Confidence Estimation in Language Models

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24 papers in the last four weeks, up 500% on the four weeks before. 0.2% of all new papers.

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Sep 9, 2026cs.CL

ProbPlug: A Plugin Uncertainty Network for Reliable Confidence in LLM Binary Classification

Large language models (LLMs) have achieved strong performance across a broad range of classification settings, yet the reliability of their predictions remains a major obstacle to deployment in high-stakes scenarios. Although confidence estimation for LLMs has been widely studied, confidence calibration for LLM-based classification remains underexplored. We introduce ProbPlug, a lightweight confidence estimation framework for LLM-based binary classification, which predicts whether an output is correct using internal token features extracted from a frozen LLM. ProbPlug employs a self-attention module to aggregate hidden representations and can be integrated into the original inference pipeline without modifying the base model. Experiments across multiple tasks involving both text-based and multimodal large models show that ProbPlug provides more reliable confidence estimates, improves classification performance with negligible additional overhead, and exhibits strong generalization across tasks. These results indicate that ProbPlug serves as a practical solution for confidence estimation in LLM-based classification. Our code is publicly available at Github.

Jianzong Wang, Chuhang Liu, Botao Zhao +6

Ping An Technology (Shenzhen) Co., Ltd., Shenzhen, China · Tsinghua Shenzhen International Graduate School, Shenzhen, China · Hubei University of Technology, Hubei, China

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

Aug 24, 2026cs.CL

Credal Large Language Models for Semantic Commitment under Uncertainty

Large language models (LLMs) often produce fluent but incorrect answers with unwarranted confidence. A central limitation is that standard LLMs represent uncertainty through a single predictive distribution, conflating epistemic ignorance with genuine ambiguity. We introduce Credal Large Language Models (CLLMs): an ensemble of LoRA adapters induces a credal set whose lower and upper probabilities expose the spread of plausible predictive distributions rather than collapsing to a single softmax output. From this representation, we derive a single commitment rule: the model commits to an answer only when its lower probability exceeds the upper probability of every alternative, and otherwise returns the set of answers that no plausible predictor rules out. We apply this commitment rule at two depths: Credal Token Commitment (CTC) applies it to answer tokens from one ensemble forward pass, which decides constrained answers without any generation; for open-ended answers, credal decoding extends a partial answer only when no completed answer dominates it, so that the completions produced are those the plausible predictors license, and Credal Semantic Commitment (CSC) applies the rule to their meaning clusters. We evaluate CLLMs with Gemma-2-9B, Llama-3.1-8B and Qwen2.5-7B on OpenBookQA, CoQA, TriviaQA and ARC-Challenge. On multiple choice, CTC commits on 73-91% of questions at 89-98% accuracy, returns sets of 1.1-1.5 options containing the gold one on 89-98%, and its intervals contain the observed accuracy in 24 of 30 confidence bins without calibration; corrupted context lowers commitment from 87-92% to 65-71%, and on Gemma the credal bound detects corruption better than every baseline. On open-ended QA, CLLM outperforms semantic entropy and Laplace-LoRA at a fixed coverage by up to 19% and 9.5% absolute accuracy on CoQA and TriviaQA with context, for every backbone.

Shireen Kudukkil Manchingal, Sofiia Nikolenko, Fabio Cuzzolin

Oxford Dynamics Oxford · Ludwig-Maximilians-Universität München Munich · Institute for Artificial Intelligence, Data Analysis and Systems (AIDAS) School of Engineering Computing & Mathematics Oxford Brookes University, Oxford, UK

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

Aug 13, 2026cs.CL

Are You Sure You're Sure? On the Impact of Instruction Tuning on Confidence and Lexical Diversity

Instruction-tuned language models achieve strong performance across a range of generation tasks, but have also recently been shown to exhibit verbalized overconfidence. In question answering, verbalized model overconfidence may be associated with the consistency of the generated supporting rationales. In this paper, we study whether corresponding changes in the lexical diversity of generated answer rationales accompany changes in model confidence induced by instruction tuning. We evaluate three matched base and instruction-tuned models across question-answering benchmarks and find that instruction tuning consistently alters answer confidence, despite limited changes in predictive accuracy and decreases in likelihood-based calibration. Secondly, we observe a non-uniform effect of instruction tuning on rationale diversity: cross-rationale diversity consistently decreases, whereas surface-level lexical diversity varies in both direction and magnitude across models and benchmarks. Finally, we find that these differences persist after controlling for answer selection and rationale length, confirming that confidence and rationale diversity capture distinct effects of instruction tuning.

Irina Proskurina, Mayank Kumar, Oyindolapo O. Komolafe

Cohere Labs Community · Laboratoire Hubert Curien, UMR CNRS 5516, Saint-Étienne, France · School of Computer Science Engineering and Technology (SCSET), Bennett University, Greater Noida, India +1

Confidence Estimation in Language Models Question Answering Language Model Calibration Instruction Tuning Metacognition in Language Models

Aug 12, 2026cs.CL

Beyond Single-Turn Confidence: Trajectory-Adapted Uncertainty Quantification for LLM Agents

Uncertainty quantification (UQ) methods for language models are typically evaluated on single-turn outputs, where uncertainty is attached to one generated answer. For LLM agents, however, the unit of observation is an interactive trajectory, where the model can ask clarifying questions, call tools, update state, and make intermediate decisions whose errors propagate to the final outcome. We study whether three common families of single-turn UQ methods transfer to this setting. Across five LLMs and four multi-turn tool-use datasets from BFCL-v4 and

τ^2

-bench, we evaluate white-box scorers based on action-token probabilities, black-box consistency scorers based on resampled trajectories, and reflexive scorers based on model self-assessment of the trajectory. We find that transfer is often useful but uneven. Token-probability scores are highly sensitive to the choice of aggregator used across turns, reflexive scores provide the strongest low-cost baseline in most evaluated settings, and black-box self-consistency is often the strongest UQ family, with trajectory-equivalence and action-set consistency typically ranking highest among its variants. These results suggest that UQ methods developed for single generations should be revalidated at the trajectory level, with careful attention to the consistency measurement, aggregator choice, and computational budget.

Dylan Bouchard, Mohit Singh Chauhan

Confidence Estimation in Language Models LLM Agent Evaluation LLM Uncertainty Estimation Tool-Using Language Agents

Aug 11, 2026cs.CL

Attention-Path Fragility as an Uncertainty Signal in Large Language Models

We propose that a model's uncertainty about a token is reflected not only in the breadth of its output distribution but also in whether a confident prediction is \emph{fragile} under perturbation of its attention pathways. We instantiate this as ASMI (Attention-Subnetwork Mutual Information), a training-free estimator that masks attention heads and measures the BALD mutual information among the resulting subnetworks, with a semantic-agreement kernel to discount surface-form disagreement. The signal is not a restatement of output confidence: on grounded QA an out-of-fold test shows it adds error-predictive information beyond single-pass confidence and entropy, concentrated in \emph{confident-but-fragile} predictions, where acting on it roughly halves the retained error of a confidence filter. The distinctness is regime-graded, so ASMI predicts its own domain of applicability, strong where answers are routed through provided context and bounded by design where they are recalled from parametric knowledge. Sem-ASMI reads the signal from a single greedy response, without the stochastic generations the strongest baselines require, and ties or beats Semantic Entropy on ten of the twelve grounded benchmark-backbone settings. Across the same twelve settings, the best ASMI variant, typically the adaptive one reusing the ten samples already drawn for the baselines, ties or leads the strongest baseline in eight, significantly in three under a paired test. On parametric QA all variants revert to or below the zero-cost MSP baseline, exactly as predicted, and the estimates are near-deterministic across reruns. A head-level analysis shows that what tracks this boundary is not the presence of head-level fragility but whether that fragility couples to errors.

Minsoo Kim, Sungyoung Ji, Kisung Moon +1

POSCO Holdings Future Technology Research Institute 440, Teheran-ro, Gangnam-gu, Seoul, Republic of Korea

Confidence Estimation in Language Models LLM Uncertainty Estimation

Aug 9, 2026cs.CL

Unsure but Certain: Uncovering the Representation-Confidence Gap in Diffusion Language Models

Diffusion language models use broad context to create text, suggesting they might handle input noise better than standard models. Testing reveals this is only partially true. Internally, diffusion models detect text errors highly accurately. Externally, their reported certainty ignores this signal. As accuracy drops due to noise, confidence stays near its maximum and the ability to correctly rank answers degrades toward random chance. We call this mismatch the representation confidence gap. The visible concentration of high certainty scores is a misleading surface symptom. Standard math adjustments remove this concentration but fail to fix the underlying loss of ranking order. This ranking deficit favors standard models under noisy conditions and resists common remedies. Matching training recovers accuracy but not ranking, while score recalibration and input level error signals cannot reorder the final answers. However, the information needed to properly evaluate an answer survives in the hidden states. A lightweight extraction tool uses this signal to improve ranking. This approach is highly efficient because it leaves the base model completely frozen and requires zero additional text generation steps. We present this tool to prove the signal exists, while clearly noting its limits. Ultimately, certainty reliability is a more pressing limit than overall accuracy under noisy conditions.

Saurabh Yadav, Badri Narayana Patro, Vijay Srinivas Agneeswaran

Microsoft India

Confidence Estimation in Language Models Language Model Calibration LLM Uncertainty Estimation Diffusion Language Models Language Model Robustness

Aug 8, 2026cs.LG

From token probabilities to calibrated confidence: An empirical study of mathematical question answering

Confidence estimation for large language models (LLMs) aims to estimate the probability that a generated answer is correct, while calibration aligns these estimates with empirical accuracy. Prior work has shown that token probabilities are often overconfident, we investigate whether these readily available signals can nevertheless provide well-calibrated confidence estimation for mathematical question answering. We compare single-pass estimators, which reuse token probabilities from the original generation, with multi-pass estimators, which obtain additional confidence signals through verification or stochastic forward passes. While individual token probabilities can be highly saturated, we find that aggregating token probabilities over the full sequence captures small but consistent differences between correct and incorrect generations, yielding more informative confidence estimates. Multi-pass methods can yield calibrated confidence estimates. We study two such approaches: self-verification through re-prompting, including a lower-cost in-situ variant, and Monte Carlo Dropout, which derives confidence from variation across stochastic forward passes. We further evaluate two post-hoc calibration methods, Platt scaling and isotonic regression, both of which substantially reduce in-domain calibration error. However, their data efficiency varies with dataset difficulty, and the calibration mappings often transfer asymmetrically across datasets and models.

Avery Ma, Lorne Schell, Vin Bhaskara +1

RBC Borealis

LLM Answer Verification Confidence Estimation in Language Models Language Model Calibration LLM Uncertainty Estimation LLM Mathematical Reasoning

Aug 5, 2026cs.CL

Provable Limits and Certified Deferral for Verbalized Uncertainty in Small Language Models

Small open-weight language models increasingly run in private, offline, and cost-sensitive settings, where the key deployment question is not only what a model answers but when it should defer to a human. We study whether verbalized confidence can support risk-controlled deferral, evaluating eleven instruction-tuned models from three families, 0.5B to 14B parameters, on ARC-Challenge and TruthfulQA with 25,168 local predictions. Three theoretical results delimit what calibration can provide: strictly monotone calibration preserves the risk-coverage frontier and error-detection AUROC; temperature scaling cannot calibrate models whose confidence stays above one half while accuracy falls below it; and a Clopper-Pearson procedure converts a 200-question calibration set into a finite-sample risk certificate under an i.i.d. deployment assumption. Empirically, eight of 22 model-task pairs hit the temperature-scaling infeasibility floor within one percentage point of the predicted bound. Platt scaling reduces ECE to as low as 0.02, yet certified autonomy at a 20% risk budget is granted to only three model-task pairs and to none at 10%. We also identify and repair an answer-ordering artifact in the multiple-choice form of TruthfulQA. Calibration gives confidence semantics; certified deferral determines when small models are safe to use.

Jianru Shen

University of Montana, Missoula, MT 59812, USA

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

Aug 5, 2026cs.CL

Evaluation Pitfalls and Sparsity Limitations in LLM-based Confidence Estimates for Classification

Confidence estimation is essential when LLMs are used for classification, indicating when predictions can be trusted. However, common approaches such as verbalization produce extremely sparse outputs. For instance, Qwen3-32B verbalizes only eight unique confidence values on SST-2, with over half being exactly 95%, a pattern we observe consistently across four datasets and two LLMs. Besides limiting practical utility, we show that this sparsity critically affects evaluation: the choice of interpolation in area under the accuracy-rejection curve (AUARC) dramatically alters rankings, with consistency sampling dropping from best to worst under stepwise versus linear interpolation. We advocate for standardizing stepwise interpolation for a fairer comparison. Under such a fair evaluation, we find that weighting verbalized digits by token probabilities, a method we term verbalization logprobs, addresses sparsity and achieves the best AUARC (+2.3 points over vanilla verbalization) without incurring additional inference cost.

Elena Merdjanovska, Omar Zaidan, Andreas Rücklé

Humboldt-Universität zu Berlin Science of Intelligence · Amazon

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

Aug 3, 2026cs.AI

Can You Trust the Confidence? ConfBench for Vision-Language Models on Document Extraction

Intelligent document processing (IDP) with vision-language models (VLMs) hinges on confidence scores trustworthy enough to route extractions between automation and human review. Existing document benchmarks are dominated by clean, high-quality samples, leaving low accuracy regions too sparse for calibration assessment. We introduce ConfBench, the first calibration-specific benchmark for key information extraction (KIE), built by applying 20 controlled degradation pipelines to a diverse document set, yielding 1,346 variants and 70K+ entity-level evaluations spanning the full accuracy spectrum. We evaluate four proprietary and three open-weight VLMs under verbalized and log-probability confidence estimation methods across three input modalities, and find: (i) OCR+Image modality results in more accurate confidence estimates; (ii) model capability is the dominant factor: within the Claude family confidence quality scales monotonically with capability, while across families parameter count is a poor predictor; (iii) calibration quality varies widely across models, from near-perfect to severely overconfident, and per-model post-hoc correction rescales these absolute confidence values for threshold-based routing without altering ranking-based operational metrics; and (iv) log-probability with first-token aggregation consistently outperforms mean-token and margin aggregations. We also introduce ECARB, a review-budget metric translating discriminative gains into operational savings. We release ConfBench publicly to enable systematic study of confidence estimators and calibration methods for trustworthy IDP application deployment.

Priyashree Roy, Sujitha Martin, Mohammad Rostami +6

Amazon Web Services

VLM Evaluation Document Understanding Confidence Estimation in Language Models Document Information Extraction VLM Calibration

Jul 28, 2026cs.IR

Beyond Self-Knowledge: Propagating Uncertainty Across Reasoning and Retrieval in LLMs

Retrieval-augmented generation improves knowledge-intensive question answering, but indiscriminate retrieval can introduce irrelevant evidence and unnecessary computation. We investigate whether verbalized confidence from black-box language models can serve as an actionable signal for retrieval routing. Our method, BeyondUncertainty, first elicits a structured provisional answer and confidence estimate, then applies a model-specific threshold selected on held-out validation data and frozen before test evaluation. Low-confidence questions receive top-5 TF-IDF retrieval followed by a second answer call, whereas high-confidence questions return the provisional answer directly. We evaluate 27,000 policy instances across six QA benchmarks, three model families, and three retrieval policies. BeyondUncertainty achieves 0.483 mean token-level F1, compared with 0.467 for always retrieval and 0.401 for no retrieval, while reducing retrieved passages by 20.4% relative to always retrieval. When matched on the number of questions routed to retrieval within each dataset-model cell, it outperforms a post-hoc random allocation in 17 of 18 settings, with an average gain of 0.024 F1. Although poorly calibrated as an absolute probability, probe uncertainty modestly predicts question-level retrieval benefit (AUROC = 0.628). However, the additional probe increases total token usage by 28.2%, revealing a trade-off between more selective evidence acquisition and end-to-end token efficiency.

Chandan Kumar Sah, Li Zhang, Xiaoli Lian

Beihang University, Beijing, China

Retrieval-Augmented Generation Confidence Estimation in Language Models LLM Uncertainty Estimation RAG Evaluation Efficient Language Model Inference

Jul 27, 2026cs.CV

Bigger or Cheaper? Scale and Quantization Effects on Uncertainty Signals in Vision-Language Models Under Image Degradation

Vision-language models (VLMs) deployed on consumer hardware must decide when to answer and when to defer, and that decision depends on having a confidence signal that tracks correctness. A practitioner with a fixed memory budget faces a choice between a small model at full precision, the same small model quantized, and a larger model quantized into the same footprint -- three configurations that push the confidence signal in opposing directions. We measure, on identical inputs, how model scale and 4-bit quantization affect two confidence signals in the Qwen2-VL family: the confidence a model states in natural language, and its own mean token probability over the answer it generates. Across 5,700 predictions spanning six realistic photographic degradations at three severities, we find that scale sharply improves the model's internal uncertainty signal (mean error-detection AUROC 0.80 to 0.98 from 2B to 7B) while its verbalized confidence stays weak and often at chance (mean 0.61 to 0.69): the gap between what the model knows and what it says widens rather than closes with size. We find that 4-bit quantization is nearly free for accuracy (-1.6 points) but expensive for the confidence signal (internal AUROC 0.95 to 0.80, and the verbalized-confidence parse rate collapses from 99% to 64%). For a fixed memory budget the recommendation is therefore to prefer a larger quantized model over a smaller full-precision one: 7B-4bit gives both the best accuracy and the best uncertainty signal (internal AUROC 0.98) of the three configurations that fit. We frame the results as selective-prediction operating points so they translate directly into a deployment recommendation, and we argue that error-detection AUROC, not calibration error, is the metric that exposes the difference between the two signals.

M M Asif Ferdous

Independent Researcher

VLM Robustness Selective Prediction Confidence Estimation in Language Models VLM Quantization Large Vision-Language Models

Jul 24, 2026cs.CV

Small Vision-Language Models Know When They Are Wrong But Cannot Say So: A Two-Model Study of Stated versus Internal Confidence Under Realistic Image Degradation

Vision-language models (VLMs) are increasingly deployed on consumer hardware where input images are degraded by compression, camera shake, and poor lighting. In such settings, a reliable uncertainty signal matters more than raw accuracy, because it determines when a system should defer rather than answer. We evaluate two small open-weight VLMs -- Qwen2-VL-2B-Instruct and SmolVLM-Instruct -- across six realistic photographic degradations at three severity levels, comparing two confidence signals: the confidence the model states in natural language, and the model's own mean token probability over its generated answer. Across 3,800 predictions, we find a large and consistent gap. Verbalized confidence in Qwen2-VL is almost constant (mean 0.87-0.90 across all conditions) and detects its own errors at chance level (AUROC 0.39-0.75, typically ~0.50), while internal token probability from the same model separates correct from incorrect answers with AUROC 0.92-0.99. In SmolVLM, verbalized confidence proved largely unobtainable: across three prompt templates, only one of five pilot attempts produced a parseable confidence value, while internal probability again yielded above-chance error detection (AUROC 0.54-0.92). Both models fail in the same place: under severe underexposure, accuracy collapses (0.99->0.22 for Qwen2-VL, 0.97->0.42 for SmolVLM) while both confidence signals barely move, and internal error-detection falls to chance. We conclude that small VLMs encode usable self-knowledge that their verbalized output does not express, that internal probability is therefore the better deferral signal in constrained deployment, and that neither signal should be trusted under severe low-light conditions.

M M Asif Ferdous

Independent Researcher

VLM Robustness Vision-Language Models Confidence Estimation in Language Models VLM Calibration

Jul 22, 2026cs.CL

Sound Probabilistic Safety Bounds for Large Language Models

We propose a novel framework for computing rigorous bounds on the probability that a large language model (LLM) generates harmful output to a given prompt. We study a new application of the Clopper-Pearson confidence intervals to obtain probably approximately correct (PAC) bounds for this problem. As our main technical contribution, we propose an algorithm that leverages features in the latent space to prioritize exploring branches in the auto-regressive generation tree that are more likely to produce harmful outputs. Our approach in particular enables the efficient computation of useful lower bounds, even in scenarios where the true harm probability is extremely small, and crucially, the obtained lower bounds are sound, i.e., formally proven to be less than the actual harmfulness probability: our experimental results demonstrate the effectiveness of our method by computing non-trivial lower bounds on state-of-the-art LLMs. This study newly enables the evaluation and statistical certification of LLMs.

Mahdi Nazeri, Anne-Kathrin Schmuck, Sadegh Soudjani +1

Department of Computer Science, University of Oxford, UK · Max Planck Institute for Software Systems, Germany · School of Computer Science, University of Birmingham, UK

Language Model Safety Evaluation Confidence Estimation in Language Models LLM Safety

Jul 21, 2026cs.AI

The Knowing-Saying Gap: When Probes See Errors that Confidence Misses

Linear probes detect corrupted context in language models with near-perfect accuracy, yet this does not translate into reliable failure prediction. The result is a dissociation with direct implications for deployment monitoring. Across multi-hop arithmetic chains, probes that detect corruption turn out to be uninformative about final answer correctness; models forced into structured confidence formats collapse to two values with indistinguishable error rates; and probe persistence across hops fails to separate correct from incorrect outcomes, refuting our pre-registered "persistence beats peak" hypothesis. This pattern of knowing but not saying generalises across model families including reasoning models. As a real-time monitor, probe-based interventions are sharply model and error-type dependent: branch-and-pick is net-positive across models and uniquely non-breaking on Llama-3.1-8B (4 rescued, 0 broken), while reprompt and replace-prior break correct traces at roughly the rate they rescue wrong ones. Probe-based monitoring is a necessary complement to verbalised confidence, but no single intervention dominates, and the deployable answer is model-aware, error-type-aware routing.

Jyotin Goel, Ipshita Bandyopadhyay, Justin Shenk

Language Model Error Detection Confidence Estimation in Language Models Language Model Self-Assessment LLM Reliability LLM Uncertainty Estimation Causal Interventions in Language Models+1

Jul 20, 2026stat.ME

Calibrating Semantic Uncertainty from Observable Language-Model Probabilities

As generative artificial intelligence enters scientific and professional work, its uncertainty must be defined on the states that matter for inference and decision-making. Language models assign probabilities to words, whereas applications require uncertainty over meaningful states such as diagnoses, hypotheses or operational conditions. We introduce a \emph{semantic map}: a prespecified, testable bridge from probabilities over verbal responses to a posterior over declared finite states. The language distribution remains unrestricted; held-out calibration connects it to a reference posterior. We derive posterior-error bounds and conditions for existence, conditional uniqueness, presentation stability and stable inverse recovery. This distinction matters because language probabilities depend on prompt wording, while the target posterior should not change under information-equivalent rewording. Experiments use professional market text compiled from Federal Reserve economic and financial series, together with controlled simulations having exact posteriors. Across two fitted language models, language-derived probabilities outperform printed numerical confidence, recover held-out posteriors with valid uncertainty coverage, remain largely stable under paraphrase and respond appropriately to altered evidence. \textbf{Prompt engineering optimises a wording-dependent response; robust scientific use requires validated stability of application-relevant meaning.} The proposed map turns semantic uncertainty in generative systems into an identifiable and testable statistical measurement problem and, when its acceptance conditions hold, yields an auditable posterior estimate.

Matthew F. Dixon

Artificial Intelligence Finance Institute (AIFI), 69 Charlton St, New York, NY 10014, USA

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

Jul 19, 2026stat.ML

Efficient Sequential Evaluation of Large Language Models

We study the problem of sequentially evaluating a new large language model (LLM) on a fixed question set using historical performance data from prior LLMs. Our goal is to construct a confidence sequence (CS) for the model's capability on this question set and to design active querying rules that shrink the CS width as quickly as possible. For CS construction, we invert a family of test supermartingales and focus on two representative approaches: a reverse information projection (RIPr)-based approach and a testing-by-betting-based approach. We first study these approaches under an oracle setting, and demonstrate the oracle optimality of the RIPr-based construction. We then propose a growth-oriented querying rule that aims to maximize the worst-case one-step expected log-increment over the endpoints of the current CS. In practice, we build these test supermartingales and the querying rule on predictions of question-level correctness learned from historical data. We then analyze the shrinkage behavior of the resulting CSs and identify two key factors that slow the shrinkage rate of CSs: accumulated prediction mismatch and the spikiness of the querying distribution. Finally, motivated by this analysis, we propose several mixture querying rules that combine growth-oriented querying, prediction refinement, and uniform exploration, trying to mitigate the effects that slow the shrinkage rate. We provide experiments comparing different querying rules for the RIPr-based and testing-by-betting-based CSs across several synthetic testing datasets. Interestingly, we observe that the simplest querying rule, uniform sampling, can sometimes outperform more adaptive querying rules for both methods.

Chia-Yu Hsu, Shubhanshu Shekhar

EECS Department, University of Michigan

LLM Evaluation Confidence Estimation in Language Models Long-Context Language Model Evaluation Active Learning

Jul 15, 2026cs.CL

Post-Training Shifts Confidence: A Three-Stage Analysis of How SFT, RL, and OPD Shape Pre-, Intra-, and Post-CoT Calibration

Large language models have made strong reasoning gains through supervised fine-tuning, reinforcement learning, and on-policy distillation, yet these post-training methods are usually evaluated only by final-answer accuracy. We study how they reshape confidence during reasoning. We introduce a three-stage calibration framework that evaluates confidence before, during, and after chain-of-thought generation, corresponding to difficulty estimation, early termination, and answer aggregation. Through a controlled comparison on mathematical reasoning benchmarks, we find that OPD provides the most useful pre-reasoning confidence, SFT gives the strongest online signal for early stopping, and RL produces the most reliable trace-level signal for aggregation. We further show that confidence reliability is position-dependent: RL confidence becomes informative after a path-commitment phase, while OPD confidence is useful early but can become inversely calibrated later. Based on this observation, we propose PosConf, a position-aware confidence strategy that uses confidence only from reliable relative-position intervals. PosConf improves RL answer aggregation by 6.1 points over majority voting and consistently improves OPD early stopping under tight token budgets, with gains up to 4.3 points by avoiding its later inverse-calibration region, showing that \emph{confidence in reasoning models should be used both stage-wise and position-awarely}. Our code is available at https://github.com/EIT-NLP/Post-Training-Calibration.

Shuhao Li, Guodong Du, Anhao Zhao +3

Eastern Institute of Technology, Ningbo · The Hong Kong Polytechnic University

Confidence Estimation in Language Models Language Model Calibration On-Policy Distillation RL Post-Training LLM Post-Training LLM Reasoning

Jul 14, 2026cs.CL

From Critic to Confidence: PPO for Language-Based Quantitative Prediction with Confidence Estimation

LLMs can perform language-based quantitative prediction from unstructured inputs, but remain susceptible to hallucinations and overconfident errors, making it critical to know not only what a model predicts, but when its predictions can be trusted. We introduce CARE-PPO, a reinforcement learning framework that establishes a connection between loss prediction for uncertainty estimation and actor-critic PPO fine-tuning, enabling joint learning of accurate numerical estimates and reliable confidence signals in language-based quantitative prediction. CARE-PPO uses a Confidence-Aligned Reward for Estimation, defined as a function of prediction error, to provide dense error-aware feedback to the actor while inducing the critic to learn a value function aligned with prediction quality. During inference, we repurpose the critic as a confidence estimator. Across two real-world tasks in healthcare and finance and two Qwen-3 model scales (4B and 8B), CARE-PPO achieves strong quantitative prediction performance, while producing significantly better-aligned confidence estimates through the critic than logit-based and verbalized baselines. These gains persist under realistic out-of-distribution settings across domains, spanning linguistic and domain shifts. Finally, CARE-PPO reduces task-specific overfitting on general instruction-following prompts, consistent with the broader generalization advantages of RL fine-tuning over supervised approaches.

Mehak Dhaliwal, Rasta Tadayon, Andong Hua +2

University of California, Santa Barbara

RL for Language Models Confidence Estimation in Language Models Language Model Calibration LLM Uncertainty Estimation Proximal Policy Optimization

Jul 14, 2026cs.LG

The Computational Basis of Confidence in Large Language Models

Reliable confidence -- the probability that a model's own answer is correct -- is essential for the trustworthy deployment of language models. Existing work has largely evaluated confidence by how well it predicts correctness and whether it is calibrated, leaving open a more fundamental question: what does the confidence signal itself represent? Answer logits may reflect a latent decision variable sufficient to compute normative confidence, or instead a heuristic preference signal that combines the available evidence in a non-Bayesian manner. We address this using statistical decision confidence (SDC), a normative framework from computational neuroscience. Treating the answer-logit difference (LD) as a candidate readout of the latent decision variable, we test the qualitative signatures predicted by SDC. Across three perceptual discrimination tasks and a memory-based decision task, spanning three multimodal non-reasoning models and one reasoning model, LD satisfied these signatures -- including the diagnostic correct/error folded-X pattern -- showing that, in these settings, answer logits behave as monotonic readouts of a latent decision variable rather than heuristic preference scores. In complex visual reasoning, LD continued to predict correctness beyond objective task difficulty, but the full geometric signatures of SDC were absent, illustrating the current boundary of the framework when explicit normative process models are unavailable. These results provide a computational account of confidence in multimodal language models, delineate when answer logits behave as readouts of a latent decision variable, and establish SDC as a unifying framework for studying confidence across biological and artificial intelligence.

Dharshan Kumaran, Viorica Patraucean, Maks Ovsanikov +2

Google DeepMind · Google DeepMind and École Polytechnique · École Polytechnique +1

Confidence Estimation in Language Models LLM Uncertainty Estimation

Jul 9, 2026cs.CL

Two Axes of LLM Abstention: Answer Correctness and Question Answerability

A model should refuse two different things: answers it would get wrong, and questions it should not answer at all, such as unanswerable ones or ones resting on a false premise. The usual recipe thresholds a single confidence score, which cannot tell these apart. Across five instruction-tuned models from three families (2B to 14B), we find they are separate axes. Ordinary answer-confidence tracks whether an answer is right but is nearly blind to whether the question is answerable; a linear probe on hidden states does the reverse. The blind spot does not shrink with scale. It is worst on naturally occurring false-premise questions (CREPE). There, answer-confidence, P(IK), P(True), and even asking the model outright whether a premise is false all stay near chance, while a hidden-state probe reaches 0.69 to 0.77 AUROC: the model represents a problem it will not report. This turns out to be fixable. Instructing a model to check premises backfires, because it then disputes sound and false premises alike (57% false challenges), unable to tell them apart; routing the same instruction with the probe roughly triples challenge precision. We turn the two axes into a calibrated policy that answers only when an answerability score and a correctness score each clear a separately certifies behave differently: the unanswerable-answer rate is controllable at every scale, while the wrong-answer rate is capped by model accuracy, so the guarantee tightens as threshold policy certifies both budgets at 0.75 coverage of correct answers, against 0.31 for a single threshold; at 14B it is the only policy that certifies at all.

Benedikt J. Wagner

City St George’s, University of London

Selective Prediction Confidence Estimation in Language Models LLM Uncertainty Estimation Refusal Behavior in Language Models

Jul 9, 2026cs.LG

Eigenvalue Calibration for Semantic Embeddings of Large Language Models

Uncertainty quantification is central to the reliable deployment of large language models (LLMs), and eigenvalues of semantic embeddings have recently emerged as a key tool in state-of-the-art methods. However, conventional calibration results developed for classification probabilities cannot be directly transferred to eigenvalues. We address this gap by proposing a novel framework for calibrating the eigenvalues of semantic embeddings. We interpret LLMs combined with semantic embeddings of their generated answers as density matrix predictors, and we propose a novel approach to calibrate density matrix predictors by applying temperature scaling to their eigenvalues. We establish entropy-risk equivalence under calibration, derive a central calibration inequality specific to eigenvalues, and prove that temperature-scaled eigenvalues optimize calibration when minimizing proper score risks. Experiments on a variety of real-world settings show that current LLMs are systematically overconfident, and validate our theoretical findings. Together, these results advance the foundations and practice of uncertainty quantification for semantic embeddings.

Sebastian G. Gruber, Nassim Walha, Francis Bach +1

1ESAT-PSI, KU Leuven, Belgium · 2German Cancer Research Center (DKFZ), Heidelberg, Germany · 3German Cancer Consortium (DKTK), Germany +3

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

Jul 8, 2026cs.CL

Future Confidence Distillation in Large Language Models

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

Sahil Kale

University of California, Los Angeles Los Angeles, USA

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

Jul 7, 2026cs.CL

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

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

Andrea Bacciu, Andrea Alfarano, Saab Mansour +2

Amazon · INSAIT, Sofia

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

Jul 7, 2026cs.CL

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

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

Yimeng Zhang, Yingying Zhuang, Ziyi Wang +12

Amazon · Northeastern University

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

Jul 5, 2026cs.CL

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

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

α

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

1-δ

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

α

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

Sijin Dong, Hiroyuki Shinnou

1Ibaraki University, Japan.

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

Jul 5, 2026cs.LG

On the effectiveness of reward functions in reinforcement learning for confidence calibration of large language models

In this paper, we consider the setting where large language models (LLMs) are trained using reinforcement learning (RL) to simultaneously improve reasoning accuracy and verbalize their confidence. Our reward scheme uses two functions for rewarding confidence verbalized by the LLM: one for correct answers and the other for incorrect answers. If poorly designed, such a scheme may incentivize an LLM to answer incorrectly in order for its confidence to be calibrated, a phenomenon we term confidence reward hacking. We introduce the notion of non-hackable confidence reward schemes and provide methods for constructing them. We show that selective confidence reward hacking can arise in practical datasets under hackable reward schemes while non-hackable reward schemes are resistant to hacking. Finally, we place some of these schemes along an overconfidence-underconfidence spectrum for RL-based confidence calibration and demonstrate experimentally that they tend to exhibit the corresponding calibration biases relative to other schemes in the spectrum. The code of our experiments is available in https://anonymous.4open.science/r/rl-confidence-calibration-9ED4/README.md.

Chee Heng Tan, Zhuoyi Lin, Mehul Motani +1

School of Computing National University of Singapore · Institute of Advanced Intelligence and Computing Agency for Science, Technology and Research · Department of Electrical & Computer Engineering National University of Singapore

Reward Hacking Confidence Estimation in Language Models RL for Language Model Reasoning Language Model Calibration Reward Design for RL

Jun 29, 2026cs.CL

When Calibration Rankings Reverse: Accuracy-Controlled Evaluation for Fair Comparison of LLMs

Calibration evaluates whether a model confidence aligns with its empirical accuracy. Existing studies often compare the calibration of different large language models using global calibration metrics such as Expected Calibration Error and Brier Score. We begin by showing, both theoretically and empirically, that such comparisons are confounded by differences in model accuracy. For fairer cross-model comparison, we then propose ACE, an accuracy-controlled evaluation framework with three complementary views: Instance-Aligned, Distribution-Aligned, and Candidate-Aligned calibration. Across multiple benchmarks, model families, and confidence elicitation methods, we use ACE to study two practically important comparison axes, small versus large models and thinking versus non-thinking models. We find that many previously reported calibration advantages under raw global metrics weaken substantially after accuracy control. We also find that ranking reversal is frequent: models favored by raw metrics often cease to be favored once accuracy is controlled. Our results show that raw global calibration metrics are not robust for cross-model comparison, and that fair calibration comparison requires accuracy-aware evaluation.

Zhichao Yang, Caiqi Zhang, Ruihan Yang +3

Fudan University · University of Cambridge

LLM Evaluation Confidence Estimation in Language Models Language Model Calibration

Jun 28, 2026cs.LG

Reported Confidence in LLMs Tracks Commitment More Than Correctness

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

Dharshan Kumaran

Google DeepMind

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

Jun 27, 2026cs.CL

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

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

Ansh Kamthan

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

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