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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May 19, 2026cs.LG

Reading Calibrated Uncertainty from Language Model Trajectories

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

Aliai Eusebi, Alexander Herzog, Xiaoyu Liang +3

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

Confidence Estimation in Language Models LLM Reliability LLM Uncertainty Estimation Representation Geometry in Language Models Uncertainty Calibration Language Model Probing

May 19, 2026cs.CL

Retrieval-Augmented Linguistic Calibration

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

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

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

Confidence Estimation in Language Models Language Model Calibration LLM Uncertainty Estimation

May 19, 2026cs.CL

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

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

Xiaoou Liu, Tiejin Chen, Dengjia Zhang +3

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

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

May 19, 2026cs.CL

Position: Uncertainty Quantification in LLMs is Just Unsupervised Clustering

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

Tiejin Chen, Longchao Da, Xiaoou Liu +1

School of Computing and Augmented Intelligence, Arizona State University

LLM Evaluation Uncertainty Quantification Confidence Estimation in Language Models LLM Reliability LLM Hallucination Detection LLM Uncertainty Estimation

May 16, 2026cs.LG

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

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

Shuo Liu, Ding Liu, Shi-Ju Ran

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

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

May 14, 2026cs.LG

Margin-Adaptive Confidence Ranking for Reliable LLM Judgement

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

Gaojie Jin, Yong Tao, Lijia Yu +1

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

LLM Evaluation LLM-as-a-Judge Learning to Rank Confidence Estimation in Language Models Human-AI Agreement LLM Uncertainty Estimation

May 13, 2026cs.CL

Inducing Artificial Uncertainty in Language Models

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

Sophia Hager, Simon Zeng, Nicholas Andrews

Johns Hopkins University · Microsoft

Confidence Estimation in Language Models Language Model Calibration LLM Uncertainty Estimation

May 13, 2026stat.ML

LLMs as Implicit Imputers: Uncertainty Should Scale with Missing Information

Large language models (LLMs) are increasingly deployed in settings where the available context is incomplete or degraded. We argue that an LLM generating answers under incomplete context can be viewed as an implicit imputer, and evaluated against a criterion from the multiple imputation (MI) literature: uncertainty should scale with the amount of missing information. We assess this criterion on SQuAD, using a controlled framework in which context availability is varied across five levels. We evaluate two answer-level uncertainty measures that can be estimated from repeated sampling: sampling-based confidence (empirical mode frequency) and response entropy. Confidence fails to reflect increasing missingness: it remains high even as accuracy collapses. Entropy, by contrast, increases with context removal, consistent with the MI analogy, and explains substantially more variance in accuracy than confidence across all evidence levels (quadratic

R^2

gap up to 0.057). We further introduce a black-box diagnostic

ρ_R(α)

that estimates the proportion of baseline uncertainty resolved by context level

α

, requiring only repeated sampling with and without context. These results suggest that entropy is a more responsive black-box uncertainty measure than confidence under incomplete context.

Stef van Buuren

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

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

May 12, 2026cs.LG

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

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

Chen Li, Xiaoling Hu, Songzhu Zheng +2

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

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

May 12, 2026cs.CL

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

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

Ali Asad, Stephen Obadinma, Anshul Pattoo +2

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

Language Model Safety Evaluation Confidence Estimation in Language Models Deception in Language Models LLM Safety Evaluation LLM Honesty

May 11, 2026cs.LG

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

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

Jasmine Qi, Danylo Dantsev, Muyang Sun

Indeed Inc.

Post-Hoc Calibration LLM-as-a-Judge LLM Answer Verification Language Model Generation Evaluation Confidence Estimation in Language Models LLM Reliability+1

May 11, 2026cs.CL

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

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

Reza Khanmohammadi, Erfan Miahi, Simerjot Kaur +4

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

VLM Evaluation Vision-Language Models Confidence Estimation in Language Models Vision-Language Grounding Visually Grounded Reasoning VLM Calibration

May 8, 2026cs.CL

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

Calibration measures whether a model's predicted confidence aligns with its empirical accuracy, and is central to the reliable deployment of large language models (LLMs) in high-stakes domains such as medicine and law. While much recent work focuses on improving LLM calibration, the equally important question of how to evaluate it in realistic settings remains underdeveloped. Open-ended question answering (QA), the most common deployment setting for modern LLMs, is where existing evaluation methods fall short: logit-based metrics need restricted output formats and internal probabilities; verbalized confidence is self-reported and often overconfident; and sampling-based methods rely on task-specific extraction rules without a clear finite-sample target. We introduce Sem-ECE (Semantic-Sampling Expected Calibration Error), a calibration evaluation framework for open-ended QA that samples answers from the model, groups them into semantic classes, and uses the resulting frequencies as confidence. We study two estimators within this framework: Sem

_1

-ECE, the same-sample self-consistency score, and Sem

_2

-ECE, a held-out variant that separates answer selection from confidence evaluation. We prove both are asymptotically unbiased, and further show that they agree on easy questions but diverge on hard ones with Sem

_2

achieving strictly smaller calibration error, so their gap also serves as a diagnostic for question difficulty. Experiments on three open-ended QA benchmarks across five leading commercial LLMs match our theoretical predictions and show that Sem-ECE outperforms verbalized confidence and existing sampling-based methods, while complementing logit-based evaluation when internal probabilities are unavailable.

Zhanliang Wang, Jiancong Xiao, Ruochen Jin +3

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

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

May 8, 2026cs.CL

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

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

Sree Bhattacharyya, Samarth Khanna, Leona Chen +3

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

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

May 7, 2026cs.AI

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

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

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

1Novo Nordisk · University of Oxford

Confidence Estimation in Language Models CoT Reasoning LLM Uncertainty Estimation LLM Reasoning Reasoning Trace Analysis

May 7, 2026cs.LG

Towards Generation-Efficient Uncertainty Estimation in Large Language Models

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

Mingcheng Zhu, Yu Liu, Tingting Zhu

University of Oxford

LLM Inference Efficiency Uncertainty Quantification Confidence Estimation in Language Models LLM Reliability LLM Uncertainty Estimation

May 7, 2026cs.AI

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

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

Chengda Lu, Xiaoyu Fan, Wei Xu

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

Confidence Estimation in Language Models LLM Interpretability LLM Fine-Tuning Language Model Probing

May 6, 2026cs.CL

Detecting Hallucinations in Large Language Models via Internal Attention Divergence Signals

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

Gijs van Dijk

Utrecht University

Language Model Error Detection Confidence Estimation in Language Models LLM Interpretability Hallucination in Language Models LLM Reliability LLM Hallucination Detection+1

May 4, 2026cs.AI

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

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

Luong N. Nguyen

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

Apr 30, 2026cs.CL

Geometry-Calibrated Conformal Abstention for Language Models

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

Rui Xu, Yi Chen, Sihong Xie +1

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

Uncertainty Quantification Selective Prediction Confidence Estimation in Language Models Hallucination in Language Models Conformal Prediction Language Model Calibration+3

Apr 27, 2026cs.CL

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

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

Jon-Paul Cacioli

Independent Researcher, Melbourne, Australia

Supervised Fine-Tuning Confidence Estimation in Language Models Self-Consistency Decoding Language Model Calibration LLM Reliability Language Model Distillation

Apr 25, 2026cs.LG

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 (\textbf{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, 2026cs.LG

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, 2026cs.CL

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, 2026cs.CL

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

Apr 21, 2026cs.LG

Unsupervised Confidence Calibration for Reasoning LLMs from a Single Generation

Reasoning language models can solve increasingly complex tasks, but struggle to produce the calibrated confidence estimates necessary for reliable deployment. Existing calibration methods usually depend on labels or repeated sampling at inference time, making them impractical in many settings. We introduce a method for unsupervised confidence calibration of reasoning LLMs when only a single generation is available at inference time. Our approach uses offline sampling on unlabeled data to derive a self-consistency-based proxy target, then distills this signal into a lightweight deployment-time confidence predictor. In a broad evaluation across 5 math and question-answering tasks using 9 reasoning models, our method substantially outperforms baselines, including under distribution shift, and improves downstream performance in selective prediction and simulated downstream decision-making.

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, 2026cs.CL

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, 2026cs.CV

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, 2026cs.AI

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, 2026cs.CL

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

Confidence Estimation in Language Models Conformal Prediction Language Model Calibration LLM Reliability Conformal Risk Control LLM Uncertainty Estimation+1