Language Model Calibration

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43 papers in the last four weeks, up 330% on the four weeks before. 0.4% of all new papers.

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Aug 9, 2026cs.CL

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

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

Saurabh Yadav, Badri Narayana Patro, Vijay Srinivas Agneeswaran

Microsoft India

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

Aug 8, 2026cs.LG

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

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

Avery Ma, Lorne Schell, Vin Bhaskara +1

RBC Borealis

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

Aug 7, 2026cs.IR

Do LLM Recommenders Know When They're Hallucinating? Auditing Confidence Calibration in Catalog Faithfulness

LLM recommenders for top-K item suggestion regularly emit titles outside the target catalog. Prior audits report a binary out-of-domain rate; none ask whether the model knew. We jointly audit hallucination rate (OOD@10) and verbalized-confidence calibration (ECE, Brier, reliability) for four zero-shot LLM recommenders from four independent vendors (Mistral Large, Llama-3.3-70B, GPT-OSS-120B, Claude Sonnet 4.6), not grounded or fine-tuned systems, across three catalogs (MovieLens-25M, Amazon Reviews 2023 Toys, Yelp Open Dataset), stratified by item popularity. Measuring catalog membership is itself the hard part: on identical outputs the reported rate moves by an order of magnitude with the string matcher used, and F1 cannot separate the candidates. We validate the instrument against 201 human judgments and select on net bias, where the adopted one is off by -0.040 against +0.144 for the common fuzzy rule. Hallucination is then strongly catalog-dependent (0.6-2.7% on MovieLens, 11.6-38.7% on Yelp, 49.3-61.0% on Amazon Toys). Each model holds a near-constant confidence level barely responsive to the catalog, while the catalog-hit rate swings 60 points, so the sign of the error is set by where a model's constant lands against a catalog's accuracy: 7 of the twelve cells are under-confident and 5 over-confident, all four under-confident on MovieLens, all four over-confident on Amazon Toys. We read this as an elicitation mismatch: "Just Ask" elicits a generic quality rating, not a catalog-membership probability. A conformal abstention threshold over verbalized confidence changes hallucination by at most 1.65 pp across four alpha levels, because the channel cannot separate correct items from hallucinations. We recommend that audits report calibration alongside OOD, validate the matcher producing the OOD number, and use catalog-anchored elicitation.

Srijith Ravikumar

Amazon.com LLC Seattle, Washington, USA

LLM Auditing Language Model Calibration LLM Hallucination Detection Recommender Systems Large Language Model-Based Recommendation

Aug 7, 2026cs.LG

Beyond Post-Hoc Temperature Scaling: Bilevel Optimization for LLM Calibration

Preference alignment often makes large language models (LLMs) overconfident and poorly calibrated. Traditional post-hoc temperature scaling is inherently domain-dependent: a temperature fitted on one domain does not generalize across domains. This motivates us to modify model parameters during training to improve calibration. We propose maximizing the entropy of predictive distributions as the calibration objective, which directly targets overconfidence by discouraging overly concentrated predictions. Inspired by temperature scaling, we realize this through a bilevel optimization formulation, where the lower level trains the model under a parametric loss and the upper level selects loss hyperparameters to maximize entropy. To make the framework practical at LLM scale, we adopt an efficient first-order approximation that avoids explicit second-order computation. Across both multiple-choice and open-ended generative question answering, experiments demonstrate that our method yields well-calibrated LLMs with particular advantages in out-of-domain generalization.

Ruochen Jin, Zhanliang Wang, Zongyu Dai +2

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

LLM Fine-Tuning Language Model Calibration Bilevel Optimization

Aug 6, 2026cs.CL

Mitigating Scoring Bias in LLM-as-a-Judge via Random Number Generation

Large Language Models (LLMs) are often used as evaluators of text quality, known as LLM-as-a-Judge, which can outperform conventional automatic evaluation metrics that rely on reference texts. However, LLM evaluators tend to generate particular scores regardless of the context of the evaluated text, which is known as scoring bias. This study proposes a novel method to mitigate this scoring bias. An LLM is instructed to randomly generate number tokens, and the latent numerical bias of the LLM is identified by measuring the deviation of the observed distribution of numbers from the uniform distribution. A definition of a downstream task, for which an LLM evaluator is used, is added to the prompts for random number generation to measure task-specific latent number bias. In the evaluation by an LLM, the token generation probabilities for a given input are rectified considering the LLM's latent number bias. Results of the experiment on four different tasks, evaluation of LLM alignment, evaluation of summarization, Semantic Textual Similarity, and Semantic Textual Relatedness, demonstrate that our proposed method outperforms the baselines, including an LLM without debiasing and previous calibration methods. In addition, it is confirmed that scoring bias varies across LLMs, tasks, and score ranges, indicating the importance of measuring latent number bias as the case may be.

Yuma Asato, Kiyoaki Shirai, Natthawut Kertkeidkachorn

Japan Advanced Institute of Science and Technology

LLM Evaluation LLM-as-a-Judge Language Model Calibration Bias in LLM-as-a-Judge

Aug 5, 2026cs.CL

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

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

Jianru Shen

University of Montana, Missoula, MT 59812, USA

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

Aug 5, 2026cs.CL

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

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

Elena Merdjanovska, Omar Zaidan, Andreas Rücklé

Humboldt-Universität zu Berlin Science of Intelligence · Amazon

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

Aug 4, 2026cs.CL

SocietyBench: Forecasting Counterfactual Social-World Evolution

Large language models (LLMs), and the agents built on top of them, are now benchmarked heavily on whether they can finish a task -- fix a bug, drive a browser, operate a GUI. A complementary social ability, namely how well a model understands and forecasts the way real social events unfold, has barely been measured. We introduce SocietyBench, an end-to-end benchmark that takes a one-line event topic, collects Web news and social-media posts across five platforms, distills them into a date-indexed timeline that keeps factual events and a public-opinion layer separate, and then turns every cutoff date on that timeline into an audited bank of forecasting questions. Questions are scored on two orthogonal 100-point axes: probability calibration and temporal accuracy. Before any model sees a timeline, a three-phase procedure replaces every named entity and shifts every date by a per-event constant, turning a real arc into a counterfactual social world -- structurally identical to what happened, but stripped of the surface labels a model could match against pre-training memory. On five heterogeneous events and 125 prediction points in Chinese and English editions, the strongest of six frontier LLMs reaches only 75.0 out of 100, against a trivial anchor of 50. The two axes come apart: a model can be calibration-strong but time-weak, or the reverse. Three agent frameworks built on a shared base model fail to improve on that base, and two model-free heuristics trail every LLM. Per-event gaps reach 21.4 points on a single axis, which is our main argument for evaluating on several events rather than one. All anonymized timelines, question banks, ground truth, and scoring code are released.

Zhenran Wang, Zhonghan Bian, Jinsong Li +1

Counterfactual Evaluation Forecasting Benchmarks Probabilistic Forecasting Language Model Calibration

Aug 4, 2026cs.LG

Quantization Effects on Biomedical LLM Reliability

When decoder language models are used as classifiers, predicted class probabilities depend on implementation choices, including the prompt template, verbalizer (label-to-token mapping), and scoring rule, that are rarely treated as experimental variables. We present a controlled evaluation of three Mistral-7B variants (Base, BioMistral, and Instruct) on PubMed RCT sentence classification (n=2000) under FP16, INT8, and INT4 precision using four answer-text prompt templates. Our primary finding is that the probability extraction protocol dominates apparent calibration. Switching from summed to mean token log-likelihood scoring reverses the calibration ranking between models: BioMistral average expected calibration error increases from 0.097 to 0.289, whereas Instruct decreases from 0.237 to 0.096, while accuracy changes by less than 1 percentage point for the specialized models but 4-6 percentage points for the base model. Prompt template choice produces accuracy differences of 7-24 percentage points, comparable to or larger than model-level effects. On one template, BioMistral outperforms Instruct although the overall mean favors Instruct by only 1.3 percentage points. For BioMistral and Instruct, INT8 quantization changes accuracy and F1 by only 1-2 percentage points relative to FP16, whereas the base model shows larger INT8 effects on some templates (up to +4.2 percentage points). INT4 produces heterogeneous but non-catastrophic effects. Temperature scaling reduces expected calibration error under summed scoring for both models but only for that scoring rule. A fine-tuned PubMedBERT reference achieves 82.7% accuracy but uses about 176000 labeled training examples, precluding direct comparison. These results demonstrate that prompt template design and scoring normalization are first-order experimental decisions when evaluating decoder language model calibration.

Anton Rasmussen, Hong Qin

Old Dominion University Norfolk, VA 23529, USA

LLM Quantization Text Classification Language Model Calibration Medical LLMs

Aug 2, 2026cs.LG

Conformalized Large Language Models under Configuration Shift

Conformal prediction (CP) is a distribution-free framework for uncertainty quantification that has recently been adapted to large language models (LLMs), providing prediction sets with finite-sample coverage guarantees under exchangeability. Yet for LLMs, nonconformity scores are often induced by an inference pipeline, not just a fixed model, making them depend not only on the data distribution but also on configurable factors such as the prompt template, decoding parameters, and deployment setting. Since such configurations are routinely modified in practice but rarely treated as a source of shift, their impact on CP validity remains poorly understood. We call this \emph{configuration shift} and study it systematically along three axes: prompt template, decoding temperature, and weight quantization. In a broad empirical study spanning

9

LLMs,

4

datasets, and

4

nonconformity scores, we find that configuration shift consistently erodes CP validity, often driving empirical coverage below the target. By contrast, efficiency is largely preserved: valid prediction sets remain close in size to the i.i.d. baseline. We derive coverage lower bounds that attribute this loss to a discrepancy between calibration and test score distributions, and use their finite-sample plug-in versions as empirical diagnostics of shift severity. We further show that these findings lead to practical mitigations: bound-inspired recalibration is effective with limited test examples, while fragility-aware calibration ensembling recovers much of the lost coverage without test data.

Yuqicheng Zhu, Jialin Yu, Lin Li +7

University of Stuttgart · Robert Bosch GmbH · University of Oxford +4

Conformal Prediction Language Model Calibration LLM Uncertainty Estimation

Jul 31, 2026cs.LG

Abstention as an Action Can Kill Both the Reward Gradient and the KL Anchor: Collapse Law and Repair for Error-Penalized Reinforcement Learning

Error-penalized scoring rules (

+1

for a correct answer,

-λ

for a wrong one,

0

for abstaining) are increasingly prescribed against hallucination: a rational agent facing such a rule answers exactly when its correctness probability exceeds Chow's threshold

t^\ast=λ/(1+λ)

. We prove that a KL-anchored gradient learner can do the opposite. When abstention is a discrete action, the reward gradient and the anchor's restoring force are throttled by the same gate-saturation factor and die together: under explicit conditions (among them, blanket answering loses score in expectation and prompts share a bounded readout) the model drifts toward refusing everything, its mean training reward rising to zero like

1/t

in training time

t

, so the curve reads as improvement while coverage collapses. The advantage estimator compounds the failure: in its sparse-answer regime, group normalization silently replaces every designed penalty with an effective penalty of one, moving the learned threshold from

t^\ast

to

1/2

. The repair is structural: train a mandatory confidence report with a strictly proper score plus a correctness reward, and abstain only at deployment by thresholding the report. The always-emitted report has no gate to saturate, so no shared factor can kill its reward gradient and its anchor together, and its calibrated optimum is attracting. Simulations confirm every prediction, and experiments on language models at two scales confirm the mechanism live: the rule silences questions the models demonstrably still solve within ten optimizer steps, an ablation isolates the cause, and report-level training raises coverage, accuracy, and calibration together.

Xujun Che, Yuchen Yuan, Weida Zhao +1

Department of Cybersecurity, University of North Carolina at Charlotte, Charlotte, NC, USA · Department of Information Sciences and Technology, George Mason University, Fairfax, VA, USA · Department of Computer Science and Software Engineering, Auburn University, Auburn, AL, USA +1

Reinforcement Learning KL-Regularized RL Language Model Calibration RL Post-Training LLM Abstention

Jul 31, 2026cs.CL

Knowing When to Quit: Diagnosing and Training LLMs to Abort Futile Reasoning

Large language models generate computationally expensive yet semantically void reasoning on beyond-capability tasks, creating risks where plausible-sounding but incorrect derivations mislead users. We characterize this \textit{futile reasoning} phenomenon through systematic analysis, revealing universal capability overreach and systematic miscalibration between capability and behavior. The dominant failure mode is specious reasoning, which outputs look superficially valid but contain subtle errors, escalating with task difficulty. To address this, we introduce \textbf{CaRL} (\textbf{Ca}pability-\textbf{a}ligned \textbf{R}einforcement \textbf{L}earning), which aligns model behavior with capability boundaries through reward shaping that incentivizes refusal over futile reasoning and hindsight refusal augmentation that converts failures into refusal supervision. Experiments demonstrate a substantial reduction in futile reasoning while preserving performance across task difficulties, effectively achieving capability-aligned behavior without sacrificing utility. \footnote{https://github.com/icip-cas/Knowing-When-to-Quit}

Xinyan Guan, Jiali Zeng, Chunlei Xin +5

1Chinese Information Processing Laboratory, Institute of Software, Chinese Academy of Sciences · University of Chinese Academy of Sciences · 3Weixin AI, Tencent Inc, China

Overthinking in Language Models RL for Language Model Reasoning Language Model Calibration Refusal Behavior in Language Models

Jul 30, 2026cs.LG

Cybersecurity Detection Classification with Reasoning-enabled Language Models

A major issue in Security Operations Centers (SOCs) is alert fatigue, as the number of detections reported is more than staff can triage in a given day. Prior work prompts or fine-tunes large language models (LLMs) to emit a triage label directly, but does not train them to reason about whether a detection is a genuine threat. We train a chain-of-thought (CoT) reasoning-enabled triage classifier on real, human-labeled Windows endpoint detections by combining automated prompt optimization, self-training, and reinforcement learning with verifiable rewards. We find that CoT reasoning also degrades the label-token probabilities that automated triage relies on, so we separately train a calibrator that reads the full reasoning trace and estimates the probability that the verdict is correct. Our system reaches 82.6% test accuracy and, at the high-confidence operating point that governs automated triage, improves benign recall by 43.0% and malicious recall by 18.3% over a direct-label LLM classifier. We further show that the trained calibrator is necessary - an untrained confidence judge collapses high-confidence recall to zero - and that a finetuned 30B model significantly outperforms frontier general-purpose models, motivating targeted training over scale.

Amol Khanna, Manu Nandan, Cristian Viorel Popa +10

CrowdStrike

CoT Reasoning Language Model Calibration LLMs for Cybersecurity

Jul 29, 2026cs.CL

Selecting Open-Weight Language Models for Zero-Shot Intent Classification: A Systematic Evaluation of 41 Models

Intent classification is a core component of task-oriented dialogue systems, yet practitioners have limited systematic guidance for selecting deployable open-weight language models under compute, latency, and robustness constraints. We present a systematic zero-shot evaluation of 41 open-weight language models spanning 15 families and the 135M--9B parameter range across eight English single-label intent-classification datasets. A ninth dataset, ATIS, uses five labeled demonstrations and is reported as an auxiliary five-shot result. The evaluation includes standard benchmarks, a large-scale voice-assistant corpus, and production-derived e-commerce datasets. Beyond exact-match accuracy, we analyze confidence calibration, robustness to realistic input perturbations, statistical reliability of model rankings, deployment efficiency, and benchmark saturation. Our results show that instruction-tuned 3B models can outperform several evaluated 7B base models, that differences among leading models on MASSIVE are statistically indistinguishable under pairwise McNemar tests, and that widely used benchmarks such as SNIPS have become saturated and no longer meaningfully discriminate among current open-weight models. Instruction tuning's effect on confidence calibration is inconsistent rather than uniformly harmful. These findings provide practical guidance for selecting and evaluating open-weight language models for intent classification.

Parishruthi Ganesh, Gerry Dozier, Cheryl Seals

Department of Computer Science and Software Engineering Auburn University Auburn, Alabama, USA

LLM Evaluation Zero-Shot Text Classification Intent Classification Open-Weight Language Models Language Model Calibration Language Model Robustness

Jul 29, 2026cs.AI

Beyond the Bidirectional Promise: Re-evaluating the Robustness of Diffusion Language Models

Diffusion Language Models (DLMs) offer a compelling alternative to autoregressive (AR) generation by enabling bidirectional context and iterative refinement. However, their reliability under natural input noise and adversarial attacks remains under-explored. To address this, we systematically evaluate DLM robustness and calibration against AR baselines, using two parameter-matched pairs (LLaDA-8B vs. LLaMA-3-8B and Dream-7B vs. Qwen2.5-7B) across 32 natural perturbation conditions, adversarial gradient probes, and mechanistic hidden-state analyses. This paired design effectively isolates architecture-intrinsic properties from weight-dependent behaviors. We find a nuanced robustness profile: while highly stochastic DLM loss landscapes naturally resist gradient-based adversarial suffixes, they provide no guaranteed defense against natural noise, proving that everyday robustness is weight-dependent rather than inherently architectural. Furthermore, DLMs exhibit systematic overconfidence, presenting a practical deployment hazard. Most crucially, mechanistic probing reveals that all models perfectly encode input corruption, isolating behavioral fragility entirely to a decoder routing failure. Consistent with this diagnosis, we show that surface-level prompt patching fails to improve over noisy baselines. Ultimately, DLM robustness cannot be patched on; it must be fundamentally integrated into the iterative decoding loop.

Saurabh Yadav, Badri Narayana Patro, Vijay Srinivas Agneeswaran

Microsoft

Language Model Calibration Diffusion Language Models Language Model Robustness

Jul 28, 2026stat.AP

Laplace-PSN-IRT: Uncertainty Quantification for Neural Item Response Theory Models of LLM Benchmarks

Item Response Theory (IRT) has recently been proposed as a framework for evaluating large language model (LLM) benchmarks by separating a model's latent ability from the properties of individual benchmark items. Existing neural IRT approaches, including PSN-IRT, estimate these quantities using point estimates, limiting uncertainty quantification and downstream statistical inference. We introduce Laplace-PSN-IRT, a post-hoc last-layer Laplace approximation that augments a trained PSN-IRT model with approximate Bayesian posterior inference, recovering calibrated uncertainty over model ability and item difficulty without retraining. The resulting posterior enables credible intervals, probabilistic comparisons between models, and propagation of parameter uncertainty into Fisher-information-based item selection. We show that most pairwise comparisons among 12 models on a standard LLM benchmark leaderboard are not statistically distinguishable despite differing point-estimate ranks. We further show that point-estimate Fisher information can become nearly zero for many benchmark items because it is evaluated at a single reference ability, whereas posterior-expected Fisher information remains substantially more stable across the ability range. Finally, posterior-expected Fisher information more accurately recovers full-benchmark ability rankings from small benchmark subsets in most experimental settings while matching point-estimate performance for the smallest subsets. We validate the calibration of the approximate posterior using held-out predictive coverage and find that modeling item difficulty as random while treating item discrimination as fixed produces well-calibrated uncertainty in this architecture.

Juan Francisco, Mandujano Reyes

Independent Research

LLM Evaluation Language Model Calibration LLM Uncertainty Estimation Item Response Theory

Jul 27, 2026cs.AI

Hierarchical Group-Conditional Conformal Risk Control for Selective Prediction in Language Models

Large language models serve heterogeneous populations structured by domain, topic difficulty, and linguistic style. Conformal risk control (CRC) gives rigorous marginal risk guarantees for selective prediction with abstention, but marginal guarantees do not imply per-group ones: a model can meet the population budget while systematically over-exposing subgroups to errors. Under mild shift in group composition, standard CRC violates the budget in up to 47% of trials. We propose HG-CRC (Hierarchical Group-Conditional CRC), a post-hoc calibration framework enforcing simultaneous risk guarantees across all nodes of a user-defined group hierarchy. It applies a Bonferroni correction over nodes and a leaf-first policy that uses the most specific applicable threshold, falling back to coarser nodes when a finer one is uncertified or rejects the example. It needs only a held-out calibration set, with no retraining. We evaluate on three models (Qwen3-4B, Llama-3.1-8B-Instruct, Gemma-3-4B) and two benchmarks (ARC Challenge, MMLU-Pro) across eight configurations probing IID generalization, heterogeneity, mixture/domain/prompt/difficulty shift, label noise, and quantization. Main result: HG-CRC reaches an empirical 0% violation rate and WGER=0 on ARC Challenge for high-accuracy models (Qwen3-4B, Llama-3.1-8B). At 500 bootstrap trials these zeros are empirical upper bounds (true rate up to 0.6%), not certified. Results are benchmark-specific: on MMLU-Pro these models abstain entirely or (Llama) retain WGER=0.014. Gemma-3-4B, poorly calibrated here, degrades gracefully by abstaining. Participation cost vs. global CRC is 22 to 37 points. Ablations show hierarchical depth clears the budget: removing difficulty level returns violations to about 11%. Bonferroni is needed for the theoretical guarantee, though its empirical effect matters only with many nodes.

Murilo Salem, Luísa Böhm, Daniel Pontes +1

CDTec (Centro de Desenvolvimento Tecnológico) Universidade Federal de Pelotas Pelotas, RS, Brasil

Selective Prediction Group-Conditional Conformal Prediction Language Model Calibration Conformal Risk Control Language Model Robustness

Jul 24, 2026cs.NI

A Self-Calibrating Agentic AI Framework for Autonomous Edge Resource Allocation

Large Language Models (LLMs) are increasingly deployed as autonomous agents, transitioning from static conversational interfaces to dynamic systems capable of complex reasoning, tool execution, and decision-making. However, the operational reliability of these agentic AI systems is fundamentally challenged by the absence of reliable ground truth in open-ended environments and the risk of increasing operational drift over time. To address this challenge, we propose and experimentally evaluate an agentic AI framework, designed to enforce autonomous integrity within LLM-driven systems. We design a self-calibration mechanism that mitigates drift and dynamically approximates ground truth by incorporating an ARIMA forecaster, without requiring continuous human oversight. To demonstrate the effectiveness and reliability of our methodology, we apply it to the complex domain of profiling the resource usage of zero-knowledge workloads in edge computing networks. Experimental results show that the proposed self-calibrating agentic framework successfully profiles the zero-knowledge workloads, achieving a higher accuracy than baseline LLM agents by 91.7% for resource usage prediction and improving the prediction speed by 71.7% compared to pure profiling, establishing a robust foundation for deploying autonomous AI in decentralized infrastructures. Furthermore, the ground truth generation using the proposed ARIMA leaping algorithm is 52% faster than a standard ARIMA forecasting algorithm, while achieving the same accuracy.

Fin Gentzen, Marla Grunewald, Iulisloi Zacarias +2

Institut für Datentechnik und Kommunikationsnetze Technische Universität Braunschweig, Germany

Edge Computing Language Model Calibration LLM Agents LLM Agent Reliability

Jul 23, 2026cs.CL

Artificial Epanorthosis: Why large language models overuse a classical rhetorical figure, and how to mitigate it

A rhetorical figure that Cicero and Quintilian catalogued two thousand years ago reappears, systematically, in the text of large language models: epanorthosis, the self-correction of the specimen «This is not a course. It is a journey of transformation». This essay argues that the overuse is a trained disposition, driven mainly by a training distribution rich in promotional prose and by preference tuning (RLHF) that rewards confident, emphatic phrasing; the left-to-right nature of generation is an amplifier rather than the root cause. Building on evidence that models diverge from human rhetorical style, and on Fontanier's classification of epanorthosis as a figure of thought, it sets out a programme that scores the figure against genre-specific human baselines through an Epanorthosis Index (density relative to the human rate). A first measurement, on three sizes of one instruction-tuned model family, finds mis-calibration by register in both directions: the models overshoot in oratory (about twofold, near threefold in Italian, concentrated in the larger tiers) and undershoot in informal question-and-answer writing, while matching humans in argument, journalism, and encyclopedic prose. Three constructive contributions follow: a survey of mitigation techniques centred on lightweight LoRA adapters; a demonstration, in Italian, that a one-line instruction cuts the figure by half to nearly three-quarters and that a supervised-fine-tuning adapter removes it almost entirely, with a scaling coefficient that dials the reduction back onto the human rate; and the argument that the target is calibration to the human rate for each genre, not elimination. It closes on the stakes: the real risk is that we begin to write like the machines.

Federico Boggia

Language Model Calibration

Jul 20, 2026stat.ME

Calibrating Semantic Uncertainty from Observable Language-Model Probabilities

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

Matthew F. Dixon

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

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

Jul 17, 2026cs.LG

A Better Start for Language Models: Domain-Conditional Position Offsets

Autoregressive language models are least accurate at the beginning of a sequence, where little context forces reliance on a generic pretraining prior. We show that this cold-start penalty is domain dependent and reduce it with a domain-conditional position offset: a single learned vector added to the embedding activation at the first sequence positions while all model weights remain frozen. The offset trains in minutes on roughly one hundred documents, switches between domains without added sequence state, and has no measurable latency overhead. Across eight Mamba, GPT-NeoX, and Llama models spanning 410M to 8B parameters, it reduces held-out in-domain perplexity by up to 27%; the effect persists at 70B, and one position captures most of the benefit. A matched, converged direct logit-bias correction reaches at most only 7.9% and leaves later-token loss unchanged, showing that the offset propagates through model state rather than merely recalibrating the output prior. A tuned LoRA reaches lower perplexity but uses two to three orders of magnitude more parameters and an active low-rank weight path, while soft prompts add sequence positions. With wrong-domain controls, offsets improve retrieval reranking and domain classification when decisions depend on early in-domain tokens, For the few-shot reasoning whose signal occurs later, the results maintains unchanged. Position-aware prefill application also help generation tasks, whereas naive application at every cached decoding step causes repetition. The offset is therefore not the strongest adapter, but a lightweight, hot switchable tool for short in-domain scoring and calibration.

Ye Qiao

University of California, Irvine

Domain Adaptation Language Model Calibration Domain Adaptation for LLMs Parameter-Efficient Fine-Tuning

Jul 15, 2026cs.CL

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

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

Shuhao Li, Guodong Du, Anhao Zhao +3

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

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

Jul 15, 2026cs.LG

Temperature Scaling Is Not Enough: Calibration Gaps Under Human Label Distributions

Temperature scaling is the dominant post-hoc calibration method in modern deep learning. Its theoretical justification rests on an assumption that is rarely stated explicitly: that ground-truth labels are one-hot and deterministic. In practice, labels are frequently soft, crowd-sourced, or genuinely distributional, reflecting real disagreement among human annotators rather than annotation noise. We study whether temperature scaling retains its calibration properties when this assumption is violated, and whether any resulting degradation depends on model scale. Using CIFAR-10H and ChaosNLI, two publicly available datasets with human-annotated soft label distributions, we evaluate three model scales per modality under both hard one-hot and soft distributional label targets. Across all nine configurations we find a positive soft-label calibration gap: temperature scaling calibrated on hard labels consistently underperforms an oracle calibrated directly on soft labels, with Brier Score gaps ranging from 0.002 to 0.134. The gap grows monotonically with model scale in the vision domain and on the SNLI-derived split of ChaosNLI, and is substantially larger in the language domain (mean gap 0.079) than in vision (mean gap 0.003). A scale-ordering reversal on the MNLI-derived split remains after matched-domain training; we treat it as inconclusive for the scale hypothesis and attribute it primarily to near-chance accuracy on that split. As a second post-hoc baseline, multiclass isotonic regression yields the same qualitative conclusion: positive soft-label gaps in all nine configurations, and larger gaps in language than in vision. These findings suggest that calibration protocols built on majority-vote labels systematically misstate model reliability wherever label ambiguity is structural, with direct consequences for deployment in safety-critical settings.

Wisdom Dogah

Faculty of Computing and Mathematical Sciences, University of Mines and Technology (UMaT), Tarkwa, Ghana. · BlackMatrix AI Research, Accra, Ghana.

Post-Hoc Calibration Language Model Calibration Model Calibration

Jul 14, 2026cs.CL

LLM Judges Can Be Too Generous When There Is No Reference Answer

LLM judges are increasingly being used to evaluate open-ended model responses, often in no-reference settings where a ground-truth answer is unavailable. However, can they reliably assess in such evaluation setups? We explore this question in this paper through a two stage pipeline with a) calibration experiments that assess the judge model's knowledge of the task it is evaluating, and b) sensitivity experiments that assess how the judge model's performance is impacted by the presence and positioning of the reference answer in the prompt. Across experiments covering three languages, we show that the judge models we evaluated tend to over-credit incorrect answers in the absence of a reference answer, and adding reference answer information to the prompt flips the judge model's correct/incorrect decisions by as much as 85% in some experimental settings. Comparison with a subset of human annotations shows that these reference-driven changes generally align with human judgments. Our results emphasize the need for calibrating the LLM judges with a sample with reference-aware evaluation before using them in reference-free setups reliably, and our methodology provides a blueprint for researchers and practitioners in doing such calibration of LLM judges for other tasks.

Chalamalasetti Kranti, Sowmya Vajjala

Computational Linguistics, Department of Linguistics, University of Potsdam, Germany · National Research Council, Ottawa, Canada

LLM Evaluation LLM-as-a-Judge Language Model Calibration Reference-Free Evaluation Bias in LLM-as-a-Judge

Jul 14, 2026cs.CL

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

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

Mehak Dhaliwal, Rasta Tadayon, Andong Hua +2

University of California, Santa Barbara

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

Jul 13, 2026cs.SD

CHARM: Charge Calibration and Acoustic Rescue for LLM-based Multimodal Sarcasm Detection

Sarcasm detection, the identification of discrepancies between literal and intended meaning, is a fundamental task in affective computing. However, zero-shot instruction-tuned Large Language Models (LLMs) systematically over-predict the positive (sarcastic) class across the entire capability spectrum, while the prosodic cues humans rely on remain underexploited and transfer unevenly across languages. We introduce CHARM (Charge Calibration and Acoustic Rescue for Multimodal Sarcasm Detection), a training-free framework that couples two modules. Bidirectional Charge Calibration (BiCAL) steers the LLM toward opposing sarcastic and literal verdicts along a symmetric axis of charged prompts; the induced directional biases cancel by construction, and a simple aggregation recovers an unbiased pragmatic signal. Acoustic Late-Fusion Rescue (ALFR) then fuses the calibrated votes with prosodic descriptors and LLM-generated auditory-perception probes through a shallow classifier, actively down-weighting saturated text votes in favour of acoustic evidence. Without fine-tuning any backbone, BiCAL attains the highest reported zero-shot text-only Macro-F1 of 0.787 on MUStARD, while ALFR lifts weak backbones by up to +0.382 Macro-F1 on CMMA. A Stouffer meta-analysis confirms statistical significance on MUStARD and CMMA (Z = 13.89 and Z = 34.64, respectively; p < 10^-43). Our analysis further uncovers a cross-cultural prosodic decoupling: low-level acoustics fail to transfer across languages, whereas high-level perceptual abstractions remain robust. Together, these components yield an explainable, cross-lingual multimodal detector.

Qiyang Sun, Yi Chang, Yupei Li +3

GLAM – the Group on Language, Audio, & Music, Imperial College London, UK · College of Telecommunications and Information Engineering, Nanjing University of Posts and Telecommunications, China · College of Computer Science and Electronic Engineering, Hunan University, China +2

Language Model Calibration Multimodal Sentiment Analysis Multimodal Fusion

Jul 12, 2026cs.LG

Reliability Scaling Laws for Quantized Large Language Models

Quantization is a powerful strategy to build capable and resource-efficient large language models (LLMs) by reducing the bitwidth of the parameters. While quantized LLMs achieve state-of-the-art performance on unperturbed inputs using standard predictive metrics, their performance on perturbed inputs, measured using reliability metrics, remains underexplored, despite its importance for reliable deployment. To address this gap, we first conduct a comprehensive reliability evaluation of quantized LLMs consisting of three key components: (1) Uncertainty: We assess the trustworthiness of LLMs quantized to 2, 3, 4, and 8 bits using six different quantization methods, employing established uncertainty metrics. (2) Calibration: We assess how well-calibrated the uncertainty estimates of quantized models are across model scales and bit precisions. (3) Robustness: We design character-level and word-level input perturbations to evaluate the reliability of quantized models under semantically-preserving variations in the inputs that arise in real-world applications. Second, we characterize how reliability scales with the total number of model bits. Our study reveals that while the performance scales monotonically with the total number of bits, the reliability scalings are nonlinear. A reliability peak occurs for 4-bit quantized models, indicating that quantizing moderately sized models offers the best reliability-efficiency trade-off. Additionally, our empirical findings reveal that quantization enhances the robustness of LLMs to natural input perturbations.

Sirine Ayadi, Sándor Daróczi, Stephan Günnemann +1

School of Computation, Information and Technology, Technical University of Munich Munich Data Science Institute · Pruna AI

LLM Quantization Language Model Calibration LLM Reliability LLM Uncertainty Estimation Language Model Robustness

Jul 9, 2026cs.CL

Validity of LLMs as data annotators: AMALIA on authority

A national language model offers a linguistic community its own instrument for measuring what its citizens say and value. Portugal's AMALIA, a publicly funded 9B-parameter model for European Portuguese, appears competitive on agreement alone: asked to code the moral foundation of authority, it agrees with trained human coders to within six F1 points of open models eight to thirteen times its size. Yet agreement is reliability, not validity. For theoretical constructs that must be inferred rather than read from surface features, the question is whether the model follows the construct's theory or reaches the right code by correlated shortcuts. We test this with the recovery gap: the loss in performance when a holistic prompt is decomposed into the codebook's atomic clauses and recombined by the theory's explicit rule. If calibration closes that gap, some portability should survive across models and languages; where it does not, the construct-model instrument is the likely locus of failure. We ask whether a calibrated English instrument transfers to AMALIA-9B and to European Portuguese. For one construct and one corpus, it does not. Decomposition recovers only about half of AMALIA's holistic performance, and error analysis suggests reliance on surface correlates, especially moral outrage near authority figures. An open multilingual LLM closes the gap on the same Portuguese corpus under the same instructions, pointing away from the corpus as the main explanation. AMALIA can still screen and pre-code at scale, but it cannot yet measure this construct well enough to stand alone. The study is a single counterexample, not a verdict on national models; it argues that sovereign-LLM benchmark batteries should test not only agreement with human coders, but the evidential route by which that agreement is warranted.

Manuel Pita

Artificial Intelligence, Social Interaction and Complexity Laboratory · CICANT, Universidade Lusófona

Multilingual Language Model Evaluation Moral Reasoning in Language Models LLM-Assisted Annotation Language Model Calibration LLM Reliability

Jul 9, 2026cs.CL

Do You Need a Frontier Model as a Citation Verifier? Benchmarking Rubric LLMs for Deep-Research Source Attribution

Reinforcement learning increasingly relies on an LLM judge to score each rubric criterion, and that judge acts as the reward model during training. Before such a signal can be trusted, we need to know how capable the judge must be and how biased it is. We study this calibration question for citation quality in deep-research systems, where a search-grounded LLM must support each claim it writes with a cited source. Citation quality is a structured rubric task in which each attribution-citation pair is judged along two dimensions that require an LLM, source relevance and factual support. On an adversarial long-form benchmark, we score 8 off-the-shelf LLM judges from 3 model families against gold labels over 1,248 rubric decisions, all of which were human-reviewed and 378 of which were hard cases adjudicated from judge disagreements. Cheaper judges remain competitive across both dimensions, with GPT-5-mini attaining the strongest source-relevance pass-class F1 at 0.908 (

κ

=0.636), while on factual support the judges are statistically indistinguishable (overlapping confidence intervals), so no single model dominates. At comparable F1, the judges still differ substantially in pass-rate drift, false positive rate, and false negative rate. Scalar F1 obscures this directional bias, yet it is exactly what a downstream reinforcement learning loop would reinforce. Calibrating the judge is therefore a prerequisite for using citation rubrics as reward signals, and our results show that this calibration does not require the most expensive available model.

Ethan Leung, Elias Lumer, Corey Feld +3

Commercial Technology and Innovation Office, PricewaterhouseCoopers, U.S.

LLM-as-a-Judge Citation Verification Language Model Calibration Language Model Bias Evaluation Rubric-Based Evaluation Bias in LLM-as-a-Judge

Jul 9, 2026cs.LG

Eigenvalue Calibration for Semantic Embeddings of Large Language Models

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

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

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

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