Language Model Calibration

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Overview

Language model calibration asks whether a model’s stated or computed confidence corresponds to how often its answers are correct, so systems can decide when to answer, retrieve evidence, defer, or abstain. Researchers estimate confidence from verbal reports, token probabilities, self-consistency, or hidden representations, then improve it with post-hoc methods such as temperature scaling and isotonic regression, conformal prediction, or training methods including supervised fine-tuning and reinforcement learning. Evaluations commonly use question answering and mathematical reasoning benchmarks, and increasingly test retrieval routing, model judges, medical tasks, and performance under domain or prompt shifts. A central tension is that calibration can change with the elicitation protocol and deployment context, and well-calibrated probabilities do not necessarily rank errors well or guarantee safe decisions.

Latest papers

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386 papers67 papers in the last four weeks, up 40% on the four weeks before. 0.4% of all new papers.

Apr 9, 2026

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

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

Haokai Ma, Lee Yan Zhen, Gang Yang +4

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

RL for Language ModelsReinforcement LearningReasoning DistillationConfidence Estimation in Language ModelsLLM Fine-TuningLanguage Model Calibration
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Apr 9, 2026

Rethinking Residual Errors in Compensation-based LLM Quantization

Methods based on weight compensation, which iteratively apply quantization and weight compensation to minimize the output error, have recently demonstrated remarkable success in quantizing Large Language Models (LLMs). The representative work, GPTQ, introduces several key techniques that make such iterative methods practical for LLMs with billions of parameters. GPTAQ extends this approach by introducing an asymmetric calibration process that aligns the output of each quantized layer with its full-precision counterpart, incorporating a residual error into the weight compensation framework. In this work, we revisit the formulation of the residual error. We identify a sub-optimal calibration objective in existing methods: during the intra-layer calibration process, they align the quantized output with the output from compensated weights, rather than the true output from the original full-precision model. Therefore, we redefine the objective to precisely align the quantized model's output with the original output of the full-precision model at each step. We then reveal that the residual error originates not only from the output difference of the preceding layer but also from the discrepancy between the compensated and original weights within each layer, which we name the 'compensation-aware error'. By inheriting the neuron decomposition technique from GPTAQ, we can efficiently incorporate this compensation-aware error into the weight update process. Extensive experiments on various LLMs and quantization settings demonstrate that our proposed enhancements integrate seamlessly with both GPTQ and GPTAQ, significantly improving their quantization performance. Our code is publicly available at https://github.com/list0830/ResComp.

Shuaiting Li, Juncan Deng, Kedong Xu +5

Zhejiang University · vivo Mobile Communication Co., Ltd

Quantization Error CompensationLLM QuantizationNeural Network QuantizationPost-Training QuantizationWeight-Only QuantizationLanguage Model Calibration
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Apr 8, 2026

SYN-DIGITS: A Synthetic Control Framework for Calibrated Digital Twin Simulation

AI-based persona simulation -- often referred to as digital twin simulation -- is increasingly used for market research, recommender systems, and social sciences. Despite their flexibility, large language models (LLMs) often exhibit systematic bias and miscalibration relative to real human behavior, limiting their reliability. Inspired by synthetic control methods from causal inference, we propose SYN-DIGITS (SYNthetic Control Framework for Calibrated DIGItal Twin Simulation), a principled and lightweight calibration framework that learns latent structure from digital-twin responses and transfers it to align predictions with human ground truth. SYN-DIGITS operates as a post-processing layer on top of any LLM-based simulator and thus is model-agnostic. We develop a latent factor model that formalizes when and why calibration succeeds through latent space alignment conditions, and we systematically evaluate ten calibration methods across thirteen persona constructions, three LLMs, and two datasets. SYN-DIGITS supports both individual-level and distributional simulation for previously unseen questions and unobserved populations, with provable error guarantees. Experiments show that SYN-DIGITS achieves up to 50% relative improvements in individual-level correlation and 50--90% relative reductions in distributional discrepancy compared to uncalibrated baselines.

Grace Jiarui Fan, Chengpiao Huang, Tianyi Peng +2

Finance Division, Columbia Business School. · Department of IEOR, Columbia University · Decision, Risk, and Operations Division, Columbia Business School. +1

Synthetic ControlLanguage Model CalibrationLarge Language Model-Based Social SimulationHuman Behavior SimulationDigital Twins
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Apr 8, 2026

Improving Semantic Uncertainty Quantification in Language Model Question-Answering via Token-Level Temperature Scaling

Calibration is central to reliable semantic uncertainty quantification, yet prior work has largely focused on discrimination, neglecting calibration. As calibration and discrimination capture distinct aspects of uncertainty, focusing on discrimination alone yields an incomplete picture. We address this gap by systematically evaluating both aspects across a broad set of confidence measures. We show that current approaches, particularly fixed-temperature heuristics, produce systematically miscalibrated and poorly discriminative semantic confidence distributions. We demonstrate that optimising a single scalar temperature, which, we argue, provides a suitable inductive bias, is a surprisingly simple yet effective solution. Our exhaustive evaluation confirms that temperature scaling consistently improves semantic calibration, discrimination, and downstream entropy, outperforming both heuristic baselines and more expressive token-level recalibration methods on question-answering tasks.

Tom A. Lamb, Desi R. Ivanova, Philip H. S. Torr +1

University of Oxford · University of Toronto & Vijil

Language Model CalibrationLLM Uncertainty EstimationSemantic Uncertainty EstimationModel CalibrationQuestion Answering
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Apr 8, 2026

Persona Matters: Effects of Activation Steering on Short Answer Generation and Scoring

Activation-based steering enables inference-time personalization of large language models, but its effects in educational applications are not well understood. We study activation-based persona vectors representing seven character traits in short-answer generation and automated scoring on the ASAP-SAS benchmark, across three language models spanning dense and mixture-of-experts architectures. Persona steering lowers answer quality overall, with much larger effects on open-ended English Language Arts (ELA) prompts than on factual science prompts. Interpretive and argumentative tasks are particularly sensitive, showing up to 11×\times larger degradation. On the scoring side, we observe predictable valence-aligned calibration shifts: evil'' and impolite'' scorers grade more harshly, while good'' and optimistic'' scorers grade more leniently. ELA tasks are 2.5-3×\times more susceptible to scorer personalization than science tasks, and the mixture-of-experts model shows roughly 6×\times larger calibration shifts than the dense models. To our knowledge, this is the first study to systematically examine the effects of activation-steered persona traits in educational generation and scoring. Our findings highlight the need for task- and architecture-aware calibration when deploying personalized models in educational settings.

Yongchao Wu, Aron Henriksson

Stockholm University, NOD-huset, Borgarfjordsgatan 12, 16455 Stockholm, Sweden

Open-Ended GenerationLanguage Model SteeringLanguage Model Generation EvaluationAI in EducationAutomated GradingLanguage Model Calibration+3
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Apr 8, 2026

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

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

Hong Yi Lin, Chunhua Liu, Haoyu Gao +2

Confidence Estimation in Language ModelsLanguage Model CalibrationAutomated Program Repair
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Apr 7, 2026

Identifying Influential N-grams in Confidence Calibration via Regression Analysis

While large language models (LLMs) improve performance by explicit reasoning, their responses are often overconfident, even though they include linguistic expressions demonstrating uncertainty. In this work, we identify what linguistic expressions are related to confidence by applying the regression method. Specifically, we predict confidence of those linguistic expressions in the reasoning parts of LLMs as the dependent variables and analyze the relationship between a specific nn-gram and confidence. Across multiple models and QA benchmarks, we show that LLMs remain overconfident when reasoning is involved and attribute this behavior to specific linguistic information. Interestingly, several of the extracted expressions coincide with cue phrases intentionally inserted on test-time scaling to improve reasoning performance. Through our test on causality and verification that the extracted linguistic information truly affects confidence, we reveal that confidence calibration is possible by simply suppressing those overconfident expressions without drops in performance.

Shintaro Ozaki, Wataru Hashimoto, Hidetaka Kamigaito +2

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

Language Model CalibrationConfidence Estimation in Language ModelsLLM ReliabilityConfidence EstimationCausal Interventions in Language Models
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Apr 7, 2026

Same Graph, Different Likelihoods: Calibration of Autoregressive Graph Generators via Permutation-Equivalent Encodings

Autoregressive graph generators define likelihoods via a sequential construction process, but these likelihoods are only meaningful if they are consistent across all linearizations of the same graph. Segmented Eulerian Neighborhood Trails (SENT), a recent linearization method, converts graphs into sequences that can be perfectly decoded and efficiently processed by language models, but admit multiple equivalent linearizations of the same graph. We quantify violations in assigned negative log-likelihood (NLL) using the coefficient of variation across equivalent linearizations, which we call Linearization Uncertainty (LU). Training transformers under four linearization strategies on two datasets, we show that biased orderings achieve lower NLL on their native order but exhibit expected calibration error (ECE) two orders of magnitude higher under random permutation, indicating that these models have learned their training linearization rather than the underlying graph. On the molecular graph benchmark QM9, NLL for generated graphs is negatively correlated with molecular stability (AUC =0.43=0.43), while LU achieves AUC =0.85=0.85, suggesting that permutation-based evaluation provides a more reliable quality check for generated molecules. Code is available at https://github.com/lauritsf/linearization-uncertainty

Laurits Fredsgaard, Aaron Thomas, Michael Riis Andersen +2

Technical University of Denmark · University of Birmingham · National Institute of Informatics

Autoregressive GenerationPermutation-Invariant LearningLanguage Model CalibrationMolecular Graph Generation
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Apr 7, 2026

Confidence Should Be Calibrated More Than One Turn Deep

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

Zhaohan Zhang, Chengzhengxu Li, Xiaoming Liu +3

Queen Mary University of London · Xi’an Jiaotong University

Confidence Estimation in Language ModelsLanguage Model CalibrationLLM Reliability
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Apr 7, 2026

From Exposure to Internalization: Dual-Stream Calibration for In-context Clinical Reasoning

Contextual clinical reasoning demands robust inference grounded in complex, heterogeneous clinical records. While state-of-the-art fine-tuning, in-context learning (ICL), and retrieval-augmented generation (RAG) enable knowledge exposure, they often fall short of genuine contextual internalization: dynamically adjusting a model's internal representations to the subtle nuances of individual cases at inference time. To address this, we propose Dual-Stream Calibration (DSC), a test-time training framework that transcends superficial knowledge exposure to achieve deep internalization during inference. DSC facilitates input internalization by synergistically aligning two calibration streams. Unlike passive context exposure, the Semantic Calibration Stream enforces a deliberative reflection on core evidence, internalizing semantic anchors by minimizing entropy to stabilize generative trajectories. Simultaneously, the Structural Calibration Stream assimilates latent inferential dependencies through an iterative meta-learning objective. By training on specialized support sets at test-time, this stream enables the model to bridge the gap between external evidence and internal logic, synthesizing fragmented data into a coherent response. Our approach shifts the reasoning paradigm from passive attention-based matching to an active refinement of the latent inferential space. Validated against thirteen clinical datasets, DSC demonstrates superiority across three distinct task paradigms, consistently outstripping state-of-the-art baselines ranging from training-dependent models to test-time learning frameworks.

Chuang Zhao, Hongke Zhao, Xiaofang Zhou +1

Department of Electronic and Computer Engineering, The Hong Kong University of Science and Technology, Hong Kong, SAR, China · College of Management and Economics, Laboratory of Computation and Analytics of Complex Management Systems (CACMS), Tianjin University, Tianjin 30072, China · Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Hong Kong, SAR, China

Clinical ReasoningAdaptive InferenceLanguage Model CalibrationTest-Time Training
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Apr 3, 2026

Confidence Calibration in Large Language Models

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

Noam Michael, Daniel BenShushan, Jacob Bien +1

U.C. Berkeley · University of Southern California

Language Model CalibrationConfidence Estimation in Language ModelsLLM Evaluation
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Apr 3, 2026

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

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

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

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

LLM EvaluationConfidence Estimation in Language ModelsLLM ReliabilityLanguage Model CalibrationLLM Abstention
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Apr 2, 2026

Overconfidence and Calibration in Medical VQA: Empirical Findings and Hallucination-Aware Mitigation

As vision-language models (VLMs) are increasingly deployed in clinical decision support, more than accuracy is required: knowing when to trust their predictions is equally critical. Yet, a comprehensive and systematic investigation into the overconfidence of these models remains notably scarce in the medical domain. We address this gap through a comprehensive empirical study of confidence calibration in VLMs, spanning three model families (Qwen3-VL, InternVL3, LLaVA-NeXT), three model scales (2B--38B), and multiple confidence estimation prompting strategies, across three medical visual question answering (VQA) benchmarks. Our study yields three key findings: First, overconfidence persists across model families and is not resolved by scaling or prompting, such as chain-of-thought and verbalized confidence variants. Second, simple post-hoc calibration approaches, such as Platt scaling, reduce calibration error and consistently outperform the prompt-based strategy. Third, due to their (strict) monotonicity, these post-hoc calibration methods are inherently limited in improving the discriminative quality of predictions, leaving AUROC at the same level. Motivated by these findings, we investigate hallucination-aware calibration (HAC), which incorporates vision-grounded hallucination detection signals as complementary inputs to refine confidence estimates. We find that leveraging these hallucination signals improves both calibration and AUROC, with the largest gains on open-ended questions. On closed-ended questions, format-specific signals such as the logit margin show more informative. Overall, our findings suggest post-hoc calibration as standard practice for medical VLM deployment over raw confidence estimates, and highlight the practical usefulness of hallucination signals to enable more reliable use of VLMs in medical VQA.

Ji Young Byun, Young-Jin Park, Jean-Philippe Corbeil +1

Johns Hopkins University, School of Medicine · Massachusetts Institute of Technology · Microsoft Healthcare & Life Sciences

Vision-Language ModelsVLM HallucinationMedical VQALanguage Model CalibrationVLM Calibration
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Apr 2, 2026

Social Meaning in Large Language Models: Structure, Magnitude, and Pragmatic Prompting

Large language models (LLMs) increasingly exhibit human-like patterns of pragmatic and social reasoning. This paper addresses two related questions: do LLMs approximate human social meaning not only qualitatively but also quantitatively, and can prompting strategies informed by pragmatic theory improve this approximation? To address the first, we introduce two calibration-focused metrics distinguishing structural fidelity from magnitude calibration: the Effect Size Ratio (ESR) and the Calibration Deviation Score (CDS). To address the second, we derive prompting conditions from two pragmatic assumptions: that social meaning arises from reasoning over linguistic alternatives, and that listeners infer speaker knowledge states and communicative motives. Applied to a case study on numerical (im)precision across three frontier LLMs, we find that all models reliably reproduce the qualitative structure of human social inferences but differ substantially in magnitude calibration. Prompting models to reason about speaker knowledge and motives most consistently reduces magnitude deviation, while prompting for alternative-awareness tends to amplify exaggeration. Combining both components is the only intervention that improves all calibration-sensitive metrics across all models, though fine-grained magnitude calibration remains only partially resolved. LLMs thus capture inferential structure while variably distorting inferential strength, and pragmatic theory provides a useful but incomplete handle for improving that approximation.

Roland Mühlenbernd

Leibniz-Centre General Linguistics, Berlin, Germany

Pragmatic Reasoning in Language ModelsLanguage Model CalibrationLLM Prompting
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Apr 1, 2026

Wired for Overconfidence: A Mechanistic Perspective on Inflated Verbalized Confidence in LLMs

Large language models are often not just wrong, but confidently wrong: when they produce factually incorrect answers, they tend to verbalize overly high confidence rather than signal uncertainty. Such verbalized overconfidence can mislead users and weaken confidence scores as a reliable uncertainty signal, yet its internal mechanisms remain poorly understood. We present a circuit-level mechanistic analysis of this inflated verbalized confidence in LLMs, organized around three axes: capturing verbalized confidence as a differentiable internal signal, identifying the circuits that causally inflate it, and leveraging these insights for targeted inference-time recalibration. Across two instruction-tuned LLMs on three datasets, we find that a compact set of MLP blocks and attention heads, concentrated in middle-to-late layers, consistently writes the confidence-inflation signal at the final token position. We further show that targeted inference-time interventions on these circuits substantially improve calibration. Together, our results suggest that verbalized overconfidence in LLMs is driven by identifiable internal circuits and can be mitigated through targeted intervention.

Tianyi Zhao, Yinhan He, Wendy Zheng +2

University of Virginia

Confidence Estimation in Language ModelsLanguage Model CalibrationVerbalized Confidence EstimationLLM InterpretabilityCausal Interventions in Language Models
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Apr 1, 2026

Online Reasoning Calibration: Test-Time Training Enables Generalizable Conformal LLM Reasoning

While test-time scaling has enabled large language models to solve highly difficult tasks, state-of-the-art results come at exorbitant compute costs. These inefficiencies can be attributed to the miscalibration of post-trained language models, and the lack of calibration in popular sampling techniques. Here, we present Online Reasoning Calibration (ORCA), a framework for calibrating the sampling process that draws upon conformal prediction and test-time training. Specifically, we introduce a meta-learning procedure that updates the calibration module for each input. This allows us to provide valid confidence estimates under distributional shift, e.g. in thought patterns that occur across different stages of reasoning, or in prompt distributions between model development and deployment. ORCA not only provides theoretical guarantees on conformal risks, but also empirically shows higher efficiency and generalization across different reasoning tasks. At risk level δ=0.1δ=0.1, ORCA improves Qwen2.5-32B efficiency on in-distribution tasks with savings up to 47.5% with supervised labels and 40.7% with self-consistency labels. Under zero-shot out-of-domain settings, it improves MATH-500 savings from 24.8% of the static calibration baseline to 67.0% while maintaining a low empirical error rate, and the same trend holds across model families and downstream benchmarks. Our code is publicly available at https://github.com/wzekai99/ORCA.

Cai Zhou, Zekai Wang, Menghua Wu +6

Department of Electrical Engineering and Computer Science (MIT EECS) · Computer Science and Artificial Intelligence Laboratory (MIT CSAIL) · Laboratory for Information and Decision Systems (MIT LIDS) +1

Conformal Prediction for Language ModelsLanguage Model CalibrationConfidence Estimation in Language ModelsEfficient Language Model ReasoningConformal PredictionTest-Time Training
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Apr 1, 2026

Towards Reliable Truth-Aligned Uncertainty Estimation in Large Language Models

Uncertainty estimation (UE) aims to quantify uncertainty in large language model (LLM) outputs to flag potential hallucinations and support reliable deployment. However, UE metrics often exhibit unstable performance across models and datasets, limiting their practical utility. We formalise this phenomenon as proxy failure, arising because UE metrics are derived from model behaviour rather than being explicitly grounded in factual correctness. We show that when mutual information between a UE score and correctness is low, the score's discriminability must be close to chance. To address this, we propose Truth AnChoring (TAC), a lightweight post-hoc calibration method that maps raw UE scores to truth-aligned correctness probabilities. Even with noisy and few-shot supervision, TAC continues to improve calibration, providing a practical calibration protocol. Our findings highlight the limitations of treating heuristic UE metrics as direct indicators of uncertainty about factual correctness, and position our TAC as a principled step toward more reliable uncertainty estimation for LLMs. The code repository is available at https://github.com/ponhvoan/TruthAnchor/.

Ponhvoan Srey, Quang Minh Nguyen, Xiaobao Wu +1

Nanyang Technological University, Singapore · KAIST, South Korea · Shanghai Jiao Tong University

LLM Uncertainty EstimationUncertainty CalibrationLLM ReliabilityLanguage Model Calibration
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Mar 31, 2026

Act or Escalate? Evaluating Escalation Behavior in Automation with Language Models

Effective automation hinges on deciding when to act and when to escalate. We model this as a decision under uncertainty: an LLM forms a prediction, estimates its probability of being correct, and compares the expected costs of acting and escalating. Using this framework across five domains of recorded human decisions-demand forecasting, content recommendation, content moderation, loan approval, and autonomous driving-and across multiple model families, we find marked differences in the implicit thresholds models use to trade off these costs. These thresholds vary substantially and are not predicted by architecture or scale, while self-estimates are miscalibrated in model-specific ways. We then test interventions that target this decision process by varying cost ratios, providing accuracy signals, and training models to follow the desired escalation rule. Prompting helps mainly for reasoning models. SFT on chain-of-thought targets yields the most robust policies, which generalize across datasets, cost ratios, prompt framings, and held-out domains. These results suggest that escalation behavior is a model-specific property that should be characterized before deployment, and that robust alignment benefits from training models to reason explicitly about uncertainty and decision costs.

Matthew DosSantos DiSorbo, Harang Ju

Harvard Business School · Johns Hopkins Carey Business School

LLM Decision-MakingAI-Assisted Decision MakingSelective PredictionLanguage Model Calibration
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Mar 31, 2026

When Can We Trust LLM Graders? Calibrating Confidence for Automated Assessment

Large Language Models (LLMs) show promise for automated grading, but their outputs can be unreliable. Rather than improving grading accuracy directly, we address a complementary problem: predicting when an LLM grader is likely to be correct. This enables selective automation where high-confidence predictions are processed automatically while uncertain cases are flagged for human review. We compare three confidence estimation methods (self-reported confidence, self-consistency voting, and token probability) across seven LLMs of varying scale (4B to 120B parameters) on three educational datasets: RiceChem (long-answer chemistry), SciEntsBank, and Beetle (short-answer science). Our experiments reveal that self-reported confidence consistently achieves the best calibration across all conditions (avg ECE 0.166 vs 0.229 for self-consistency). Surprisingly, self-consistency remains 38% worse despite requiring 5×\times the inference cost. Larger models exhibit substantially better calibration though gains vary by dataset and method (e.g., a 28% ECE reduction for self-reported), with GPT-OSS-120B achieving the best calibration (avg ECE 0.100) and strong discrimination (avg AUC 0.668). We also observe that confidence is strongly top-skewed across methods, creating a ``confidence floor'' that practitioners must account for when setting thresholds. These findings suggest that simply asking LLMs to report their confidence provides a practical approach for identifying reliable grading predictions. Code is available here.

Robinson Ferrer, Damla Turgut, Zhongzhou Chen +1

University of Central Florida

Confidence Estimation in Language ModelsLanguage Model CalibrationAutomated GradingSelective PredictionLLM-as-a-Judge
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Mar 26, 2026

Do LLMs Know What They Know? Measuring Metacognitive Efficiency with Signal Detection Theory

Standard evaluation of LLM confidence relies on calibration metrics (ECE, Brier score) that conflate two capacities: how much a model knows (Type-1 accuracy) and how well its confidence signal tracks that knowledge (Type-2 metacognitive sensitivity). We apply Signal Detection Theory to decompose them, treating token-level normalised log-probability as a graded confidence variable and answer correctness as the state to be discriminated. We characterise the Type-2 ROC of this signal, including its unequal-variance structure via z-ROC analysis, and -- because the meta-d' efficiency ratio is not well defined for open-ended QA, which lacks a two-alternative Type-1 decision -- quantify efficiency with a model-free information measure, normalised metacognitive information (meta-I_2r). Across four LLMs and 224,000 factual QA trials we find: (1) metacognitive information varies by a factor of 1.98 across models and is not predicted by accuracy, the rank correlation being -0.80 on TriviaQA and +0.00 on Natural Questions; (2) the confidence signal has model-specific unequal-variance structure (z-ROC slopes 0.78 to 1.18) invisible to calibration metrics, the slope ordering replicating on NQ; (3) efficiency is domain-specific, weakest in Science & Technology for every model; (4) temperature dissociates accuracy from metacognitive information, which stays near-flat for three of four models while accuracy falls; and (5) metacognitive information tracks the accuracy gain from confidence-based abstention exactly (rho = +1.00) while accuracy does not. All estimates carry permutation nulls and bootstrap confidence intervals. This version (v3) corrects a differential length bias in the automated correctness scorer, validated against 1,830 human adjudications; the inverse accuracy-efficiency coupling reported in v1 and v2 does not survive relabelling. See the version note on page 1.

Jon-Paul Cacioli

Independent Researcher, Melbourne, Australia

Confidence Estimation in Language ModelsLanguage Model CalibrationLLM Uncertainty EstimationMetacognition in Language Models
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Mar 26, 2026

Closing the Confidence-Faithfulness Gap in Large Language Models

Large language models (LLMs) tend to verbalize confidence scores that are largely detached from their actual accuracy, yet the geometric relationship governing this behavior remain poorly understood. In this work, we present a mechanistic interpretability analysis of verbalized confidence, using linear probes and contrastive activation addition (CAA) steering to show that calibration and verbalized confidence signals are encoded linearly but are orthogonal to one another -- a finding consistent across three open-weight models and four datasets. Interestingly, when models are prompted to simultaneously reason through a problem and verbalize a confidence score, the reasoning process disrupts the verbalized confidence direction, exacerbating miscalibration. We term this the "Reasoning Contamination Effect." Leveraging this insight, we introduce a two-stage adaptive steering pipeline that reads the model's internal accuracy estimate and steers verbalized output to match it, substantially improving calibration alignment across all evaluated models.

Miranda Muqing Miao, Lyle Ungar

University of Pennsylvania · Department of Computer and Information Science

Confidence Estimation in Language ModelsVerbalized Confidence EstimationLanguage Model CalibrationLLM InterpretabilityActivation Steering
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Mar 24, 2026

Set-Valued Prediction for Large Language Models with Feasibility-Aware Coverage Guarantees

Large language models (LLMs) inherently operate over a large generation space, yet conventional usage typically reports the most likely generation (MLG) as a point prediction, which underestimates the model's capability: although the top-ranked response can be incorrect, valid answers may still exist within the broader output space and can potentially be discovered through repeated sampling. This observation motivates moving from point prediction to set-valued prediction, where the model produces a set of candidate responses rather than a single MLG. In this paper, we propose a principled framework for set-valued prediction, which provides feasibility-aware coverage guarantees. We show that, given the finite-sampling nature of LLM generation, coverage is not always achievable: even with multiple samplings, LLMs may fail to yield an acceptable response for certain questions within the sampled candidate set. To address this, we establish a minimum achievable risk level (MRL), below which statistical coverage guarantees cannot be satisfied. Building on this insight, we then develop a data-driven calibration procedure that constructs prediction sets from sampled responses by estimating a rigorous threshold, ensuring that the resulting set contains a correct answer with a desired probability whenever the target risk level is feasible. Extensive experiments on six language generation tasks with five LLMs demonstrate both the statistical validity and the predictive efficiency of our framework.

Ye Li, Anqi Hu, Yuanchang Ye +3

University of Electronic Science and Technology of China, Chengdu, Sichuan, China · Zhejiang University of Finance and Economics, Hangzhou, Zhejiang, China · Southeast University, Nanjing, Jiangsu, China

Set-Valued PredictionLLM Uncertainty EstimationLanguage Model CalibrationText Generation
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Mar 22, 2026

Entropy Alone is Insufficient for Safe Selective Prediction in LLMs

Selective prediction systems can mitigate harms resulting from language model hallucinations by abstaining from answering in high-risk cases. Uncertainty quantification techniques are often employed to identify such cases, but are rarely evaluated in the context of the wider selective prediction policy and its ability to operate at low target error rates. We identify a model-dependent failure mode of entropy-based uncertainty methods that leads to unreliable abstention behaviour, and address it by combining entropy scores with a correctness probe signal. We find that across three QA benchmarks (TriviaQA, BioASQ, MedicalQA) and four model families, the combined score generally improves both the risk--coverage trade-off and calibration performance relative to entropy-only baselines. Our results highlight the importance of deployment-facing evaluation of uncertainty methods, using metrics that directly reflect whether a system can be trusted to operate at a stated risk level.

Edward Phillips, Fredrik K. Gustafsson, Sean Wu +2

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

Selective PredictionLLM Uncertainty EstimationLLM ReliabilityLLM Hallucination MitigationLanguage Model Calibration
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Mar 21, 2026

DiscoUQ: Structured Disagreement Analysis for Uncertainty Quantification in LLM Agent Ensembles

Multi-agent LLM systems, where multiple prompted instances of a language model independently answer questions, are increasingly used for complex reasoning tasks. However, existing methods for quantifying the uncertainty of their collective outputs rely on shallow voting statistics that discard the rich semantic information in agents' reasoning. We introduce DiscoUQ, a framework that extracts and leverages the structure of inter-agent disagreement -- both linguistic properties (evidence overlap, argument strength, divergence depth) and embedding geometry (cluster distances, dispersion, cohesion) -- to produce well-calibrated confidence estimates. We propose three methods of increasing complexity: DiscoUQ-LLM (logistic regression on LLM-extracted structure features), DiscoUQ-Embed (logistic regression on embedding geometry), and DiscoUQ-Learn (a neural network combining all features). Evaluated on four diverse benchmarks (StrategyQA, MMLU, TruthfulQA, ARC-Challenge) with a 5-agent system using Qwen3.5-27B, DiscoUQ-LLM achieves an average AUROC of 0.802, outperforming the best baseline (LLM Aggregator, 0.791) while being substantially better calibrated (ECE 0.036 vs. 0.098). The learned features generalize across benchmarks with near-zero performance degradation and provide the largest improvements where they are most needed: in the ambiguous "weak disagreement" tier where simple vote counting fails.

Bo Jiang

Temple University

Uncertainty QuantificationLLM Uncertainty EstimationLanguage Model EnsemblesLanguage Model Calibration
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Mar 18, 2026

Self-Calibrating Language Models via Test-Time Discriminative Distillation

Large language models (LLMs) are systematically overconfident: they routinely express high certainty on questions they often answer incorrectly. Existing calibration methods either require labeled validation data, degrade under distribution shifts, or incur substantial inference costs. Recent work has shown that LLMs already contain a better-calibrated signal than the one they verbalize: the token probability of "True" when the model is asked "Is this answer correct?" (P(True)P(\text{True})) consistently outperforms their stated confidence, a gap that is theoretically grounded as generative error is lower-bounded by roughly twice the corresponding discriminative error. We introduce SECL\textbf{SECL} (SE\textbf{SE}lf-C\textbf{C}alibrating L\textbf{L}anguage Models), a test-time training (TTT) pipeline that exploits this gap as label-free self-supervision, requiring no labeled data or human supervision. SECL adapts only when the input distribution shifts, training on just 6--26% of the question stream at lower cost than the baseline it distills from. Across four small language models from three model families and four diverse domains, SECL reduces Expected Calibration Error (ECE) by 56--78%, outperforming its own supervision signal and matching or outperforming recent inference-time methods. SECL is the first method to apply TTT to calibration; seven ablations covering signal quality, gating strategy, weight accumulation, loss design, domain ordering, hyperparameter sensitivity, and layer selection confirm that each component is crucial and robust across configurations. Code: https://anonymous.4open.science/r/secl-emnlp26-submission-C890

Mohamed Rissal Hedna, Jan Strich, Martin Semmann +1

Hub of Computing and Data Science (HCDS), University of Hamburg, Germany

Inference-Time Adaptation of Language ModelsLanguage Model CalibrationConfidence Estimation in Language ModelsSelf-Training for Language Models
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Mar 17, 2026

Noise-Response Calibration: A Causal Intervention Protocol for LLM-Judges

Large language models (LLMs) are increasingly used as automated judges and synthetic labelers, especially in low-label settings. Yet these systems are stochastic and often overconfident, which makes deployment decisions difficult when external ground truth is limited. We propose a practical calibration protocol based on controlled input interventions: if noise severity increases, task performance should exhibit a statistically significant deterioration trend. We operationalize this with a slope-based hypothesis test over repeated trials, using signal-to-noise-ratio (SNR) perturbations for tabular data and lexical perturbations for text data. Across UCI tabular benchmarks and four text classification datasets, we find clear modality-dependent behavior. Our results reveal a modality gap: while text-based judges degrade predictably, the majority of tabular datasets show a lack of statistically significant performance deterioration even under significant signal-to-noise reduction. Interestingly we find that model performance is lower on datasets that are insensitive to noise interventions. We present a reproducible methodology and reporting protocol for robust LLM-judge calibration under distribution shift.

Maxim Khomiakov, Jes Frellsen

Technical University of Denmark, Kgs. Lyngby, Denmark · Normal Computing Corporation, New York, NY, USA · Pioneer Centre for Artificial Intelligence, Copenhagen, Denmark

Language Model CalibrationLLM-as-a-JudgeLanguage Model RobustnessCausal Interventions in Language Models
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Mar 16, 2026

LLMs as Signal Detectors: Sensitivity, Bias, and the Temperature-Criterion Analogy

Large language models (LLMs) are evaluated for calibration using metrics such as Expected Calibration Error that conflate two distinct components: the model's ability to discriminate correct from incorrect answers (sensitivity) and its tendency toward confident or cautious responding (bias). Signal Detection Theory (SDT) decomposes these components. While SDT-derived metrics such as AUROC are increasingly used, the full parametric framework - unequal-variance model fitting, criterion estimation, z-ROC analysis - has not been applied to LLMs as signal detectors. In this pre-registered study, we treat three LLMs as observers performing factual discrimination across 168,000 trials and test whether temperature functions as a criterion shift analogous to payoff manipulations in human psychophysics. Critically, this analogy may break down because temperature changes the generated answer itself, not only the confidence assigned to it. Our results confirm the breakdown with temperature simultaneously increasing sensitivity (AUC) and shifting criterion. All models exhibited unequal-variance evidence distributions (z-ROC slopes 0.52-0.84), with instruct models showing more extreme asymmetry (0.52-0.63) than the base model (0.77-0.87) or human recognition memory (~0.80). The SDT decomposition revealed that models occupying distinct positions in sensitivity-bias space could not be distinguished by calibration metrics alone, demonstrating that the full parametric framework provides diagnostic information unavailable from existing metrics.

Jon-Paul Cacioli

Independent Researcher, Melbourne, Australia

LLM EvaluationLanguage Model CalibrationConfidence Estimation in Language Models
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Mar 12, 2026

CHiL(L)Grader: Calibrated Human-in-the-Loop Short-Answer Grading

Scaling educational assessment with large language models requires not just accuracy, but the ability to recognize when predictions are trustworthy. Instruction-tuned models tend to be overconfident, and their reliability deteriorates as curricula evolve, making fully autonomous deployment unsafe in high-stakes settings. We introduce CHiL(L)Grader, the first automated grading framework that incorporates calibrated confidence estimation into a human-in-the-loop workflow. Using post-hoc temperature scaling, confidence-based selective prediction, and continual learning, CHiL(L)Grader automates only high-confidence predictions while routing uncertain cases to human graders, and adapts to evolving rubrics and unseen questions. Across three short-answer grading datasets, CHiL(L)Grader automatically scores 35-65% of responses at expert-level quality (QWK >= 0.80). A QWK gap of 0.347 between accepted and rejected predictions confirms the effectiveness of the confidence-based routing. Each correction cycle strengthens the model's grading capability as it learns from teacher feedback. These results show that uncertainty quantification is key for reliable AI-assisted grading.

Pranav Raikote, Korbinian Randl, Ioanna Miliou +2

Department of Computer and Systems Sciences, Stockholm University, 164 25 Kista, Sweden

Automated GradingAI in EducationHuman-in-the-Loop EvaluationLanguage Model Calibration
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Mar 10, 2026

Beyond 0-100: How Confidence Scale Design Shapes Verbalized Confidence and LLM Metacognition

Verbalized confidence, in which LLMs report a numerical certainty score, is widely used to estimate uncertainty in black-box settings, yet the confidence scale itself (typically 0--100) is rarely examined. We show that this design choice is not neutral. Across six LLMs and three datasets, verbalized confidence is heavily discretized, with more than 78% of responses concentrating on just three round-number values. To investigate this phenomenon, we systematically manipulate confidence scales along three dimensions: granularity, boundary placement, and range regularity, and evaluate metacognitive sensitivity using meta-d′meta\text{-}d'. We find that a 0--20 scale consistently improves metacognitive efficiency over the standard 0--100 format, while boundary compression degrades performance and round-number preferences persist even under irregular ranges. These results demonstrate that confidence scale design directly affects the quality of verbalized uncertainty and should be treated as a first-class experimental variable in LLM evaluation.

Yuyang Dai, Yuxia Wang

INSAIT

Confidence Estimation in Language ModelsLanguage Model CalibrationLLM Uncertainty EstimationVerbalized Confidence EstimationMetacognition in Language ModelsConfidence Estimation
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Mar 10, 2026

Decoupling Reasoning and Confidence: Resurrecting Calibration in Reinforcement Learning from Verifiable Rewards

Reinforcement Learning from Verifiable Rewards (RLVR) significantly enhances large language models (LLMs) reasoning but severely suffers from calibration degeneration, where models become excessively over-confident in incorrect answers. Previous studies devote to directly incorporating calibration objective into existing optimization target. However, our theoretical analysis demonstrates that there exists a fundamental gradient conflict between the optimization for maximizing policy accuracy and minimizing calibration error. Building on this insight, we propose DCPO, a simple yet effective framework that systematically decouples reasoning and calibration objectives. Extensive experiments demonstrate that our DCPO not only preserves accuracy on par with GRPO but also achieves the best calibration performance and substantially mitigates the over-confidence issue. Our study provides valuable insights and practical solution for more reliable LLM deployment.

Zhengzhao Ma, Xueru Wen, Boxi Cao +6

Chinese Information Processing Laboratory, Institute of Software, Chinese Academy of Sciences, Beijing, China · University of Chinese Academy of Sciences, Beijing, China · Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China +2

Reinforcement LearningRL for Language Model ReasoningLanguage Model CalibrationReinforcement Learning with Verifiable Rewards
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