Language Model Calibration

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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

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

Mar 6, 2026

From Entropy to Calibrated Uncertainty: Training Language Models to Reason About Uncertainty

Large Language Models (LLMs) that can express interpretable and calibrated uncertainty are crucial in high-stakes domains. While methods to compute uncertainty post-hoc exist, they are often sampling-based and therefore computationally expensive or lack calibration. We propose a three-stage pipeline to post-train LLMs to efficiently infer calibrated uncertainty estimates for their responses. First, we compute fine-grained entropy-based uncertainty scores on the training data, capturing the distributional variability of model outputs in embedding space. Second, these scores are calibrated via Platt scaling, producing reliable and human-interpretable uncertainty signals. Finally, the target LLM is post-trained via reinforcement learning to align its policy with these calibrated signals through a verifiable reward function. Unlike post-hoc uncertainty estimation methods, our approach provides interpretable and computationally efficient uncertainty estimates at test time. Experiments show that models trained with our pipeline achieve better calibration than baselines and generalize to unseen tasks without further processing, suggesting that they learn a robust uncertainty reasoning behavior.

Azza Jenane, Nassim Walha, Lukas Kuhn +1

German Cancer Research Center (DKFZ) German Cancer Consortium (DKTK) Goethe University Frankfurt, Germany

LLM Uncertainty Estimation Language Model Calibration

Mar 4, 2026

Believe Your Model: Distribution-Guided Confidence Calibration

Large Reasoning Models have demonstrated remarkable performance with the advancement of test-time scaling techniques, which enhances prediction accuracy by generating multiple candidate responses and selecting the most reliable answer. While prior work has analyzed that internal model signals like confidence scores can partly indicate response correctness and exhibit a distributional correlation with accuracy, such distributional information has not been fully utilized to guide answer selection. Motivated by this, we propose DistriVoting, which incorporates distributional priors as another signal alongside confidence during voting. Specifically, our method (1) first decomposes the mixed confidence distribution into positive and negative components using Gaussian Mixture Models, (2) then applies a reject filter based on positive/negative samples from them to mitigate overlap between the two distributions. Besides, to further alleviate the overlap from the perspective of distribution itself, we propose SelfStepConf, which uses step-level confidence to dynamically adjust inference process, increasing the separation between the two distributions to improve the reliability of confidences in voting. Experiments across 16 models and 5 benchmarks demonstrate that our method significantly outperforms state-of-the-art approaches.

Xizhong Yang, Haotian Zhang, Huiming Wang +1

Southeast University · Kuaishou Technology

Language Model Calibration Confidence Estimation in Language Models

Mar 4, 2026

Confidence-Calibrated Small-Large Language Model Collaboration for Cost-Efficient Reasoning

Large language models (LLMs) demonstrate superior reasoning capabilities compared to small language models (SLMs), but incur substantially higher costs. We propose COllaborative REAsoner (COREA), a system that cascades an SLM with an LLM to achieve a balance between accuracy and cost in complex reasoning tasks. COREA first attempts to answer questions using the SLM, which outputs both an answer and a verbalized confidence score. Questions with confidence below a predefined threshold are deferred to the LLM for more accurate resolution. We introduce a reinforcement learning-based training algorithm that aligns the SLM's confidence through an additional confidence calibration reward. Extensive experiments demonstrate that our method jointly improves the SLM's reasoning ability and confidence calibration across diverse datasets and model backbones. Compared to using the LLM alone, COREA reduces cost by 21.5% and 16.8% on out-of-domain math and non-math datasets, respectively, with only an absolute pass@1 drop within 2%.

Chuang Zhang, Zizhen Zhu, Yihao Wei +5

Amazon Web Services · Tsinghua University

Language Model Cascading Efficient Language Model Reasoning Confidence Estimation in Language Models Language Model Calibration RL for Language Model Reasoning

Mar 2, 2026

Frontier Models Can Take Actions at Low Probabilities

Pre-deployment evaluations inspect only a limited sample of model actions. A malicious model seeking to evade oversight could exploit this by randomizing when to "defect": misbehaving so rarely that no malicious actions are observed during evaluation, but often enough that they occur eventually in deployment. But this requires taking actions at very low rates, while maintaining calibration. Are frontier models even capable of that? We prompt the GPT-5, Claude-4.5 and Qwen-3 families to take a target action at low probabilities (e.g. 0.01%), either given directly or requiring derivation, and evaluate their calibration (i.e. whether they perform the target action roughly 1 in 10,000 times when resampling). We find that frontier models are surprisingly good at this task. If there is a source of entropy in-context (such as a UUID), they maintain high calibration at rates lower than 1 in 100,000 actions. Without external entropy, some models can still reach rates lower than 1 in 10,000. When target rates are given, larger models achieve good calibration at lower rates. Yet, when models must derive the optimal target rate themselves, all models fail to achieve calibration without entropy or hint to generate it. Successful low-rate strategies require explicit Chain-of-Thought (CoT) reasoning, so malicious models attempting this approach could currently be caught by a CoT monitor. However, scaling trends suggest future evaluations may be unable to rely on models' lack of target rate calibration, especially if CoT is no longer legible.

Alex Serrano, Wen Xing, David Lindner +1

MATS† · Google DeepMind

Language Model Safety Evaluation Strategic Reasoning Risks in Language Models Language Model Calibration

Mar 1, 2026

Self-Anchoring Calibration Drift in Large Language Models: How Multi-Turn Conversations Reshape Model Confidence

We introduce Self-Anchoring Calibration Drift (SACD), a hypothesized tendency for large language models (LLMs) to show systematic changes in expressed confidence when building iteratively on their own prior outputs across multi-turn conversations. We report an empirical study comparing three frontier models -- Claude Sonnet 4.6, Gemini 3.1 Pro, and GPT-5.2 -- across 150 questions spanning factual, technical, and open-ended domains, using three conditions: single-turn baseline (A), multi-turn self-anchoring (B), and independent repetition control (C). Results reveal a complex, model-heterogeneous pattern that partially diverges from pre-registered hypotheses. Claude Sonnet 4.6 exhibited significant decreasing confidence under self-anchoring (mean CDS = -0.032, t(14) = -2.43, p = .029, d = -0.627), while also showing significant calibration error drift (F(4,56) = 22.77, p < .001, eta^2 = .791). GPT-5.2 showed the opposite pattern in open-ended domains (mean CDS = +0.026) with significant ECE escalation by Turn 5. Gemini 3.1 Pro showed no significant CDS (t(14) = 0.38, p = .710), but its Condition C data reveals a striking ECE pattern: without self-anchoring, Gemini's calibration error drops from .327 to near zero across repetitions, whereas self-anchoring holds ECE flat at approximately .333 -- indicating that SACD can manifest as suppression of natural calibration improvement rather than ac

Harshavardhan

Independent Researcher

Confidence Estimation in Language Models Language Model Calibration

Mar 1, 2026

HypeLoRA: Hyper-Network-Generated LoRA Adapters for Calibrated Language Model Fine-Tuning

Modern Transformer-based models frequently suffer from miscalibration, producing overconfident predictions that do not reflect true empirical frequencies. This work investigates the calibration dynamics of LoRA: Low-Rank Adaptation and a novel hyper-network-based adaptation framework as parameter-efficient alternatives to full fine-tuning for RoBERTa. Evaluating across the GLUE benchmark, we demonstrate that LoRA-based adaptation consistently achieves calibration parity with (and in specific tasks exceeds) full fine-tuning, while maintaining significantly higher parameter efficiency. We further explore a dynamic approach where a shared hyper-network generates LoRA factors (A and B matrices) to induce structural coupling across layers. This approach produced results similar to standard LoRA fine-tuning, even achieving better MCC on CoLA dataset. Our study also reveal a critical trade-off: constraining the adaptation space (e.g., freezing matrices A) acts as a powerful regularizer that enhances Expected Calibration Error (ECE), but necessitates a carefully balanced sacrifice in downstream task accuracy. To support future research, we provide a unified and reproducible implementation of contemporary calibration metrics, including ECE, MCE, and ACE. Our findings clarify the relationship between parameter efficiency and probabilistic reliability, positioning structured low-rank updates as a viable foundation for uncertainty-aware Transformer architectures. Code available at: https://github.com/btrojan-official/HypeLoRA

Bartosz Trojan, Filip Gębala

Upper-Secondary Schools of Communications in Cracow

Low-Rank Adaptation Language Model Calibration Parameter-Efficient Fine-Tuning Hypernetworks

Mar 1, 2026

Conformal Prediction for Risk-Controlled Medical Entity Extraction Across Clinical Domains

Large Language Models (LLMs) are increasingly used for medical entity extraction, yet their confidence scores are often miscalibrated, limiting safe deployment in clinical settings. We present a conformal prediction framework that provides finite-sample coverage guarantees for LLM-based extraction across two clinical domains. First, we extract structured entities from 1,000 FDA drug labels across eight sections using GPT-4.1, verified via FactScore-based atomic statement evaluation (97.7% accuracy over 128,906 entities). Second, we extract radiological entities from MIMIC-CXR reports using the RadGraph schema with GPT-4.1 and Llama-4-Maverick, evaluated against physician annotations (entity F1: 0.81 to 0.84). Our central finding is that miscalibration direction reverses across domains: on well-structured FDA labels, models are underconfident, requiring modest conformal thresholds (

τ\approx 0.06

), while on free-text radiology reports, models are overconfident, demanding strict thresholds (

τ

up to 0.99). Despite this heterogeneity, conformal prediction achieves target coverage (

\geq 90\%

) in both settings with manageable rejection rates (9--13%). These results demonstrate that calibration is not a global model property but depends on document structure, extraction category, and model architecture, motivating domain-specific conformal calibration for safe clinical deployment.

Manil Shrestha, Edward Kim

Department of Computer Science, Drexel University, Philadelphia, USA

Named Entity Recognition Language Model Calibration Conformal Prediction Medical LLMs Clinical Information Extraction

Feb 28, 2026

Rubric-Guided Fine-tuning of SpeechLLMs for Multi-Aspect, Multi-Rater L2 Reading-Speech Assessment

Reliable and interpretable automated assessment of second-language (L2) speech remains a central challenge, as large speech-language models (SpeechLLMs) often struggle to align with the nuanced variability of human raters. To address this, we introduce a rubric-guided reasoning framework that explicitly encodes multi-aspect human assessment criteria: accuracy, fluency, and prosody, while calibrating model uncertainty to capture natural rating variability. We fine-tune the Qwen2-Audio-7B-Instruct model using multi-rater human judgments and develop an uncertainty-calibrated regression approach supported by conformal calibration for interpretable confidence intervals. Our Gaussian uncertainty modeling and conformal calibration approach achieves the strongest alignment with human ratings, outperforming regression and classification baselines. The model reliably assesses fluency and prosody while highlighting the inherent difficulty of assessing accuracy. Together, these results demonstrate that rubric-guided, uncertainty-calibrated reasoning offers a principled path toward trustworthy and explainable SpeechLLM-based speech assessment.

Aditya Kamlesh Parikh, Cristian Tejedor-Garcia, Catia Cucchiarini +1

Centre for Language Studies, Radboud University, The Netherlands

Speech Quality Assessment Speech Language Models Language Model Calibration

Feb 26, 2026

Empirical Characterization of Inference-Time Elicited Probability Transformations in Large Language Models

Large language models increasingly rely on inference-time procedures such as chain-of-thought reasoning, self-refinement, retrieval augmentation, and verifier-guided revision, yet the structure of elicited probability transformations under these procedures remains poorly understood. We study externally elicited probability assignments over candidate answers and observe recurring approximate log-ratio relationships:

\log \tilde q_t(i) = α_t \left( \log q_t(i) + \log b_t(i) \right) + c_t,

where

q_t

and

\tilde q_t

are pre- and post-elicitation probabilities,

b_t

is an externally constructed evidence signal, and

α_t

is an empirical descriptor of the prompting configuration. Across 4,975 reasoning problems from GPQA Diamond, TheoremQA, MMLU-Pro, and ARC-Challenge, evaluated on multiple instruction-tuned model families, we observe approximate log-ratio relationships with mean

R^2 \approx 0.76

over about

1.3 \times 10^5

candidate-level observations. Coefficients vary across elicitation settings, but qualitatively similar relationships persist across evaluated conditions. Robustness analyses using alternative statistical representations, prompting configurations, held-out evaluation, and token-level log-probabilities suggest that the observed structure is not tied to one prompting procedure or probability estimation method. The main contribution is not the algebraic form itself, which is related to generalized Bayesian updating and probability-transformation frameworks, but the empirical observation that diverse inference-time prompting pipelines repeatedly exhibit reproducible log-ratio structure under controlled conditions. The framework provides a protocol-sensitive perspective for analyzing calibration, evidence amplification, uncertainty propagation, and interaction sensitivity in inference-time LLM pipelines.

Mike Farmer, Abhinav Kochar, Yugyung Lee

Bloch School of Management, Regnier Institute for Entrepreneurship & Innovation, University of Missouri–Kansas City. · Department of Computer Science, School of Science and Engineering, University of Missouri–Kansas City.

LLM Inference Belief Updating in LLMs Confidence Estimation in Language Models Language Model Calibration

Feb 26, 2026

Know What You Know: Metacognitive Entropy Calibration for Verifiable RL Reasoning

Large reasoning models (LRMs) have emerged as a powerful paradigm for solving complex real-world tasks. In practice, these models are predominantly trained via Reinforcement Learning with Verifiable Rewards (RLVR), yet most existing outcome-only RLVR pipelines rely almost exclusively on a binary correctness signal and largely ignore the model's intrinsic uncertainty. We term this discrepancy the uncertainty-reward mismatch, under which high- and low-uncertainty solutions are treated equivalently, preventing the policy from "Know What You Know" and impeding the shift from optimizing for correct answers to optimizing effective reasoning paths. This limitation is especially critical in reasoning-centric tasks such as mathematics and question answering, where performance hinges on the quality of the model's internal reasoning process rather than mere memorization of final answers. To address this, we propose EGPO, a metacognitive entropy calibration framework that explicitly integrates intrinsic uncertainty into RLVR for enhancing LRMs. EGPO estimates per-sample uncertainty using a zero-overhead entropy proxy derived from token-level likelihoods and aligns it with extrinsic correctness through an asymmetric calibration mechanism that preserves correct reasoning while selectively regulating overconfident failures, thereby enabling stable and uncertainty-aware policy optimization. Moreover, EGPO recovers informative learning signals from otherwise degenerate group-based rollouts without modifying the verifier or reward definition. Extensive experiments across multiple benchmarks demonstrate that the proposed EGPO leads to substantial and consistent improvements in reasoning performance, establishing a principled path for advancing LRMs through metacognitive entropy calibration.

Qiannian Zhao, Chen Yang, Jinhao Jing +5

RL for Language Model Reasoning Large Reasoning Models Language Model Calibration Reinforcement Learning with Verifiable Rewards Metacognition in Language Models

Feb 25, 2026

Algorithmic Blindness in Large Language Models: A Calibration Study of Performance Prediction

Large language models (LLMs) demonstrate remarkable breadth of knowledge, yet their ability to reason about computational processes remains poorly understood. Closing this gap matters for practitioners who rely on LLMs to guide algorithm selection and deployment. We address this limitation using causal discovery as a testbed and evaluate eight frontier LLMs against ground truth derived from algorithm executions. We find systematic, near-total failure across models. The predicted ranges are far wider than true confidence intervals yet still fail to contain the true algorithmic mean in most cases. Most models perform worse than random guessing. The best model's marginal improvement points to benchmark memorization rather than principled reasoning. We term this failure algorithmic blindness and argue it reflects a fundamental gap between declarative knowledge about algorithms and calibrated procedural prediction.

Sohan Venkatesh, Ashish Mahendran Kurapath, Tejas Melkote

Manipal Institute of Technology Bengaluru

Algorithmic Reasoning LLM Evaluation Language Model Calibration Confidence Estimation in Language Models

Feb 23, 2026

How Confident Is the First Token? An Uncertainty-Calibrated Prompt Optimization Framework for Large Language Model Classification and Understanding

With the widespread adoption of large language models (LLMs) in natural language processing, prompt engineering and retrieval-augmented generation (RAG) have become mainstream to enhance LLMs' performance on complex tasks. However, LLMs generate outputs autoregressively, leading to inevitable output uncertainty. Since model performance is highly sensitive to prompt design, precise uncertainty measurement is crucial for reliable prompt optimization. For multi-class multiple-choice (understanding) tasks, conventional uncertainty measures (e.g., entropy) based on output probabilities treat all classes equally and ignore class prior differences in pretraining corpora. This failure to distinguish spurious confidence (from priors) from true certainty (from contextual understanding) results in poor confidence calibration. To address this, we propose Log-Scale Focal Uncertainty (LSFU), a first-token-based metric inspired by focal loss. LSFU incorporates label prior probabilities as a risk-modulation factor to suppress noise from high-frequency classes and emphasize risk for low-frequency long-tail classes, with a dynamic weighting mechanism unifying the measurement scale. Based on LSFU, we further propose the uncertainty-calibrated prompt optimization framework (UCPOF), which leverages the first token of model outputs to select high-quality exemplars and dynamically optimize prompts. Comprehensive evaluations show UCPOF improves average accuracy by 6.03% over few-shot baselines, surpasses always-on full RAG by 5.75% in overall average accuracy, and reduces the average retrieval trigger rate by 50.66%. By adaptively triggering RAG only for high-uncertainty samples, our framework significantly lowers computational costs while maintaining state-of-the-art performance.

Wei Chen, Guoyang Ju, Yuanyuan Qi

China Jiliang University, Hangzhou, China

LLM Input Optimization LLM Prompting LLM Uncertainty Estimation Language Model Calibration Efficient Language Model Inference Retrieval-Augmented Generation

Feb 21, 2026

UniRank: A Multi-Agent Calibration Pipeline for Estimating University Rankings from Anonymized Bibliometric Signals

We present UniRank, a multi-agent LLM pipeline that estimates university positions across global ranking systems using only publicly available bibliometric data from OpenAlex and Semantic Scholar. The system employs a three-stage architecture: (a) zero-shot estimation from anonymized institutional metrics, (b) per-system tool-augmented calibration against real ranked universities, and (c) final synthesis. Critically, institutions are anonymized -- names, countries, DOIs, paper titles, and collaboration countries are all redacted -- and their actual ranks are hidden from the calibration tools during evaluation, preventing LLM memorization from confounding results. On the Times Higher Education (THE) World University Rankings (

n=352

), the system achieves MAE = 251.5 rank positions, Median AE = 131.5, PNMAE = 12.03%, Spearman

ρ= 0.769

, Kendall

τ= 0.591

, hit rate @50 = 20.7%, hit rate @100 = 39.8%, and a Memorization Index of exactly zero (no exact-match zero-width predictions among all 352 universities). The systematic positive-signed error (+190.1 positions, indicating the system consistently predicts worse ranks than actual) and monotonic performance degradation from elite tier (MAE = 60.5, hit@100 = 90.5%) to tail tier (MAE = 328.2, hit@100 = 20.8%) provide strong evidence that the pipeline performs genuine analytical reasoning rather than recalling memorized rankings. A live demo is available at https://unirank.scinito.ai .

Pedram Riyazimehr, Seyyed Ehsan Mahmoudi

NotionWave

Higher Education Language Model Calibration Learning to Rank

Feb 19, 2026

Calibrated Adaptation: Bayesian Stiefel Manifold Priors for Reliable Parameter-Efficient Fine-Tuning

Parameter-efficient fine-tuning methods such as LoRA enable practical adaptation of large language models but provide no principled uncertainty estimates, leading to poorly calibrated predictions and unreliable behavior under domain shift. We introduce Stiefel-Bayes Adapters (SBA), a Bayesian PEFT framework that places a Matrix Langevin prior over orthonormal adapter factors on the Stiefel manifold

\St

and performs approximate posterior inference via tangent space Laplace approximation with geodesic retraction. Unlike Gaussian priors in flat space projected onto orthogonality constraints, our prior on the manifold naturally encodes the inductive bias that adapter subspaces should be well conditioned and orthogonal, while the posterior provides calibrated predictive uncertainty without recalibration. We prove formally that the tangent space approximation strictly avoids the structural variance inflation inherent in projecting from ambient space, establishing a rigorous theoretical advantage for intrinsic manifold inference. Across GLUE and SuperGLUE benchmarks on RoBERTa-large, LLaMA-2-7B, LLaMA-2-13B, Mistral-7B, and Qwen2.5-7B, domain shift evaluations, selective prediction protocols, and an abstractive summarization task, SBA achieves task performance comparable to LoRA and DoRA while reducing Expected Calibration Error by 18 to 34% over deterministic baselines, improving selective prediction AUROC by 12 to 25% under domain shift, and outperforming deep ensembles of five LoRA models on OOD detection at a fraction of the parameter cost. Our results demonstrate that where you place uncertainty, on the right geometric structure, matters more than simply adding any Bayesian treatment to adapters.

Ibne Farabi Shihab, Sanjeda Akter, Anuj Sharma

Department of Computer Science, Iowa State University · Department of Civil, Construction and Environmental Engineering, Iowa State University

Bayesian LoRA Parameter-Efficient Fine-Tuning Language Model Calibration Confidence Estimation in Language Models Bayesian Inference

Feb 18, 2026

Who can we trust? LLM-as-a-jury for Comparative Assessment

Large language models (LLMs) are increasingly applied as automatic evaluators for natural language generation assessment often using pairwise comparative judgements. Existing approaches typically rely on single judges or aggregate multiple judges assuming equal reliability. In practice, LLM judges vary substantially in performance across tasks and evaluation aspects, and their judgment probabilities may be biased and inconsistent. Furthermore, human-labelled supervision for judge calibration may be unavailable. We first empirically demonstrate that inconsistencies in LLM comparison probabilities exist and show that it limits the effectiveness of direct probability-based ranking. To address this, we study the LLM-asa-jury setting and propose BT-sigma, a judge-aware extension of the Bradley-Terry model that introduces a discriminator parameter for each judge to jointly infer item rankings and judge reliability from pairwise comparisons alone. Experiments on benchmark NLG evaluation datasets show that BT-sigma consistently outperforms averaging-based aggregation methods, and that the learned discriminators strongly correlate with independent measures of the cycle consistency of LLM judgments. Further analysis reveals that BT-sigma can be interpreted as an unsupervised calibration mechanism that improves aggregation by modelling judge reliability.

Mengjie Qian, Guangzhi Sun, Mark J. F. Gales +1

Department of Engineering, University of Cambridge, UK.

LLM-as-a-Judge Language Model Generation Evaluation Bradley–Terry Model Language Model Calibration

Feb 18, 2026

Know When You're Wrong: Aligning Confidence with Correctness for LLM Error Detection

As large language models (LLMs) are increasingly deployed in critical decision-making systems, the lack of reliable methods to measure their uncertainty presents a fundamental trustworthiness risk. We introduce a normalized confidence score based on output anchor token probabilities: classification labels for structured tasks and self-evaluation responses (Yes/No) for open-ended generation. This enables direct detection of errors and hallucinations with minimal overhead and without external validation. We make three key contributions. First, we propose a normalized confidence score and self-evaluation framework that exposes reliable confidence estimates for error detection across seven diverse benchmark tasks and five LLMs of varying architectures and sizes. Second, our theoretical analysis reveals that supervised fine-tuning (SFT) yields well-calibrated confidence through maximum-likelihood estimation, whereas reinforcement learning methods (PPO, GRPO) and DPO induce overconfidence via reward exploitation. Third, we propose post-RL SFT with self-distillation to restore confidence reliability in RL-trained models. Empirical results demonstrated that SFT improved average confidence-correctness AUROC from 0.806 to 0.879 and reduced calibration error from 0.163 to 0.034 on Qwen3-4B, while GRPO and DPO degraded confidence reliability. We demonstrated practical value through adaptive retrieval-augmented generation (RAG) that selectively retrieves context when the model lacks confidence, using only 58% of retrieval operations to recover 95% of the maximum achievable accuracy gain on TriviaQA

Xie Xiaohu, Liu Xiaohu, Yao Benjamin

Alexa AI, Amazon, Seattle, WA, USA

Language Model Error Detection Confidence Estimation in Language Models LLM Reliability Language Model Calibration

Feb 16, 2026

The Well-Tempered Classifier: Some Elementary Properties of Temperature Scaling

Temperature scaling is a simple method that allows to control the uncertainty of probabilistic models. It is mostly used in two contexts: improving the calibration of classifiers and tuning the stochasticity of large language models (LLMs). In both cases, temperature scaling is the most popular method for the job. Despite its popularity, a rigorous theoretical analysis of the properties of temperature scaling has remained elusive. We investigate here some of these properties. For classification, we show that increasing the temperature increases the uncertainty in the model in a very general sense (and in particular increases its entropy). However, for LLMs, we challenge the common claim that increasing temperature increases diversity. Furthermore, we introduce two new characterisations of temperature scaling. The first one is geometric: the tempered model is shown to be the information projection of the original model onto the set of models with a given entropy. The second characterisation clarifies the role of temperature scaling as a submodel of more general linear scalers such as matrix scaling and Dirichlet calibration: we show that temperature scaling is the only linear scaler that does not change the hard predictions of the model.

Pierre-Alexandre Mattei, Bruno Loureiro

Université Côte d’Azur, Inria, CNRS, LJAD, France · Département d’Informatique, École Normale Supérieure - PSL, CNRS, France

Model Calibration LLM Uncertainty Estimation Language Model Calibration

Feb 14, 2026

On Calibration of Large Language Models: From Response To Capability

Accurate confidence estimation is critical for reliable use of large language models (LLMs). Prior work on LLM calibration largely focuses on response-level confidence, which estimates the correctness of a single generated output. However, this formulation is misaligned with many practical settings where the central question is how likely a model is to solve a query overall. We show that this mismatch results from the stochastic nature of modern LLM decoding, under which single-response correctness fails to reflect underlying model capability. To address this issue, we introduce capability calibration, a new evaluation framework for measuring how well query-level confidence aligns with a model's expected accuracy on individual queries. We formally distinguish capability calibration (CC) from response calibration (RC) and show that the two differ both theoretically and empirically. We further show that CC is better suited than RC to applications like pass@k prediction and inference budget allocation. Finally, we evaluate common confidence estimation methods to understand the practical feasibility of CC.

Sin-Han Yang, Cheng-Kuang Wu, Chieh-Yen Lin +3

Appier AI Research · National Taiwan University

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

Feb 12, 2026

When Agents Disagree With Themselves: Behavioral Consistency as an Uncertainty Signal for LLM Agents

Running the same LLM agent on identical inputs yields 2.3-4.2 distinct action sequences per 10 runs; this behavioral variance constitutes a training-free, black-box uncertainty signal that instantiates selective classification and distribution-free calibration for agentic systems. Across 8,000 runs of four models on 200 HotpotQA questions, consistent tasks (at most 2 unique paths) achieve 82-87% accuracy while inconsistent tasks (4 or more paths) achieve 41-65%, a gap that survives controls for task difficulty. Divergence concentrates at step 2 (50.5% of Llama tasks), and consistency metrics detect failures with AUROC 0.62-0.78. Exploiting this signal, selective prediction (answering only when k=3 runs agree) achieves 87-88% accuracy at 54-62% coverage, a 6-14pp gain over single-run baselines, and matches a split-conformal baseline without a held-out calibration set. A cross-benchmark validation on SWE-bench (50 tasks, 1,000 runs) preserves the consistency hierarchy while revealing an ~8x spread in mean trajectory length across models, and bootstrap analysis shows single-run evaluations misrank models 29.3% of the time.

Aman Mehta

Snowflake AI Research

AI Agent Reliability Selective Prediction LLM Agent Evaluation Reasoning Consistency in Language Models Language Model Calibration LLM Reliability+3

Feb 9, 2026

Scalable Delphi: Large Language Models for Structured Risk Estimation

Quantitative risk assessment relies on structured expert elicitation to estimate unobservable properties. The Delphi method produces calibrated, auditable estimates but requires months of coordination and specialist time, placing rigorous risk assessment out of reach for most applications. We propose Scalable Delphi, adapting the classical protocol for LLMs with diverse expert personas, iterative refinement, and rationale sharing. Beyond lowering cost, this makes the assessment analyzable and dynamic. Rationales and revision histories record what each estimate rests on, information can be ablated to test which evidence matters, and the elicitation can be rerun with new evidence, changed assumptions, or adverse scenarios. Because target quantities are unobservable by construction, we design an evaluation framework based on necessary conditions any reliable estimator must satisfy: accuracy and calibration on verifiable proxies, and sensitivity to evidence. Agreement with expert panels and reasoning quality serve as corroboration. Across two domains (AI-augmented cybersecurity risk, ice-sheet contribution to sea-level rise), three benchmarks, and three reproduced expert studies, the estimates pass these tests: they improve systematically as evidence is added, agree with expert panels on most quantities, and correlate strongly with ground truth (Pearson r=0.91-0.98).

Tobias Lorenz, Mario Fritz

CISPA Helmholtz Center for Information Security, Germany

Language Model Calibration

Jan 28, 2026

Bayesian-LoRA: Probabilistic Low-Rank Adaptation of Large Language Models

Large Language Models usually put more emphasis on accuracy and therefore, will guess even when not certain about the prediction, which is especially severe when fine-tuned on small datasets due to the inherent tendency toward miscalibration. In this work, we introduce Bayesian-LoRA, which reformulates the deterministic LoRA update as a probabilistic low-rank representation inspired by Sparse Gaussian Processes. We identify a structural isomorphism between LoRA's factorization and Kronecker-factored SGP posteriors, and show that LoRA emerges as a limiting case when posterior uncertainty collapses. We conduct extensive experiments on various LLM architectures across commonsense reasoning benchmarks. With only approximately 0.42M additional parameters and

{\approx}1.2{\times}

training cost relative to standard LoRA, Bayesian-LoRA significantly improves calibration across models up to 30B, achieving up to 84% ECE reduction and 76% NLL reduction while maintaining competitive accuracy for both in-distribution and out-of-distribution (OoD) evaluations.

Moule Lin, Shuhao Guan, Andrea Patane +2

School of Computer Science and Statistics, Trinity College Dublin, Dublin, Ireland and Lero the Research Ireland Centre for Software, Ireland · School of Computer Science, University College Dublin, Dublin, Ireland

Bayesian Neural Networks Confidence Estimation in Language Models LLM Fine-Tuning Low-Rank Adaptation Language Model Calibration LLM Reliability+2

Jan 26, 2026

Self-Aware Knowledge Probing: Evaluating Language Models' Relational Knowledge through Confidence Calibration

Knowledge probing quantifies how much relational knowledge a language model (LM) has acquired during pre-training. Existing knowledge probes evaluate model capabilities through metrics like prediction accuracy and precision. Such evaluations fail to account for the model's reliability, reflected in the calibration of its confidence scores. In this paper, we establish an empirical framework to evaluate the calibration of relational knowledge in a closed answer-set setting. We cover three modalities of model confidence: (1) intrinsic confidence, (2) paraphrase consistency and (3) linguistic confidence. Our extensive analysis of 21 causal and 8 masked language models reveals that most models, but especially those pre-trained with the masking objective, are overconfident. The best-calibrated scores come from confidence estimates that account for inconsistencies due to statement rephrasing. Moreover, calibration improves when increasing the number of answer options.

Christopher Kissling, Elena Merdjanovska, Alan Akbik

Humboldt-Universität zu Berlin · Science of Intelligence

Language Model Probing Language Model Calibration Factual Knowledge in Language Models Confidence Estimation in Language Models

Jan 16, 2026

NOVA: NOise-aware Verbal Confidence CAlibration for Robust Large Language Models in RAG Systems

Accurately assessing model confidence is essential for deploying large language models (LLMs) in mission-critical factual domains. While retrieval-augmented generation (RAG) is widely adopted to improve grounding, confidence calibration in RAG settings remains poorly understood. We conduct a systematic study across four benchmarks, revealing that LLMs exhibit poor calibration performance especially when noisy contexts are retrieved. Specifically, contradictory or irrelevant evidence tends to exacerbate the model's overconfidence issue. To address this, we propose NOVA Rules (NOise-Aware Verbal Confidence CAlibration Rules) to provide a principled foundation for resolving overconfidence under noise. We further design NOVA, a noise-aware calibration framework that synthesizes supervision from ~2K HotpotQA examples guided by these rules. By performing supervised fine-tuning (SFT) with this data, NOVA equips models with intrinsic noise awareness without relying on stronger teacher models. Empirical results show that NOVA yields substantial gains, improving ECE scores by 10.9% in-domain and 8.0% out-of-domain. By bridging the gap between retrieval noise and verbal calibration, NOVA paves the way for both accurate and epistemically reliable LLMs.

Jiayu Liu, Rui Wang, Qing Zong +9

HKUST · UIUC · Northwestern University

Retrieval-Augmented Generation Confidence Estimation in Language Models Language Model Calibration LLM Reliability Language Model Robustness

Jan 12, 2026

Calibration Is Not Enough: Evaluating Confidence Estimation Under Language Variations

Confidence estimation (CE) indicates how reliable the answers of large language models are and impacts user trust and decision-making. Existing evaluations mainly concern the alignment between confidence and correctness, but ignore the variability of language: confidence estimates should remain consistent under semantically equivalent prompts or answer variations, while changing when answer meaning differs, as this may indicate a change in correctness. Therefore, we introduce a novel evaluation framework based on three complementary properties: robustness to prompt perturbations, stability across semantically equivalent answers, and sensitivity to semantically different answers. We show that these metrics are largely independent from existing CE metrics, and that common CE methods often fail on them: while most methods achieve high robustness and stability, they struggle to distinguish semantically different answers, potentially because they do not effectively leverage generation-side information. Overall, our framework exposes overlooked limitations of current CE evaluations and provides guidance for selecting confidence estimators for real-world applications.

Yuxi Xia, Dennis Ulmer, Terra Blevins +3

Faculty of Computer Science, UniVie Doctoral School Computer Science · Faculty of Philological and Cultural Studies, University of Vienna, Austria · ILLC, University of Amsterdam, Netherlands +2

LLM Uncertainty Estimation Confidence Estimation in Language Models Language Model Self-Assessment LLM Evaluation Language Model Calibration LLM Reliability+1

Oct 3, 2025

Beyond the Final Layer: Intermediate Representations for Better Multilingual Calibration in Large Language Models

Confidence calibration, the alignment of a model's predicted confidence with its actual accuracy, is crucial for the reliable deployment of Large Language Models (LLMs). However, this critical property remains largely under-explored in multilingual contexts. In this work, we conduct the first large-scale, systematic studies of multilingual calibration across six model families and over 100 languages, revealing that non-English languages suffer from systematically worse calibration. To diagnose this, we investigate the model's internal representations and find that the final layer, biased by English-centric training, provides a poor signal for multilingual confidence. In contrast, our layer-wise analysis uncovers a key insight that late-intermediate layers consistently offer a more reliable and better-calibrated signal. Building on this, we introduce a suite of training-free methods, including Language-Aware Confidence Ensemble (LACE), which adaptively selects an optimal ensemble of layers for each specific language. Our study highlights the hidden costs of English-centric alignment and offer a new path toward building more globally equitable and trustworthy LLMs by looking beyond the final layer.

Ej Zhou, Caiqi Zhang, Tiancheng Hu +4

Language Technology Lab, University of Cambridge

Multilingual Language Models Multilingual Language Model Evaluation Confidence Estimation in Language Models Language Model Calibration

Jul 29, 2025

Post-Training Large Language Models via Reinforcement Learning from Self-Feedback

Large Language Models (LLMs) often produce plausible but poorly-calibrated answers, limiting their reliability on reasoning-intensive tasks. Recent research suggests that Chain-of-Thought (CoT) reasoning paths are inherent in pre-trained LLMs and can be elicited by simply altering the decoding process, where the presence of a CoT path correlates with higher answer confidence. Building on these insights, we present Reinforcement Learning from Self-Feedback (RLSF), a post-training stage that utilises the model's intrinsic confidence as a self-generated reward. By generating multiple CoT decoding beams from a frozen LLM, we compute the confidence of each final answer span and rank the resulting traces accordingly to create synthetic preferences. These preferences are subsequently utilised to fine-tune the policy through standard preference optimisation, requiring no human labels, gold answers, or externally curated rewards. RLSF simultaneously (i) refines the model's probability estimates--restoring well-behaved calibration--and (ii) strengthens step-by-step reasoning, yielding improved performance on arithmetic reasoning and multiple-choice question answering. By converting a model's own uncertainty into structured self-feedback, RLSF affirms reinforcement learning on intrinsic model behaviour as a principled and data-efficient component of the LLM post-training pipeline. Our results demonstrate that leveraging these inherent reasoning capabilities provides a robust path for enhancing model reliability without manual prompt engineering or external supervision.

Carel van Niekerk, Renato Vukovic, Benjamin Ruppik +3

Heinrich Heine University Düsseldorf, Germany

RL for Language Models RL for Language Model Reasoning Language Model Calibration LLM Reliability RL Post-Training