Estimation in Language Models

Apr 13, 2026

Confidence under Visual Token Pruning: Removed Evidence and Risk-Controlled Token Budgets for MLLMs

Visual token pruning speeds up multimodal large language models (MLLMs) by keeping a small subset of the visual tokens, and pruning methods are compared by the accuracy they retain. We study what pruning does to the confidence of these models, across common selectors, several MLLMs, and different output formats. Pruning errors concentrate on questions whose evidence the selector removed, and confidence does not register the removal. When the queried object loses all of its tokens, accuracy on these questions drops from 59% to 17%, while confidence stays at the unpruned level. Returning a few object tokens to the kept set recovers most of the lost accuracy. Selectors that keep the most attended tokens remove such evidence most often and produce confident errors, which temperature scaling cannot re-rank. Selectors that avoid keeping redundant tokens stay close to the calibration of the unpruned model. We then use the confidence of the pruned model to set a per-question token budget. The model answers with few tokens first and again with all tokens when its confidence is low. Conformal risk control sets the threshold to bound the expected deviation from the unpruned model. With coverage-based selection, this cascade needs about a third of the prefill tokens of the unpruned model, while with FastV it needs more than the unpruned model. The savings come mainly from how well the confidence ranks the answers that differ from the unpruned ones.

Kaizhen Tan, Yang Feng, Heqing Du +3

Carnegie Mellon University, Pittsburgh, PA, USA · Columbia University, New York, NY, USA

VLM Evaluation Confidence Estimation for VLMs Confidence Estimation in Language Models Efficient VLM Inference Conformal Risk Control Visual Token Pruning+1

Apr 13, 2026

CLSGen: A Dual-Head Fine-Tuning Framework for Joint Probabilistic Classification and Verbalized Explanation

With the recent progress of Large Language Models (LLMs), there is a growing interest in applying these models to solve complex and challenging problems. Modern LLMs, capable of processing long contexts and generating verbalized explanations, offer significant potential in addressing real-world applications. However, a critical hurdle in deploying LLMs for practical decision-making is their inability to provide reliable, quantitative probabilities. While task-specific fine-tuning of LLMs using traditional discriminative objectives (similar to encoder-only models) can yield probability estimates, this often leads to catastrophic forgetting and linguistic collapse. Consequently, the model loses its ability to generate explanations, severely undermining its interpretability and usability. To address this challenge, we propose CLSGen, a novel LLM fine-tuning framework designed for binary classification tasks. The CLSGen framework encompasses a new model architecture, training methodology, and data construction strategy to enable robust probability estimation without sacrificing the model's inherent explanation-generation capabilities. Experimental results across multiple benchmark datasets demonstrate that models fine-tuned with CLSGen outperform existing baselines in classification metrics (AUROC and F1-score). Regarding explanation, the results showed strong alignment between predicted labels and generated justifications, as well as high readability.

WonJin Yoon, Kangyu Zhu, Ian Bulovic +5

Boston Children’s Hospital · Harvard Medical School · University of Colorado Anschutz Medical Campus +2

LLM Fine-Tuning Confidence Estimation in Language Models Faithfulness of Language Model Explanations

Apr 10, 2026

Quantisation Reshapes the Metacognitive Geometry of Language Models

We report that model quantisation restructures domain-level metacognitive efficiency in LLMs rather than degrading it uniformly. Evaluating Llama-3-8B-Instruct on the same 3,000 questions at Q5_K_M and f16 precision, we find that M-ratio profiles across four knowledge domains are uncorrelated between formats (Spearman rho = 0.00). Arts & Literature moves from worst-monitored (M-ratio = 0.606 at Q5_K_M) to best-monitored (1.542 at f16). Geography moves from well-monitored (1.210) to under-monitored (0.798). However, Type-2 AUROC profiles are perfectly stable across formats (rho = 1.00), localising the restructuring to the M-ratio normalisation rather than the underlying discrimination signal. This finding emerged from a pre-registered attempt to improve metacognition through domain-conditional training. We prescribed confidence-amplification SFT for the diagnosed weak domain, with matched-budget agnostic and wrong-prescription controls. All four confirmatory hypotheses were null (10,000 bootstrap resamples, seed = 42). The training successfully reshaped confidence distributions, doubling the NLP gap in Science from 0.076 to 0.152, but did not improve meta-d' because the diagnostic profile did not transfer across formats. Any system relying on domain-level M-ratio profiles has an unexamined dependency on inference format. Systems using AUROC_2 are safer. We release all code, pre-registrations, and trial-level data.

Jon-Paul Cacioli

Independent Researcher, Melbourne, Australia

Language Model Self-Assessment Metacognition in Language Models Confidence Estimation in Language Models LLM Evaluation LLM Quantization

Apr 10, 2026

Confident in a Confidence Score: Investigating the Sensitivity of Confidence Scores to Supervised Fine-Tuning

Uncertainty quantification techniques measure confidence in language model outputs to support critical applications like hallucination detection and selective prediction. While prior work has developed various confidence metrics and demonstrated their calibration for classification tasks or using verbalized confidence, the robustness of probability-based and self-consistency-based UQ metrics for natural language generation remains underexplored particularly under model adaptation. Since practitioners routinely apply supervised fine-tuning to adapt models to new tasks, a key question arises: do confidence metrics maintain their calibration when models are fine-tuned? We investigate this question across NLG tasks including translation, question answering, and mathematical reasoning. We find that calibration shifts substantially after SFT: across 216 configurations, it degrades in 112 cases and improves in 104, with confidence scores shifting due to factors beyond output quality, such as proximity to the training distribution. Degradation is therefore neither universal nor rare, and its direction cannot be anticipated from the pre-SFT model. Through a downstream task evaluation, we show that this miscalibration substantially reduces the practical utility of confidence scores for identifying correct answers. Our findings reveal that existing confidence metrics for NLG cannot be reliably deployed off-the-shelf after fine-tuning, highlighting the need for calibration-robust UQ methods under model adaptation.

Lorenzo Jaime Yu Flores, Cesare Spinoso Di-Piano, Jackie Chi Kit Cheung

Mila - Quebec AI Institute · McGill University · Canada CIFAR AI Chair, Mila

Confidence Estimation in Language Models Language Model Calibration Model Calibration LLM Fine-Tuning

Apr 9, 2026

Less Data Approximates More: Earning Faithful Confidence in High-Stakes Domains

Large language models are increasingly deployed in high-stakes domains, where confident yet incorrect inferences may cause severe real-world harm, bringing the long-overlooked issue of confidence faithfulness to the forefront. A promising solution jointly optimizes unsupervised Reinforcement Learning from Internal Feedback (RLIF) with reasoning-trace-guided Reasoning Distillation (RD), yet it faces three persistent challenges, namely the scarcity of high-quality training corpora, factually unwarranted overconfidence, and erroneous updates amplified by indiscriminate fusion. Inspired by how human confidence accumulates from uncertainty to certainty, we propose Progressive Reasoning Gain (PRG) to measure whether reasoning steps progressively strengthen confidence in the final answer. Building on PRG, we introduce HyTuning, a hybrid post-training framework that adaptively reweights RD and RLIF, using scarce supervised reasoning traces as a stable anchor while exploiting abundant unlabeled queries for scalability. Experiments on several domain-specific and general benchmarks demonstrate that HyTuning improves accuracy while achieving confidence faithfulness under limited supervision, supporting a practical ``Less Data Approximates More'' effect. Our code will be released upon acceptance.

Haokai Ma, Lee Yan Zhen, Gang Yang +4

National University of Singapore, Singapore · Singapore Management University, Singapore

RL for Language Models Reinforcement Learning Reasoning Distillation Confidence Estimation in Language Models LLM Fine-Tuning Language Model Calibration

Apr 8, 2026

When Should a Language Model Trust Itself? Same-Model Self-Verification as a Conditional Confidence Signal

Same-model self-verification, prompting a model to audit its own predicted answer, is a plausible confidence signal for selective prediction, but its practical value remains unclear once strong likelihood-based baselines are taken seriously. We evaluate self-verification against two such baselines, LL-AVG and LL-SUM, on ARC-Challenge and TruthfulQA-MC across multiple model families, scales, and prompt variants. We measure not only correctness ranking, but also abstention quality through AURC and operating-point analyses. The results are sharply task- and model-dependent. On ARC-Challenge, self-verification substantially improves over LL-AVG for Phi-2 and the Qwen models, with the largest gains appearing in Qwen-7B. On TruthfulQA-MC, however, the signal is less reliable: smaller models can become prompt-sensitive, DeepSeek-R1-Distill-8B degrades relative to LL-AVG, and LL-SUM often remains the stronger practical baseline. We therefore do not treat self-verification as a general-purpose uncertainty estimator. In this setting, it is better understood as a conditional confidence signal whose value depends on task type, model family, prompt formulation, and, crucially, the baseline it must beat.

Aditya Ajay Phalod

Independent Researcher

Language Model Self-Verification Language Model Self-Assessment Confidence Estimation in Language Models Selective Prediction

Apr 8, 2026

Fine-grained Approaches for Confidence Calibration of LLMs in Automated Code Revision

In today's AI-assisted software engineering landscape, developers increasingly depend on LLMs that are highly capable, yet inherently imperfect. The tendency of these models to produce incorrect outputs can reduce developer productivity. To this end, a canonical mitigation method is to provide calibrated confidence scores that faithfully reflect their likelihood of correctness at the instance-level. Such information allows users to make immediate decisions regarding output acceptance, abstain error-prone outputs, and better align their expectations with the model's capabilities. Since post-trained LLMs do not inherently produce well-calibrated confidence scores, researchers have developed post-hoc calibration methods, with global Platt-scaling of sequence-level confidence scores proving effective in many generative software engineering tasks but remaining unreliable or unexplored for automated code revision (ACR) tasks such as program repair, vulnerability repair, and code refinement. We hypothesise that the coarse-grained nature of this conventional method makes it ill-suited for ACR tasks, where correctness is often determined by local edit decisions and miscalibration can be sample-dependent, thereby motivating fine-grained confidence calibration. To address this, our study proposes local Platt-scaling applied separately to three different fine-grained confidence scores. Through experiments across 3 separate tasks and correctness metrics, as well as 14 different models of various sizes, we find that fine-grained confidence scores consistently achieve lower calibration error across a broader range of probability intervals, and this effect is further amplified when global Platt-scaling is applied. Our proposed approaches offer a practical solution to eliciting well-calibrated confidence scores, enabling more trustworthy and streamlined usage of imperfect models in ACR tasks.

Hong Yi Lin, Chunhua Liu, Haoyu Gao +2

Confidence Estimation in Language Models Language Model Calibration Automated Program Repair

Apr 7, 2026

SELFDOUBT: Uncertainty Quantification for Reasoning LLMs via the Hedge-to-Verify Ratio

Uncertainty estimation for reasoning language models remains difficult to deploy in practice: sampling-based methods are computationally expensive, while common single-pass proxies such as verbalized confidence or trace length are often inconsistent across models. This problem is compounded for proprietary reasoning APIs that expose neither logits nor intermediate token probabilities, leaving practitioners with no reliable uncertainty signal at inference time. We propose SELFDOUBT, a single-pass uncertainty framework that resolves this impasse by extracting behavioral signals directly from the reasoning trace itself. Our key signal, the Hedge-to-Verify Ratio (HVR), detects whether a reasoning trace contains uncertainty markers and, if so, whether they are offset by explicit selfchecking behavior. Unlike methods that require multiple sampled traces or model internals, SELFDOUBT operates on a single observed reasoning trajectory, making it suitable for latency- and cost-constrained deployment over any proprietary API. We evaluate SELFDOUBT across seven models and three multi-step reasoning benchmarks (BBH, GPQA-Diamond, and MMLU-Pro). Most notably, traces containing no hedging markers are correct 96% of the time, revealing an emergent high-precision confidence gate at zero additional cost. For the remaining cases, the full SELFDOUBT score significantly outperforms sampling-based semantic entropy at 10x lower inference cost. A deployment cascade combining both stages attains 90% accuracy at 71% coverage without any task-specific labels. These results establish SELFDOUBT as a scalable, production-ready foundation for uncertainty estimation over proprietary reasoning models.

Satwik Pandey, Suresh Raghu, Shashwat Pandey

Independent Researcher · Zillow Group

LLM Uncertainty Estimation Confidence Estimation in Language Models Confidence Estimation LLM Reasoning

Apr 7, 2026

Towards Trustworthy Report Generation: A Deep Research Agent with Progressive Confidence Estimation and Calibration

As agent-based systems continue to evolve, deep research agents are capable of automatically generating research-style reports across diverse domains. While these agents promise to streamline information synthesis and knowledge exploration, existing evaluation frameworks-typically based on subjective dimensions-fail to capture a critical aspect of report quality: trustworthiness. In open-ended research scenarios where ground-truth answers are unavailable, current evaluation methods cannot effectively measure the epistemic confidence of generated content, making calibration difficult and leaving users susceptible to misleading or hallucinated information. To address this limitation, we propose a novel deep research agent that incorporates progressive confidence estimation and calibration within the report generation pipeline. Our system leverages a deliberative search model, featuring deep retrieval and multi-hop reasoning to ground outputs in verifiable evidence while assigning confidence scores to individual claims. Combined with a carefully designed workflow, this approach produces trustworthy reports with enhanced transparency. Experimental results and case studies demonstrate that our method substantially improves interpretability and significantly increases user trust.

Yi Yuan, Xuhong Wang, Shanzhe Lei

Shanghai Artificial Intelligence Laboratory · Southeast University

Deep Research Agents Trust in AI Confidence Estimation in Language Models LLM Uncertainty Estimation Agentic RAG

Apr 7, 2026

Identifying Influential N-grams in Confidence Calibration via Regression Analysis

While large language models (LLMs) improve performance by explicit reasoning, their responses are often overconfident, even though they include linguistic expressions demonstrating uncertainty. In this work, we identify what linguistic expressions are related to confidence by applying the regression method. Specifically, we predict confidence of those linguistic expressions in the reasoning parts of LLMs as the dependent variables and analyze the relationship between a specific

n

-gram and confidence. Across multiple models and QA benchmarks, we show that LLMs remain overconfident when reasoning is involved and attribute this behavior to specific linguistic information. Interestingly, several of the extracted expressions coincide with cue phrases intentionally inserted on test-time scaling to improve reasoning performance. Through our test on causality and verification that the extracted linguistic information truly affects confidence, we reveal that confidence calibration is possible by simply suppressing those overconfident expressions without drops in performance.

Shintaro Ozaki, Wataru Hashimoto, Hidetaka Kamigaito +2

Nara Institute of Science and Technology (NAIST) · The University of Tokyo

Language Model Calibration Confidence Estimation in Language Models LLM Reliability Confidence Estimation Causal Interventions in Language Models

Apr 7, 2026

Confidence Should Be Calibrated More Than One Turn Deep

Large Language Models (LLMs) are increasingly applied in high-stakes domains such as finance, healthcare, and education, where reliable multi-turn interactions with users are essential. However, existing work on confidence estimation and calibration, a major approach to building trustworthy LLM systems, largely focuses on single-turn settings and overlooks the risks and potential of multi-turn conversations. In this work, we introduce the task of multi-turn calibration to reframe calibration from a static property into a dynamic challenge central to reliable multi-turn conversation, where calibrating model confidence at each turn conditioned on the conversation history is required. We first reveal the risks of this setting: using Expected Calibration Error at turn T (ECE@T), a new metric that tracks calibration dynamics over turns, we show that user feedback (e.g., persuasion) can degrade multi-turn calibration. To address this, we propose MTCal, which minimises ECE@T via a surrogate calibration target, and further leverage calibrated confidence in ConfChat, a decoding strategy that improves both factuality and consistency of the model response in multi-turn interactions. Extensive experiments demonstrate that MT-Cal achieves outstanding and consistent performance in multi-turn calibration, and ConfChat preserves and even enhances model performance in multi-turn interactions. Our results mark multi-turn calibration as one missing link for scaling LLM calibration toward safe, reliable, and real-world use.

Zhaohan Zhang, Chengzhengxu Li, Xiaoming Liu +3

Queen Mary University of London · Xi’an Jiaotong University

Confidence Estimation in Language Models Language Model Calibration LLM Reliability

Apr 6, 2026

Early Stopping for Large Reasoning Models via Confidence Dynamics

Large reasoning models rely on long chain-of-thought generation to solve complex problems, but extended reasoning often incurs substantial computational cost and can even degrade performance due to overthinking. A key challenge is determining when the model should stop reasoning and produce the final answer. In this work, we study the confidence of intermediate answers during reasoning and observe two characteristic behaviors: correct reasoning trajectories often reach high-confidence answers early, while incorrect rollouts tend to produce long, unproductive reasoning traces and exhibit less reliable confidence dynamics. Motivated by these observations, we propose CoDE-Stop (Confidence Dynamics Early Stop), an early stopping method that leverages the dynamics of intermediate answer confidence to decide when to terminate reasoning, requiring no additional training and easily integrating into existing models. We evaluate CoDE-Stop on diverse reasoning and science benchmarks across multiple models. Compared to prior early stopping methods, it achieves a more favorable accuracy-compute tradeoff and reduces total token usage by 25-50% compared to standard full-length reasoning. In addition, we provide analyses of confidence dynamics during reasoning, offering insights into how confidence changes in both correct and incorrect trajectories.

Parsa Hosseini, Sumit Nawathe, Mahdi Salmani +2

University of Maryland · University of Southern California

Early Stopping for Language Model Reasoning Early Stopping Efficient Language Model Reasoning Large Reasoning Models Overthinking in Language Models Confidence Estimation in Language Models

Apr 5, 2026

I-CALM: Incentivizing Confidence-Aware Abstention for LLM Selective Answering

Large language models (LLMs) often produce confident but incorrect answers, in part because standard evaluation incentives reward guessing over expressing uncertainty. We study epistemic abstention for factual questions with verifiable answers, where the goal is to improve selective answering, making LLMs abstain when they are likely to be wrong while preserving correct answers. Inspired by human behavioral decisions in question answering, we introduce I-CALM, a prompt-level framework for black-box LLMs. I-CALM combines elicited verbal confidence, announced answer/abstain payoffs, and normative guidance emphasizing truthfulness, humility, evidential support, and responsibility. To distinguish targeted abstention from indiscriminate refusal, we use a two-stage evaluation protocol, in which LLMs first choose whether to answer or abstain, and are then forced to provide a best guess for the abstained ones. Across models and factual QA datasets, I-CALM improves selective answering by reducing false-answer rate among surfaced responses and improving abstention quality, shifting error-prone cases into abstention while retaining answers the model would have answered correctly. Overall, I-CALM offers a lightweight way to improve inference-time selective answering without retraining or access to model's internal states. Code is available at https://github.com/FayLONG03/hallucinationControl.

Haotian Zong, Binze Li, Yufei Long +3

Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD 21218, USA · Department of Computer Science, Johns Hopkins University, Baltimore, MD 21218, USA · School of Government and Policy, Johns Hopkins University, Washington, D.C. 20001, USA +1

Selective Prediction LLM Hallucination Mitigation LLM Uncertainty Estimation Confidence Estimation in Language Models

Apr 4, 2026

Entropy and Attention Dynamics in Small Language Models: A Trace-Level Structural Analysis on the TruthfulQA Benchmark

Small language models (SLMs) have been increasingly deployed in edge devices and other resource-constrained settings. However, these models make confident mispredictions and produce unstable output, making them risky for factual and decision-critical tasks. Current evaluation methodology relies on final accuracy or hallucination rates without explaining how internal model behavior affects outputs. Specifically, how entropy evolves during decoding, how attention is distributed across layers, and how hidden representations contribute to uncertainty, logical inconsistencies, and misinformation propagation are often overlooked. Consequently, this study introduces a trace-level analysis of entropy and attention dynamics in SLMs evaluated with the TruthfulQA dataset. Four models with parameter ranges of 1B-1.7B parameters were examined via token-level output entropy, attention entropy, head dispersion, and hidden-state representation. The results reflect three model classifications by entropy patterns. Deterministic models (DeepSeek-1.5B and LLaMA-1B): output entropy decreases over time. Exploratory models (Gemma-1B): with increasing entropy, and balanced models (Qwen-1.7B): have moderate and stable entropy. Also, each group has distinctively different hidden-state movement and attention dispersion patterns. The analysis demonstrates that truthfulness in SLMs emerges from structured entropy and attention dynamics. Monitoring and optimizing these internal uncertainty patterns can guide the design of a more reliable, hallucination-aware, and application-specific edge SLMs.

Adeyemi Adeseye, Aisvarya Adeseye, Hannu Tenhunen +1

Brilloconnetz Partners avoin yhtiö, Turku, Finland · University of Turku, Turku, Finland · Royal Institute of Technology, Stockholm, Sweden

Small Language Models LLM Honesty Confidence Estimation in Language Models LLM Interpretability

Apr 3, 2026

Confidence Calibration in Large Language Models

We investigate the calibration of large language models' (LLMs') confidence across diverse tasks. The results of our preregistered study show that the current crop of LLMs are, like people, too sure they are right: confidence exceeds accuracy, on average. Importantly, however, this tendency is moderated by a powerful hard-easy effect, wherein overconfidence is greatest on difficult tests; by contrast, easy tests actually show substantial underconfidence. We develop LifeEval, a test for evaluating model calibration across levels of difficulty.

Noam Michael, Daniel BenShushan, Jacob Bien +1

U.C. Berkeley · University of Southern California

Language Model Calibration Confidence Estimation in Language Models LLM Evaluation

Apr 3, 2026

BAS: A Decision-Theoretic Approach to Evaluating Large Language Model Confidence

Large language models (LLMs) often produce confident but incorrect answers in settings where abstention would be safer. Standard evaluation protocols, however, require a response and do not account for how confidence should guide decisions under different risk preferences. To address this gap, we introduce the Behavioral Alignment Score (BAS), a decision-theoretic metric for evaluating how well LLM confidence supports abstention-aware decision making. BAS is derived from an explicit answer-or-abstain utility model and aggregates realized utility across a continuum of risk thresholds, yielding a measure of decision-level reliability that depends on both the magnitude and ordering of confidence. We show theoretically that truthful confidence estimates uniquely maximize expected BAS utility, linking calibration to decision-optimal behavior. BAS is related to proper scoring rules such as log loss, but differs structurally: log loss penalizes underconfidence and overconfidence symmetrically, whereas BAS imposes an asymmetric penalty that strongly prioritizes avoiding overconfident errors. Using BAS alongside widely used metrics such as ECE and AURC, we then construct a benchmark of self-reported confidence reliability across multiple LLMs and tasks. Our results reveal substantial variation in decision-useful confidence, and while larger and more accurate models tend to achieve higher BAS, even frontier models remain prone to severe overconfidence. Importantly, models with similar ECE or AURC can exhibit very different BAS due to highly overconfident errors, highlighting limitations of standard metrics. We further show that simple interventions, such as top-

k

confidence elicitation and post-hoc calibration, can meaningfully improve confidence reliability. Overall, our work provides both a principled metric and a comprehensive benchmark for evaluating LLM confidence reliability.

Sean Wu, Fredrik K. Gustafsson, Edward Phillips +3

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

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