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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Jun 1, 2026cs.CL

Identifying High-Confidence Social Biases in LLMs for Trustworthy Conversational Tutoring Agents

Conversational tutoring agents have been shown to improve learning engagement and student outcomes, and large language models (LLMs) are increasingly used in these systems to provide scalable, personalized feedback. However, LLMs may perpetuate or amplify stereotypical social biases, posing particular risks in educational settings. In this study, we evaluate LLMs in conversational tutoring scenarios to identify high-confidence social biases, instances where models are unable to identify biased judgments in tutoring conversations while maintaining strong confidence in their assessments, potentially affecting their reasoning and the feedback they provide to learners. We present a new dataset generation method that enables bias evaluation under naturalistic instructional conditions by regenerating student-AI tutor interactions and introducing turns with controlled bias derived from a benchmark dataset. Using this data, we assess multiple LLMs' ability to detect stereotypical biases and analyze the confidence and reasoning underlying their responses through computational and human evaluations. We find that bias detection is substantially more challenging in conversational tutoring contexts than in benchmark-based evaluations, and that state-of-the-art LLMs are overconfident in their incorrect assessments of stereotypical bias statements. Moreover, model confidence strongly influences reasoning and feedback, highlighting the risks of overconfident, biased behavior in LLM-based tutoring agents. We conclude by discussing implications, mitigation considerations, and directions for future research.

Aitor Arronte Alvarez, Naiyi Xie Fincham

University of Hawaii at Manoa, Honolulu HI 96822, USA

Intelligent Tutoring Systems Social Bias in Language Models Language Model Calibration Language Model Bias Evaluation

May 31, 2026cs.CL

Low-Resource Safety Failures Are Action Failures, Not Representation Failures

Language models often answer harmful requests in low-resource languages (LRLs) that they refuse in high-resource languages (HRLs). Across three instruction-tuned models and 23 languages, harmful refusal falls from 87.9% in HRLs to 43.9% in LRLs, while harmless refusal remains low. A common explanation is that models represent harmfulness weakly in LRLs. We test whether harmfulness is instead represented but does not reliably produce refusal. Across three models, a harmfulness direction learned from HRL activations still separates harmful from harmless LRL prompts, showing that complete absence of harmfulness information cannot explain many failures. However, harmfulness scores shift downward for LRL prompts, making harmful prompts less likely to reach the range associated with refusal. Motivated by this shift, we train a low-rank logistic classifier on HRL activations and calibrate its threshold with a few target-language examples. During generation, the classifier conditionally adds or ablates the HRL harmfulness direction. With the same HRL data and 32 target-language examples per class, CAST remains limited by low harmful refusal and AdaSteer by high harmless refusal, yielding mean refusal selectivity (

Δ

= harmful - harmless refusal) of 33.6 and 6.8, respectively. Our intervention reaches 54.5 while preserving MMLU utility. HRL-only calibration improves selectivity for Qwen and Gemma, whereas Llama benefits from target-language calibration. These results show that recalibrating existing representations can offer a training-free method for repairing low-resource safety failures.

Rashad Aziz, Ikhlasul Akmal Hanif, Fajri Koto

Mohamed bin Zayed University of Artificial Intelligence

Language Model Calibration LLM Safety Low-Resource Language Processing Refusal Behavior in Language Models Activation Steering

May 31, 2026cs.CL

A Finite-Calibration Regime Map for LLM Judge Panels

We study when LLM judge panels should be calibrated with low-dimensional stackers versus joint output tables under finite human-label budgets. Low-dimensional stackers have small estimation cost but miss interactions, whereas joint-table calibrators can represent interactions but pay for cell counts and unseen patterns. We cast this tradeoff as a finite-calibration regime map and instantiate it as Finite-Calibration Panel Selection, a deployable validation selector over judge path, prefix size, and aggregator family with table and parametric estimation diagnostics. On RewardBench, LLMBar, SummEval, and Arena100K with a seven-judge pool including DeepSeek V4 Flash, scalar/reliability aggregation wins 16 of 20 real dataset--budget cells, indicating that current judge outputs are often additive or redundant. Controlled calibration-growth data show the complementary regime: additive labels remain scalar-favored, whereas a six-way interaction selects a larger joint table and its test MSE drops from 0.224 to 0.061 once unseen mass vanishes. Thus the practical question is not ``how many judges?'' but whether the next judge's information is estimable under the available human labels.

Bin Zhu, Yanghui Rao

School of Computer Science and Engineering Sun Yat-sen University

LLM-as-a-Judge Language Model Calibration Language Model Ensembles

May 30, 2026cs.LG

Sequential statistical inference for Large Language Models: Representation, validity, and monitoring

This discussion argues that sequential statistical inference can naturally contribute to LLM trustworthiness. In deployment, LLM systems are queried repeatedly, conditioned on evolving contexts, and incorporate user or tool feedback, and may exhibit behavioral shifts after model updates or distribution changes. The discussion is organized around three tasks: representation, modeling LLM interactions as dependent stochastic processes rather than isolated prompt--response pairs; validity, developing uncertainty guarantees that remain meaningful under dependence, repeated use, and adaptation; and monitoring, using sequential alarms and change-point detection to identify shifts in calibration, hallucination rates, refusal behavior, fairness, or other task-relevant properties. This perspective complements recent surveys by viewing trustworthy LLM deployment as a problem of statistical process control.

Yao Xie

H. Milton Stewart School of Industrial and Systems Engineering Georgia Institute of Technology

Language Model Calibration LLM Reliability LLM Uncertainty Estimation

May 30, 2026cs.LG

EST-PRM: Stress-Testing Process Reward Models Before They Become Load-Bearing

Process reward models (PRMs) are widely used in language-model training with dense step-level supervision. They assume PRM scores are stable proxies for step correctness under label-preserving transformations. These transformations change reasoning structure but preserve final answers. We argue this assumption is not well validated. Such transformations can change how PRM scores relate to correctness signals, leading to different failure modes across models.To address this gap, we introduce \textbf{EST-PRM}, a stress-testing framework for dense process rewards. It applies three transformations: (1) step inflation, (2) dependency-aware step reordering, and (3) confidence markers. A vulnerability decomposition is defined that separates reward inflation from loss of correctness sensitivity. Five PRM-style models are evaluated on 4,687 reasoning chains from MATH-500, GSM8K, and PRMBench.The results indicate clear differences in vulnerability patterns across models. Math-Shepherd shows the strongest sensitivity to position perturbations, with a Pearson correlation drop of

0.152 \pm 0.038

and a

32.8 \pm 4.9\%

score inflation rate. Qwen2.5-Math-PRM is most affected by step inflation, reaching a

47.6 \pm 4.3\%

inflation rate. Confidence-based perturbations also distort reward calibration, revealing inconsistencies in correctness estimation. Three mitigation strategies are evaluated, highlighting trade-offs between robustness coverage and false-positive rates.

Ibne Farabi Shihab, Fariya Afrin, Sanjeda Akter +1

Department of Computer Science, Iowa State University · Department of Computer Science, Kalinga Institute of Industrial Technology · Department of Civil, Construction & Environmental Engineering, Iowa State University

Process Reward Models Language Model Calibration Language Model Robustness Reward Model Evaluation

May 29, 2026cs.CL

BenHalluEval: A Multi-Task Hallucination Evaluation Framework for Large Language Models on Bengali

Despite Bengali being the sixth most spoken language in the world, no prior work has systematically evaluated hallucination in large language models (LLMs) for Bengali. We introduce BenHalluEval, a fine-grained hallucination evaluation framework for Bengali covering four tasks: Generative Question Answering (GQA), Bangla-English Code-Mixed QA, Summarization, and Reasoning. We construct 12,000 hallucinated candidates using GPT-5.4 across twelve task-specific hallucination types, drawn from three existing Bengali datasets, and evaluate seven LLMs spanning reasoning-oriented, multilingual, and Bengali-centric categories under a dual-track protocol that independently measures false-positive rate on ground-truth instances (Track A) and hallucination detection rate on hallucinated candidates (Track B). To jointly penalise both failure modes and prevent inflated scores from uniform response bias, we propose BenHalluScore, a dual-track calibration metric that ranges from 7.72% to 55.42% across models and tasks, revealing substantial variation in hallucination calibration. Chain-of-thought prompting, applied as a mitigation strategy, shifts response distributions without consistently improving hallucination discrimination. BenHalluEval establishes the first dedicated hallucination benchmark for Bengali and highlights the inadequacy of single-track and prompting-only evaluation approaches for low-resource language settings. The dataset and code are available at https://anonymous.4open.science/r/BanglaHalluEval-EB77.

Shefayat E Shams Adib, Ahmed Alfey Sani, Ekramul Alam Esham +3

Department of Computer Science and Engineering, Islamic University of Technology · Department of Computer Science and Engineering, University of California

Multilingual Language Model Evaluation Language Model Error Detection Language Model Generation Evaluation Hallucination Detection Hallucination in Language Models Language Model Calibration+1

May 29, 2026cs.CL

Human-Alignment, Calibration, and Activation Patterns in Large Language Model Uncertainty

Uncertainty Quantification is a large and growing subfield of large language model behavioral analysis. Primarily to recognize and combat hallucination, the field has largely focused on measuring and improving calibration, the accuracy of uncertainty judgments to task efficacy. In this work, we investigate the relatively underexplored question of how similar large language model uncertainty is to human uncertainty. We investigate the presence and strength of human-similar uncertainty signals, deemed uncertainty alignment, in large language model overt behavior and internal activation patterns. We identify whether the models show evidence of simultaneous alignment and calibration on a variety of datasets covering both multiple choice and open ended factual recall. And we characterize the effect of instruct fine-tuning on each of these facets.

Kyle Moore, Jesse Roberts, Daryl Watson +2

1Vanderbilt University · 2Tennessee Technological University

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

May 28, 2026cs.CL

Counterfactual Graph for Multi-Agent LLM Calibration

Multi-agent LLM systems often treat agreement as evidence: when many agents in a panel give the same answer, that answer is assumed to be more reliable. We show that this assumption can fail after agents communicate. Communication can induce correlated failures and false consensus, so the same vote share may reflect reliable agreement in one topology but over-confidence in another. We propose CAGE-CAL, a counterfactual agent-graph calibration framework for multi-agent LLMs. For each query, CAGE-CAL compares an observed post-communication agent graph with a matched counterfactual no-communication graph, capturing both pairwise failure correlations and group-level dependencies. Rather than simply counting how many agents agree, CAGE-CAL estimates the counterfactual shift between observed and no-communication dependence, and calibrates confidence accordingly. Across five benchmarks, CAGE-CAL improves reliability discrimination with competitive ECE, and its calibrated confidence further improves topology selection over the best fixed-topology strategy.

Jiatan Huang, Mingchen Li, Ziming Li +3

University of Connecticut · University of Massachusetts, Amherst

AI Agent Reliability Language Model Calibration Multi-Agent Consensus Causal Interventions in Language Models Multi-Agent Communication LLM Agent Reliability

May 28, 2026cs.AI

Conformal Certification of Reasoning Trace Prefixes

Language model reasoning traces are rarely all-or-nothing; they frequently contain valid intermediate steps before a critical error occurs. Existing uncertainty quantification methods typically certify final answers or entire responses, failing to provide statistical guarantees for the proportion of a sequential trace that can be safely retained. To address this, we introduce CROP (Conformal Reasoning Output Prefixes), a verifier-agnostic calibration procedure for clean-prefix certification. Given any step-level risk proxy, CROP selects a calibrated threshold and returns the longest contiguous prefix whose step risk proxies remain below it, routing the uncertified suffix for downstream review or repair. Assuming exchangeability, CROP rigorously controls the marginal probability that the returned prefix contains an annotated error. Across six process-labeled reasoning datasets, we demonstrate that standard step-level metrics such as AUROC do not fully capture prefix utility, suggesting verifiers should instead be evaluated by certified prefix length. Furthermore, CROP balances over- and under-withholding, improving downstream repair accuracy by preserving valid intermediate reasoning while discarding misleading suffixes. Ultimately, this work positions prefix certification as a rigorous, practical bridge between process supervision, abstention, and repair.

Matt Y. Cheung, Ashok Veeraraghavan, Hanjie Chen +1

Department of Electrical & Computer Engineering, Rice University · Department of Computer Science, Rice University

Conformal Prediction Language Model Calibration Conformal Risk Control LLM Reasoning Reasoning Verification Reasoning Trace Analysis

May 28, 2026cs.AI

FinVerBench: Benchmark Validity and Calibration in Large Language Model Financial Statement Verification

We introduce FinVerBench, a benchmark and validity study for financial statement verification: determining whether a set of corporate financial statements is numerically consistent from the information shown to the model. FinVerBench is built from SEC 10-K XBRL filings for 43 S&P 500 companies and defines a four-category error taxonomy covering arithmetic, cross-statement linkage, year-over-year, and magnitude perturbations. We attempt fifteen contemporary LLM evaluations and report fourteen complete runs; a Gemini 2.5 Pro run is excluded from the main comparison because 40/108 gateway calls failed. All binary metrics exclude underdetermined positive instances whose perturbed line item is not rendered, leaving a 105-instance observable diagnostic subset (43 clean, 62 error-injected). Under the original guided-checklist prompt on the unrounded diagnostic subset, nine of fourteen complete LLM runs produce 95-100% false positives on clean statements, while one run achieves 0% observed false positives. Benchmark rendering choices materially affect measured recall: on a realistic rounded variant of the same observable subset, the calibrated model's recall is 79.0% with 0% observed FPR, compared with 100.0% recall on the unrounded diagnostic variant. These results support a construct-validity conclusion rather than a final leaderboard: financial statement verification is not merely arithmetic detection, but calibrated judgment under incomplete observability, prompt-induced assumptions, and realistic numerical rendering. FinVerBench and all code are publicly available.

Silu Panda

LLM Evaluation Language Model Calibration Benchmark Validity Finance

May 27, 2026cs.CL

Can LLMs Use Linguistic Uncertainty Markers to Reliably Reflect Intrinsic Confidence?

LLMs' linguistically expressed confidence should faithfully reflect their intrinsic uncertainty. While recent work shows LLMs struggle to use epistemic markers (e.g., "it is likely...") in a human-aligned fashion, it remains unclear whether models can apply their own linguistic confidence framework to associate markers with specific confidence levels in a stable and generalizable way, and how contextual features impact this ability. We conduct the first systematic study of this question, formalizing marker internal confidence (MIC) as the estimated intrinsic confidence a model associates with a specific epistemic marker in a given task domain. We present 7 metrics to evaluate the stability of MICs within and across distributions. Applying our analysis framework to diverse models and tasks, we find that LLMs remain faithfully miscalibrated even under model-centric interpretation of marker meanings, struggling to differentiate markers by internal confidence across distributions despite preserving a somewhat consistent ranking order across tasks. This supplies critical, complementary evidence to existing work toward a holistic understanding of faithful calibration in LLMs, emphasizing the need for more aligned and stable marker use to improve trustworthiness and reliability.

Gabrielle Kaili-May Liu, Arman Cohan

Yale University

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

May 27, 2026cs.CL

Functional Entropy: Predicting Functional Correctness in LLM-Generated Code with Uncertainty Quantification

Large language models have shown impressive capabilities in code generation, yet they often produce functionally incorrect code. Uncertainty quantification (UQ) methods have emerged as a promising approach for detecting hallucinations in natural language generation, but their effectiveness for code generation tasks remains underexplored. We systematically evaluate how UQ techniques transfer to code generation across three programming languages, five LLMs, and over 1,700 problems. We find that some token-probability-based methods generalize effectively without modification, while sampling-based methods relying on natural language inference (NLI) fail because NLI models cannot distinguish functionally different code, causing most responses to collapse into a single semantic cluster. To address this, we introduce functional equivalence methods, a family of code-specific methods that replace NLI-based semantic equivalence with an LLM-based functional equivalence assessment, including functional entropy, a code-specific analog of semantic entropy. Functional equivalence methods achieve top AUROC in 11 out of 15 model-benchmark combinations and the best calibration across most settings, consistently outperforming both NLI-based counterparts and all other methods evaluated.

Dylan Bouchard, Mohit Singh Chauhan, Zeya Ahmad +1

CVS Health®, Wellesley, MA, USA

Language Model Calibration LLM Uncertainty Estimation Automated Evaluation LLM Code Generation

May 26, 2026cs.AI

Asking Is Not Enough: Protocol Sensitivity in LLM Confidence Calibration

LLM confidence calibration is often evaluated by comparing two signals: token-probability scores and verbalized confidence. These signals are sometimes treated as direct readouts of model uncertainty, but their comparison depends on measurement choices that are rarely made explicit. In the main analysis, we hold the verbalized-confidence elicitation fixed: a single prompt template, probability scale, and output format. We then vary the measurement axes that define the verbalized-vs-token comparison: which answer string receives the token-probability score, how that score is read from the answer tokens, and under which conditioning context it is measured. We evaluate this design on four QA benchmarks across three open 7--8B base/Instruct model families, with larger Qwen2.5 variants as same-family robustness checks. The resulting comparison is sensitive to these choices: conditioning context changes the sign or magnitude of the ECE gap across settings, token readout produces smaller but still sign-moving changes, and changing the ECE estimator has little effect. Under the default generated-answer, bare-context protocol, Instruct settings are close to parity rather than showing a large calibration gain for verbalized confidence. In a separate supplied-answer analysis, surface-plausible wrong answers receive nearly the same confidence as supplied gold answers, suggesting that verbalized confidence also reflects answer plausibility and provenance rather than correctness alone. We argue that both confidence signals should be treated as protocol-dependent behavioral measurements, and provide a reporting checklist covering elicitation provenance, scored answer, token-probability readout, and conditioning context.

Hankyeol Kim, Pilsung Kang

Seoul National University

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

May 26, 2026cs.AI

Prefix-Safe Bayesian Belief Tracking for LLM Reasoning Reliability:Separating Calibration from Ranking

Long reasoning traces need reliability estimates before final answers are known. We study prefix-conditioned eventual-success estimation,

P(y=1 \mid o_{1:t})

, using prefix-safe observations. Sequential Bayesian Belief Tracking (SBBT) calibrates observation likelihoods and recursively updates a two-state belief, providing a common tracker for scalar scores, text and self-verification markers, hidden clusters, token-pooling probes, and latent-trajectory features. Across generated open-weight traces on MATH-500, GSM8K, AIME 2025, and RIMO-N, probability quality and ranking separate: score-only SBBT often improves Brier, while AUROC gains require structure-aware evidence beyond strong prefix-safe baselines. In the strongest hard math setting, structure-aware observations reach +0.110 AUROC against standard prefix-safe baselines. Under a same-prefix classifier audit, MATH-500 text markers and RIMO-N self-verification signals remain positive. Together, these findings support SBBT as a calibration-aware online inference framework and expose an evidence regime: scalar scores mainly support probability quality, while structure-aware prefix signals support ranking only when strong prefix-safe baselines have not already absorbed the rank evidence.

Zhenghan Song, Yunyi Li, Yulong Liu

Cornell University · Columbia University

Bayesian Filtering Language Model Calibration LLM Uncertainty Estimation

May 26, 2026cs.LG

Aligning LLMs with Human Uncertainty: A Beta-Bernoulli Calibrator for LLM Forecasting

Probabilistic forecasting estimates the likelihood of uncertain future events. To improve LLM forecasting, existing methods typically learn from binary outcomes to output verbalized forecasts. However, while aggregated human forecasts contain rich information in both the crowd probability estimate and the degree of agreement among forecasters, how to utilize these signals remains underexplored. To address this, we propose the Beta-Bernoulli Calibrator (BBC), which converts an initial point estimate forecast from any model into a distribution over event likelihood, using supervision from both binary outcomes and human forecasts. BBC models event likelihood

p \sim \text{Beta}(α, β)

and outcome

y \sim \text{Bernoulli}(p)

, with the mean as the calibrated point forecast and the variance as the epistemic uncertainty. Our results show that BBC generally provides better calibrated and more accurate forecasts than both traditional post-hoc calibration methods and models fine-tuned specifically for forecasting, while remaining lightweight and having good generalization. We also show that the epistemic uncertainty captured by BBC is a more reliable predictor of forecasting error than verbalized confidence.

Hui Dai, Ryan Teehan, Parsa Torabian +1

Agentic Learning AI Lab, New York University · Chronologies AI

Post-Hoc Calibration Probabilistic Forecasting Language Model Calibration LLM Uncertainty Estimation

May 26, 2026cs.CL

Using Probabilistic Programs to Train Inductive Reasoning in Large Language Models

Post-training Large Language Models (LLMs) for reasoning typically focuses on deductive tasks such as mathematics and coding where correctness is verifiable. Yet, many real-world reasoning problems are inductive: agents must infer uncertain beliefs from sparse, ambiguous observations. There are challenges to using standard fine-tuning methods for inductive reasoning, including difficulties in curating large-scale, high-quality labeled datasets and in handling targets that are inherently distributional. In this work, we introduce a novel approach, called Program-based Posterior Training (PPT), to address these limitations: we use an LLM to generate diverse open-world scenarios as probabilistic programs, run probabilistic inference to produce distributional target responses to queries, and then fine-tune on these probabilistic soft labels. Using this approach, we fine-tune LLMs on 10,000 programmatically generated scenarios and evaluate on held-out motifs, human-labeled judgments, and external benchmarks. Overall, PPT substantially improves estimation accuracy on held-out inductive tasks, increases alignment with human judgments, and transfers to external benchmarks for estimation and calibration. Additionally, the gains in raw calibration are not subsumed by post-hoc temperature scaling, showing that the models have more deeply internalized uncertainty compared to output rescaling. Together, these results suggest that probabilistic-program-mediated fine-tuning is a promising approach for post-training LLMs to reliably perform approximate inductive inference.

Liyi Zhang, Akshay K. Jagadish, Brenden M. Lake +1

Department of Computer Science Princeton University · Princeton AI Lab Princeton University · Department of Psychology and Computer Science Princeton University

Language Model Calibration LLM Uncertainty Estimation LLM Post-Training Probabilistic Programming Large Reasoning Models

May 26, 2026cs.LG

Innovation: An Almost Characterization of Hallucination

Hallucination is a central limitation of large language models (LLMs), and substantial effort has been devoted to understanding and mitigating it. Towards this, Kalai and Vempala (STOC 2024) introduced a probabilistic framework formalizing calibration and hallucination, and showed that, with high probability, calibrated LLMs hallucinate roughly at the rate of the "missing mass", a measure of how incomplete the training data is relative to its source. This raises two fundamental questions: (i) what property of a calibrated LLM makes hallucinations unavoidable? and (ii) can hallucinations be avoided by giving up calibration? We answer these questions by introducing a simpler property we call innovation that measures the tendency of a model to produce outputs outside the training data. We show that innovation is implied by the condition for hallucination identified by Kalai and Vempala, and, further, that it is an almost characterization of hallucination: hallucination implies innovation, and conversely, innovation implies hallucination with high probability. We also provide lower bounds on the hallucination rate based on the "innovation rate", and by relating innovation rate back to missing mass, we obtain new hallucination rate lower bounds based on missing mass that extend the results of Kalai and Vempala.

Nishant P. Das, Piyush Srivastava

School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai, Maharashtra - 400 005, India.

Hallucination in Language Models Language Model Calibration LLM Reliability Language Modeling

May 25, 2026cs.CL

Confidence and Calibration of Activation Oracles for Reliable Interpretation of Language Model Internals

Activation oracles aim to make the activations of other models legible to humans and yield promising results compared to white-box interpretability techniques. However, uncertainty quantification (UQ) for the natural-language outputs of such activation oracles is so far understudied. Here, we investigate 6 different methods for estimating the confidence of activation oracles and evaluate how well-calibrated their confidence scores are. Our experiments on 6,000 samples per oracle (varying verbalizer and context prompts) reveal that bootstrap mode frequency is the best-calibrated method among those tested (ECE 5.7% vs. 25.5% for the answer-word log-probability on Qwen3-8B; 10.3% vs. 13.1% on Qwen3.6-27B), and that the log-prob baseline can serve as a fast triage signal at a fraction of the cost. Code and the patched trainer are available at https://github.com/federicotorrielli/probabilistic_activation_oracles.

Federico Torrielli, Peter Schneider-Kamp, Lukas Galke Poech

University of Turin · University of Southern Denmark

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

May 25, 2026cs.CL

Toward a Benchmark for Controllable Simulation of Imperfect Students with Large Language Models

Teacher education requires deliberate practice with learners who exhibit identifiable strengths, weaknesses, and partial mastery. Large language models could support such practice by simulating students with known skill components, enabling teachers to rehearse explanations, diagnoses, and instructional responses. For this purpose, however, the central requirement is neither to maximize benchmark accuracy nor to suppress isolated facts, but to control model behavior so that it reflects a specified skill profile. This paper investigates whether prompted language models can be steered to retain some skills while suppressing others. We introduce a benchmark-oriented framework in which an explicit skill vector represents a simulated student, prompt-based control specifies retained and missing competencies, and behavior is evaluated using profile-alignment metrics, retained-versus-forgotten comparisons, and cross-skill calibration analyses. The results show that selective partial mastery can be induced and measured in a structured mathematics setting, although the degree of controllability remains model-dependent. These findings position controllable learner simulation as a distinct research problem at the intersection of teacher education, educational simulation, and language-model control.

Alexander Apartsin, Omri Sason, Yehudit Aperstein

Holon Institute of Technology, Holon, Israel. · Afeka Tel Aviv Academic College of Engineering, Tel Aviv, Israel

LLM Evaluation Language Model-Based Control AI in Education Language Model Calibration User Simulation

May 23, 2026cs.AI

Uncertainty Decomposition via Cyclical SG-MCMC and Soft-label Learning for Subjective NLP

Annotator disagreement in emotion classification reflects ambiguity intrinsic to emotion concepts and is essential for predictor-quality assessment in subjective NLP. Yet no prior work integrates soft-label learning with Bayesian deep learning to evaluate uncertainty along axes including annotator-distribution fidelity. We train a linear head on a frozen RoBERTa via cyclical stochastic gradient Markov chain Monte Carlo (cSG-MCMC), targeting the empirical annotator distribution with a soft-label objective under a five-axis evaluation. On the 28-emotion GoEmotions benchmark, the proposed method outperforms Monte Carlo Dropout and Deep Ensemble simultaneously on three axes -- Jensen-Shannon divergence (JSD) to the annotator distribution, Spearman correlation between per-emotion aleatoric uncertainty and disagreement, and selective-prediction Area Under the Risk-Coverage Curve (AURC) and Area Under the ROC Curve (AUROC) -- showing independent axes are jointly attainable from one posterior. Post-hoc temperature scaling exhibits a bidirectional effect, establishing hard-label calibration and annotator-JSD as independent dimensions and motivating joint reporting as an honest protocol.

Keito Inoshita, Takato Ueno

Faculty of Business and Commerce, Kansai University, Suita, Japan · Data Science and AI Innovation Research Promotion Center, Shiga University, Hikone, Japan · Graduate School of Data Science, Shiga University, Hikone, Japan

Soft-Label Learning Bayesian Neural Networks Annotator Disagreement Uncertainty Quantification Language Model Calibration Uncertainty Decomposition+1

May 22, 2026cs.LG

LLMs Show No Signs Of Individuated Metacognition

Confidence-weighted routing, selective abstention, and ensemble weighting all assume that a model's stated confidence is informative about its capability on the question being asked. They presume functional metacognition, the capacity to assess one's own capabilities, without exercising them. Aggregate calibration is well studied, with mixed results, but the underlying structure of elicited confidence is less well understood. We decompose binary confidence judgements from 20 frontier Large Language Models (LLMs) across six benchmarks using tetrachoric factor analysis paired with pairwise calibration, asking whether two models that differ in confidence also differ in performance. On factual recall and information retrieval benchmarks the cross-model confidence matrix is approximately rank-one and a single dominant factor captures most of the latent variance. Models retrieving facts share an item-level difficulty axis and differ mainly in their decision thresholds along it. Across all benchmarks the relationship between confidence and performance collapses once items that all models agree on are removed. Inter-model pairwise calibration is small even where statistically significant, and what remains shrinks to nothing once base-rate differences along the shared factor are controlled for. Mathematical reasoning is the apparent exception, but this turns out to be a confound where reasoning models answer questions about their confidence by trying to solve them in their chain of thought, bypassing the sub-symbolic self-knowledge we seek to measure. We find no evidence for significant verbalised individuated metacognition in any tested domain.

M. Moran, Mark Whiting

Pareto AI

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

May 22, 2026cs.CL

Self-Improving In-Context Learning

We propose to improve in-context learning (ICL) by optimizing the continuous embeddings of a fixed few-shot prompt at test time. The key observation is that the log-probabilities a model assigns to its demonstrated outputs

\unicode{x2013}

available from a single forward pass without generating any tokens

\unicode{x2013}

provide a meaningful signal for how well the model has inferred the task from its demonstrations. We formalize this signal as a bounded, self-supervised confidence proxy and maximize it via zeroth-order optimization over the prompt embeddings, yielding a test-time calibration procedure. The approach requires no finetuning, no token generation, no predefined label set, and no external data, making it equally applicable to both classification and free-form generation tasks. Across a comprehensive suite of ICL tasks, the proposed calibration consistently matches or improves upon the base model and outperforms classification-specific baselines on most tasks. The statistically significant correlation between proxy improvement and downstream accuracy gain confirms that the proposed proxy encodes a reliable optimization signal for in-context learning.

Baturay Saglam, Dionysis Kalogerias

Department of Electrical and Computer Engineering Yale University

Language Model Calibration In-Context Learning Test-Time Prompt Tuning

May 21, 2026cs.LG

MARGIN: Runtime Confidence Calibration for Multi-Agent Foundation Model Coordination

When a coordinator compares answers from heterogeneous foundation models, self-reported confidence may have different meanings across responders and changing workloads. This paper presents MARGIN (Multi-Agent Runtime Grading via Incremental Normalisation), a runtime calibration method that learns model-specific confidence corrections from observed answer outcomes without retraining the models or requiring a held-out calibration set. MARGIN tracks recent accuracy and stated confidence within confidence bands, uses their ratio to correct reported confidence, and blends sparse-band corrections toward a model-level estimate. The corrected scores weight candidate answers in a collective decision. Evaluation covers code generation, question answering, and mathematics, using an 18-model pool and a nine-model subset for distribution-shift experiments. On BigCodeBench, model-mean confidence is negatively related to accuracy; among correct/incorrect response pairs, choosing the more confident responder performs below chance. Against five online calibration baselines receiving identical feedback and retaining their learned state across each transition, MARGIN achieves lower post-shift expected calibration error than all five in two code-generation transitions and than four in a question-answering transition; the remaining question-answering comparison is inconclusive. In separate code-generation coordination experiments, calibration improves the ranking of correct responses and increases answer-selection accuracy by 4.3 and 14.0 percentage points on two of three benchmarks relative to uncalibrated confidence weighting. These results support model-specific runtime calibration for coordination under changing workloads when correctness feedback is available for the participating responders.

Joss Armstrong

Ericsson, Athlone, Ireland

AI Agent Reliability Multi-Agent Coordination Language Model Calibration Uncertainty Calibration

May 21, 2026cs.AI

Is Capability a Liability? More Capable Language Models Make Worse Forecasts When It Matters Most

We document inverse scaling in LLMs on forecasting problems whose underlying time series exhibit superlinear growth and tail risk of regime change, a structure common in finance and epidemiology. On these tasks, more capable models produce worse distributional forecasts. The pattern appears on ForecastBench-Sim (FBSim), a contamination-free, simulated-world benchmark we release, in forecasting synthetic SIR epidemics with a matched linear control, and replicates in real-world datasets on COVID-19, measles, housing markets, and hyperinflation. A per-quantile decomposition shows the failure concentrates at the upper tail, which more capable models shift upward to track aggressive extrapolations of growth, while the lower tail stays put. A within-family study of Llama-3.1 shows that both model scale and post-training independently contribute to this effect. Domain knowledge does not reliably rescue calibration. This inverse scaling does not appear on single-threshold metrics common in LLM forecasting benchmarks, reversing the sign of the capability--accuracy relationship on identical outputs. Single-threshold scoring at conventional cutoffs misses the upper-tail cost; tail-inclusive scoring reverses the sign of the capability--accuracy relationship on the same outputs. We recommend that LLM forecasting evaluations use continuous (and unbounded) measures of accuracy alongside bounded binary threshold metrics.

Nick Merrill, Jaeho Lee, Ezra Karger

Forecasting Research Institute · UC Berkeley

Language Model Scaling Laws Forecasting Benchmarks Probabilistic Forecasting LLM-Based Time Series Forecasting Language Model Calibration Probabilistic Time Series Forecasting

May 20, 2026cs.LG

Why Semantic Entropy Fails: Geometry-Aware and Calibrated Uncertainty for Policy Optimization

Post-training has become central to improving reasoning and alignment in large language models, where critic-free models enable scalable learning from model-generated outputs but lack principled mechanisms to distinguish informative from noisy signals. Recent approaches leverage response-level measures as uncertainty signals to regulate group-based optimization methods such as GRPO. Yet their empirical success remains unstable and unclear in how they influence optimization dynamics. In this paper, we provide, to our knowledge, the first principled formulation that interprets uncertainty signals as mechanisms for characterizing and regulating gradient variance and learning signal quality. Based on both empirical and theoretical analysis, we identify two critical gaps of current entropy-based estimators: The anisotropic gap and The calibration gap. Motivated by this analysis, we propose Geometric-aware Calibrated Policy Optimization (GCPO), a novel framework integrating geometry-aware measures to capture semantic disagreement with reward-based calibration to align uncertainty with learning signal strength. Experiments on multiple benchmarks show that our approach more faithfully tracks gradient variability and consistently improves post-training performance. Our results highlight the importance of designing uncertainty signals that are aligned with optimization dynamics, offering a principled perspective for robust post-training.

Zheyuan Zhang, Kaiwen Shi, Han Bao +3

University of Notre Dame · †Corresponding Author

RL for Language Model Reasoning Policy Optimization Language Model Calibration Policy Gradient Methods LLM Uncertainty Estimation RL Post-Training

May 20, 2026cs.CL

Calibration vs Decision Making: Revisiting the Reliability Paradox in Unlearned Language Models

Machine unlearning aims to remove the influence of specific training data from a model while preserving reliable behavior on the remaining data, making reliable prediction and uncertainty estimation essential for evaluation. Calibration is commonly used as a proxy for reliability in language models, but low calibration error does not necessarily imply reliable decision rules, as models may rely on spurious correlations while remaining well calibrated. We investigate this gap in generative language models using the multiple-choice question-answering evaluation protocol on the TOFU benchmark, measuring probabilistic reliability with calibration metrics (ECE, MCE, Brier) and decision-rule reliability via attribution-based shortcut detection with Integrated Gradients and Local Mutual Information. We find that fine-tuned models achieve low calibration error (ECE ~ 0.04) compared to pretrained models (ECE > 0.5), and models after unlearning retain similarly low calibration despite reduced accuracy on the forget split, while attribution analysis shows increased reliance on correlation-based tokens. These results demonstrate that good calibration can coexist with shortcut-based decision rules after unlearning, extending the reliability paradox to the machine unlearning setting.

Divyaksh Shukla, Ashutosh Modi

Indian Institute of Technology Kanpur (IIT Kanpur)

Confidence Estimation in Language Models Language Model Calibration LLM Reliability LLM Unlearning Machine Unlearning Evaluation

May 20, 2026cs.LG

Reinforcement Learning over Predictive Distributions for LLM Regression

Large language models (LLMs) have emerged as flexible regressors capable of predicting real-valued quantities from heterogeneous inputs. Yet most LLM regression objectives optimize predictions independently, often yielding poor calibration. We introduce Distribution-Aware Reward (DAR), an on-policy reinforcement learning objective that instead jointly evaluates the empirical predictive distribution formed by multiple predictions for the same input. To translate this distribution-level objective into rollout-level rewards, we assign each prediction credit based on its leave-one-out contribution to the quality of the overall predictive distribution. This encourages predictions that are well-centered and appropriately dispersed around the target. We evaluate on three regression settings: a synthetic task probing interpolation and extrapolation, and two real-world scientific tasks involving code and molecular data. Across tasks, DAR produces better-calibrated uncertainty estimates while consistently reducing prediction error and improving ranking quality over supervised fine-tuning and pointwise reinforcement learning. Together, these results highlight the benefits of distribution-aware training for LLM regression.

Jungsoo Park, Hyungjoo Chae, Ethan Mendes +4

Georgia Institute of Technology · Allen Institute for AI

Distributional RL RL for Language Models Language Model Calibration

May 19, 2026cs.CL

BalanceRAG: Joint Risk Calibration for Cascaded Retrieval-Augmented Generation

Large language models (LLMs) can enhance factuality via retrieval-augmented generation (RAG), but applying RAG to every query is unnecessary when the model-only answer is reliable. This motivates cascaded RAG: each query is first handled by an LLM-only branch, escalated to a RAG fallback only if the primary branch is uncertain, and abstained from when neither branch is sufficiently trustworthy. However, calibrating such cascades stage by stage may be conservative, since the final utility depends on joint uncertainty thresholding of LLM-only and RAG. In this work, we develop BalanceRAG to certify threshold pairs at a target risk level. Given uncertainty scores from the two branches, BalanceRAG frames each threshold pair as an operating point on a two-dimensional lattice and identifies safe operating points using sequential graphical testing. This enables risk-adaptive threshold calibration, controlling the system-level error rate among accepted points, while retaining more examples. Furthermore, BalanceRAG extends to multi-risk calibration, allowing retrieval usage to be bounded together with the selection-conditioned risk. Experiments on three open-domain question answering (QA) benchmarks across multiple LLM backbones demonstrate that BalanceRAG meets prescribed risk levels, preserves higher coverage and more accepted correct examples, and reduces unnecessary retrieval calls compared with always-on RAG.

Zijun Jia, Yuanchang Ye, Sen Jia +6

Beihang University · Zhejiang University of Finance & Economics · Shenzhen Institute of Advanced Technology +1

Retrieval-Augmented Generation Selective Prediction Language Model Calibration LLM Reliability

May 19, 2026cs.CL

Retrieval-Augmented Linguistic Calibration

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

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

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

Confidence Estimation in Language Models Language Model Calibration LLM Uncertainty Estimation

May 18, 2026cs.CY

Diagnosing Korean-Language LLM Political Bias via Census-Grounded Agent Simulation

Large language models (LLMs) exhibit systematic political biases in voter simulations, but their underlying mechanisms and cross-lingual generalizations remain poorly understood. We introduce Dynamo-K, a census-grounded simulation framework evaluating Korean-language LLM political behavior across four models on six Korean elections (2017-2025). Using this framework, we identify three systematic failure modes: (1) progressive bias in moderate agents, where explicit mitigation reduces Mean Absolute Error (MAE) by 5.2 times; (2) model-dependent third-party salience collapse, distinguishing between salience failure and decision bias; and (3) regional polarization collapse, where models bidirectionally under-predict historical party strongholds. To address these failures, we demonstrate that scenario reframing recovers 62% of 2017 MAE by restoring third-party visibility. Furthermore, we introduce a learned reweighting adapter that successfully calibrates opposing-valence models without relying on candidate names at train or test time. Validating our diagnostic framework, Dynamo-K accurately predicts 3/3 presidential winners - including a 2.1%p MAE on the highly contested 0.73%p-margin 2022 race - and correctly identifies the dominant party in a held-out local election. The pipeline is open-source and provides a scalable, cost-effective method for diagnosing LLM political behavior.

Sungwoo Kang

Department of Electrical and Computer Engineering Korea University, Seoul, Republic of Korea

Political Bias in Language Models Language Model Calibration Language Model Bias Evaluation