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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May 14, 2026cs.AI

Case-Based Calibration of Adaptive Reasoning and Execution for LLM Tool Use

Tool use extends large language models beyond parametric knowledge, but reliable execution requires balancing appropriate reasoning depth with strict structural validity. We approach this problem from a case-based perspective to present CAST, a case-driven framework that treats historical execution trajectories as structured cases. Instead of reusing raw exemplar outputs, CAST extracts case-derived signals to identify complexity profiles for estimating optimal reasoning strategies, alongside failure profiles to map likely structural breakdowns. The framework translates this knowledge into a fine-grained reward design and adaptive reasoning, enabling the model to autonomously internalize case-based strategies during reinforcement learning. Experiments on BFCLv2 and ToolBench demonstrate that CAST improves both schema-faithful execution and task-level tool-use success while reducing unnecessary deliberation. The approach achieves up to 5.85 percentage points gain in overall execution accuracy and reduces average reasoning length by 26%, significantly mitigating high-impact structural errors. Ultimately, this demonstrates how historical execution cases can provide reusable adaptation knowledge for calibrated tool use.

Renning Pang, Tian Lan, Leyuan Liu +3

University of Electronic Science and Technology of China, Chengdu 611731, China

Language Model Calibration LLM Tool Use RL for Tool Use

May 13, 2026cs.CL

Inducing Artificial Uncertainty in Language Models

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

Sophia Hager, Simon Zeng, Nicholas Andrews

Johns Hopkins University · Microsoft

Confidence Estimation in Language Models Language Model Calibration LLM Uncertainty Estimation

May 13, 2026cs.LG

Discovery of Hidden Miscalibration Regimes

Calibration is commonly evaluated by comparing model confidence with its empirical correctness, implicitly treating reliability as a function of the confidence score alone. However, this view can hide substantial structure: models may be systematically overconfident on some kinds of inputs and underconfident on others, causing global reliability diagnostics to obscure localised calibration failures. To address this, we formulate the problem of discovering hidden miscalibration regimes without assuming access to predefined data slices. We define the corresponding miscalibration field and propose a diagnostic framework for estimating it. Our approach learns a calibration-aware representation of the input space and estimates signed local miscalibration by kernel smoothing in the learned geometry. Across four real-world LLM benchmarks and twelve LLMs, we find that input-dependent calibration heterogeneity is prevalent. We further show that the discovered fields are actionable: they support local confidence correction and reduce calibration error in systematically miscalibrated regions where confidence-based methods such as isotonic regression and temperature scaling are less effective.

Katarzyna Kobalczyk, Mihaela van der Schaar

University of Cambridge

Post-Hoc Calibration Language Model Calibration Model Calibration LLM Reliability Uncertainty Calibration

May 12, 2026cs.LG

Training Large Language Models to Predict Clinical Events

Longitudinal clinical notes contain rich evidence of how patients evolve over time, but converting this signal into training supervision for clinical prediction remains challenging. We extend Foresight Learning to clinical prediction by converting time-ordered MIMIC-III notes into examples consisting of past patient context, a natural-language question about a possible future event, and a label resolved from later documentation. This process yields 6,900 prediction examples from 702 admissions across medications, procedures, organ support, microbiology, and mortality. A small LoRA adapter trained on these examples improves over the prompted base model, reducing expected calibration error from 0.1269 to 0.0398 and Brier score from 0.199 to 0.145, while slightly outperforming GPT-5 point estimates on held-out questions. The approach enables reusable clinical prediction supervision from longitudinal notes without hand-engineered structured features or endpoint-specific classifiers.

Benjamin Turtel, Paul Wilczewski, Kris Skotheim

Lightning Rod Labs

Healthcare Language Model Calibration Clinical Prediction Longitudinal EHR Modeling Electronic Health Records Medical LLMs+1

May 12, 2026cs.LG

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

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

Chen Li, Xiaoling Hu, Songzhu Zheng +2

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

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

May 12, 2026cs.LG

OGLS-SD: On-Policy Self-Distillation with Outcome-Guided Logit Steering for LLM Reasoning

We study on-policy self-distillation (OPSD), where a language model improves its reasoning ability by distilling privileged teacher distributions along its own on-policy trajectories. Despite its promise, OPSD can suffer from training instability due to a pattern mismatch between teacher and student responses. Self-reflected teacher responses may introduce reflection-induced biases and response templates that miscalibrate token-level supervision, ultimately harming the student's reasoning ability. To mitigate this issue, we propose OGLS-SD, an outcome-guided logit-steering framework that leverages verifiable outcome rewards to calibrate privileged teacher logits. Specifically, OGLS-SD contrasts teacher logits induced by successful and failed on-policy trajectories, constructing an outcome-discriminative steering direction for token-level guidance. Experiments on mathematical reasoning benchmarks show that OGLS-SD stabilizes self-distillation and improves performance over standard OPSD and other variants.

Yuxiao Yang, Xiaoyun Wang, Weitong Zhang

UNC Chapel Hill · NVIDIA

Language Model Calibration Language Model Distillation On-Policy Distillation Activation Steering LLM Reasoning

May 12, 2026cs.AI

Assessing and Mitigating Miscalibration in LLM-Based Social Science Measurement

Large language models (LLMs) are increasingly used in social science as scalable measurement tools for converting unstructured text into variables that can enter standard empirical designs. Measurement validity demands more than high average accuracy, which requires well calibrated confidence that faithfully reflects the empirical probability of each measurement being correct. This paper studies the model miscalibration in LLM-based social science measurement. We begin with a case study on FOMC and show that confidence based filtering can change downstream regression estimates when LLM confidence is miscalibrated. We then audit calibration across 14 social science constructs covering both proprietary models, including GPT-5-mini, DeepSeek-V3.2, and open source models. Across tasks and model families, reported confidence is poorly aligned with tolerance-based correctness. As a simple mitigation, we propose a soft label distillation pipeline for calibrating Bert with LLM. The method converts an LLM score and its verbalized confidence into a soft target distribution, then trains a smaller discriminative classifier on encoder models for these targets. Averaged across datasets, this approach reduces ECE by 43.2% and Brier by 34.0%. These results suggest that LLM-based social science pipelines should treat calibration as part of measurement validity, rather than as an optional post-processing concern.

Jinyuan Wang, Ningyuan Deng, Yi Yang

The Hong Kong University of Science and Technology

Language Model Calibration LLM Reliability LLM Uncertainty Estimation

May 12, 2026cs.CL

Probabilistic Calibration Is a Trainable Capability in Language Models

Language models are increasingly used in settings where outputs must satisfy user-specified randomness constraints, yet their generation probabilities are often poorly calibrated to those targets. We study whether this capability can be improved directly through fine-tuning. Concretely, we fine-tune language models on synthetic prompts that require sampling from mathematical distributions, and compare two Calibration Fine-Tuning variants: a soft-target method that converts the desired output distribution into trie-derived next-token targets, and a hard-target method that trains on sampled completions from the same target distribution. Across 12 models spanning four families, both methods substantially improve structured-sampling fidelity on held-out distribution families and unseen parameter settings, showing that probabilistic calibration is a trainable capability. Under our selected training configurations, the two methods exhibit different empirical profiles: hard-target fine-tuning is often strongest on structured numeric sampling, while soft-target fine-tuning performs better on broader stochastic generation benchmarks, including open-ended random generation, multiple-choice answer-position balancing, and NoveltyBench. The gains sometimes reduce downstream capability, especially arithmetic reasoning, with costs varying by model. Overall, our results show that probabilistic calibration can be improved through fine-tuning, with our hard-target configuration favoring exact numeric fidelity and our soft-target configuration favoring broader stochastic transfer. Code is available at https://github.com/chandar-lab/calibration-finetuning.

Davide Baldelli, Sruthi Kuriakose, Maryam Hashemzadeh +2

Chandar Research Lab · Mila – Quebec AI Institute · LAMA-WeST Lab +3

LLM Fine-Tuning Controllable Text Generation Language Model Calibration

May 12, 2026cs.LG

ROMER: Expert Replacement and Router Calibration for Robust MoE LLMs on Analog Compute-in-Memory Systems

Large language models (LLMs) with mixture-of-experts (MoE) architectures achieve remarkable scalability by sparsely activating a subset of experts per token, yet their frequent expert switching creates memory bandwidth bottlenecks that compute-in-memory (CIM) architectures are well-suited to mitigate. However, analog CIM systems suffer from inherent hardware imperfections that perturb stored weights, and its negative impact on MoE-based LLMs in noisy CIM environments remains unexplored. In this work, we present the first systematic investigation of MoE-based LLMs under noise model calibrated with real chip measurements, revealing that hardware noise critically disrupts expert load balance and renders clean-trained routing decisions consistently suboptimal. Based on these findings, we propose ROMER, a post-training calibration framework that (1) replaces underactivated experts with high-frequency ones to restore load balance, and (2) recalibrates router logits via percentile-based normalization to stabilize routing under noise. Extensive experiments across multiple benchmarks demonstrate that ROMER achieves up to 58.6%, 58.8%, and 59.8% reduction in perplexity under real-chip noise conditions for DeepSeek-MoE, Qwen-MoE, and OLMoE, respectively, establishing its effectiveness and generalizability across diverse MoE architectures.

Wenyong Zhou, Yuannuo Feng, Yizhe Chen +6

The Department of Electrical and Computer Engineering, The University of Hong Kong, Hong Kong · The School of Integrated Circuit Science and Engineering, Beihang University, Beijing, China

Compute-in-Memory Mixture-of-Experts Language Models Mixture of Experts Mixture-of-Experts Inference Language Model Calibration Language Model Robustness

May 11, 2026cs.CL

Sampling More, Getting Less: Calibration is the Diversity Bottleneck in LLMs

Diversity is essential for language-model applications ranging from creative generation to scientific discovery, yet modern LLMs often collapse into a narrow subset of plausible outputs. While prior work has developed benchmarks for measuring this lack of diversity, less is known about how the step-by-step probability distributions at inference time cause the problem. We introduce a validity--diversity framework that attributes diversity collapse to how an LLM allocates probability mass across valid and invalid continuations during decoding. This framework decomposes the bottleneck into two complementary forms of miscalibration. First, order calibration: valid tokens are not reliably ranked above invalid tokens, so rank-based cutoff rules must trade off between recovering valid continuations and admitting invalid ones. Second, shape calibration: probability mass is overly concentrated only on few valid continuations while having a heavy-tail of mixed valid and invalid tokens, so maintaining high validity limits diversity. We formalize both mechanisms and show that local failures compound across decoding steps, producing strong sequence-level losses in diversity. Empirically, we develop controlled diagnostics for probing these bottlenecks, including tasks with exactly known valid sets and oracle cutoff baselines. Across 14 language models spanning multiple families and scales, we find that diversity collapse is not merely a limitation of particular sampling heuristics, but a consequence of order and shape miscalibration in the LLM distribution.

Amin Banayeeanzade, Qingchuan Yang, Dhruv Tarsadiya +6

♠University of Southern California · ♣Capital One

LLM Evaluation Language Model Decoding Language Model Calibration Diverse Text Generation

May 11, 2026cs.CL

Training-Free Cultural Alignment of Large Language Models via Persona Disagreement

Large language models increasingly mediate decisions that turn on moral judgement, yet a growing body of evidence shows that their implicit preferences are not culturally neutral. Existing cultural alignment methods either require per-country preference data and fine-tuning budgets or assume white-box access to model internals that commercial APIs do not expose. In this work, we focus on this realistic black-box, public-data-only regime and observe that within-country sociodemographic disagreement, not consensus, is the primary steering signal. We introduce DISCA (Disagreement-Informed Steering for Cultural Alignment), an inference-time method that instantiates each country as a panel of World-Values-Survey-grounded persona agents and converts their disagreement into a bounded, loss-averse logit correction. Across 20 countries and 7 open-weight backbones (2B--70B), DISCA reduces cultural misalignment on MultiTP by 10--24% on the six backbones >=3.8B, and 2--7% on open-ended scenarios, without changing any weights. Our results suggest that inference-time calibration is a scalable alternative to fine-tuning for serving the long tail of global moral preferences.

Huynh Trung Kiet, Dao Sy Duy Minh, Tuan Nguyen +5

Faculty of Information and Technology, University of Science, Vietnam National University, Ho Chi Minh City, Vietnam. · Department of Computer Science, University of Warwick, Coventry, United Kingdom. · School of Computing, Engineering and Digital Technologies, Teesside University, United Kingdom.

LLM Alignment Cultural Alignment Language Model Calibration Cultural Bias in Language Models Inference-Time Language Model Alignment

May 11, 2026cs.LG

ConQuR: Corner Aligned Activation Quantization via Optimized Rotations for LLMs

Large language models (LLMs) are costly to deploy due to their large memory footprint and high inference cost. Weight-activation quantization can reduce these costs, but low-bit activation quantization remains difficult because activation outliers induce large quantization error. Recent rotation-based methods address this by applying orthogonal transformations that redistribute activation magnitude across dimensions, but existing approaches either require expensive end-to-end rotation training or rely on stored activation corpora, introducing significant compute or storage overhead. We propose a lightweight post-training rotation calibration method for LLM activation quantization. Our method learns orthogonal rotations that align normalized activations with the corners of an inscribed hypercube, encouraging activation energy to be distributed more evenly across dimensions. This objective admits an efficient closed-form update via the orthogonal Procrustes problem, avoiding gradient-based optimization over the orthogonal group. We further introduce an online calibration procedure that updates rotations as calibration samples are processed, eliminating the need to store activations on disk and allowing rotations to adapt to quantized activation distributions during calibration. Experiments on Llama-2 and Llama-3 models from 3B to 70B parameters show that our method achieves competitive or improved performance across perplexity benchmarks and common sense reasoning tasks while avoiding both costly end-to-end training and large offline activation storage.

Chayne Thrash, Ali Abbasi, Soheil Kolouri

Department of Computer Science Vanderbilt University

Rotation-Based Quantization LLM Inference Acceleration Language Model Calibration Activation Quantization Post-Training Quantization

May 11, 2026cs.CV

Auditing Multimodal LLM Raters: Central Tendency Bias in Clinical Ordinal Scoring

Multimodal large language models (LLMs) are increasingly explored as automated evaluators in clinical settings, yet their scoring behavior on ordinal clinical scales remains poorly understood. We benchmark three frontier LLM families against supervised deep learning models for scoring Clock Drawing Test (CDT) images on two public datasets using the Shulman rubric. While fully fine-tuned Vision Transformers achieve the best calibration (MAE 0.52, within-1 accuracy 91%), zero-shot LLMs remain competitive on tolerance-based agreement (GPT-5 MAE 0.67, within-1 accuracy 92%) despite higher absolute error. However, per-score analysis reveals that all three LLM families exhibit a pronounced central tendency effect (systematic endpoint compression): predictions are systematically compressed toward the middle of the scale, with over-prediction at the low end (score 0 to 1) and under-prediction at the high end (score 5 to 4). This effect disproportionately affects the clinically critical extremes where accurate scoring most impacts screening decisions for cognitive impairment. Targeted ablations show that neither few-shot exemplars spanning the full score range nor removing clinical terminology from the prompt eliminates the effect. Our findings extend the LLM-as-a-judge bias literature from NLP evaluation to clinical assessment, and highlight the need for calibration-aware evaluation and post-hoc calibration before deploying LLM-based raters in high-stakes screening workflows.

Jiaqing Zhang, Sandeep Elluri, Bhanu Cherukuvada +7

Department of Electrical & Computer Engineering · Department of Computer and Information Science and Engineering · Department of Clinical and Health Psychology +1

LLM Auditing Multimodal Large Language Models Language Model Calibration Language Model Bias Evaluation Clinical Language Model Evaluation

May 11, 2026cs.LG

Task-Aware Calibration: Provably Optimal Decoding in LLMs

LLM decoding often relies on the model's predictive distribution to generate an output. Consequently, misalignment with respect to the true generating distribution leads to suboptimal decisions in practice. While a natural solution is to calibrate the model's output distribution, for LLMs, this is ill-posed at the combinatorially vast level of free-form language. We address this by building on the insight that in many tasks, these free-form outputs can be interpreted in a semantically meaningful latent structure, for example, discrete class labels, integers, or sets. We introduce task calibration as a paradigm to calibrate the model's predictive distribution in the task-induced latent space. We apply a decision-theoretic result to show that Minimum Bayes Risk (MBR) decoding on the task-calibrated latent distribution is the optimal decoding strategy on latent model beliefs. Empirically, it consistently improves generation quality across different tasks and baselines. We also introduce Task Calibration Error (TCE), an application-aware calibration metric that quantifies the excess loss due to miscalibration. Our work demonstrates that task calibration enables more reliable model decisions across various tasks and applications.

Tim Tomov, Dominik Fuchsgruber, Rajeev Verma +1

School of Computation, Information & Technology, Technical University of Munich · Munich Data Science Institute · Munich Center for Machine Learning +1

Language Model Decoding MBR Decoding Language Model Calibration

May 11, 2026cs.LG

UCCI: Calibrated Uncertainty for Cost-Optimal LLM Cascade Routing

LLM cascades and model routing promise lower inference cost by sending easy queries to a small model and escalating hard ones to a large model, but most deployed routers use uncalibrated confidence scores and require per-workload threshold tuning. We present UCCI, a calibration-first router that maps token-level margin uncertainty to a per-query error probability via isotonic regression and selects the escalation threshold by constrained cost minimization. Under three explicit assumptions, threshold policies on the calibrated score are cost-optimal, and isotonic calibration achieves O(n^{-1/3}) sample complexity for expected calibration error (ECE). On a production named entity recognition workload of 75,000 queries served by 4B and 12B instruction-tuned LLMs on H100 GPUs, UCCI cuts inference cost by 31% (95% CI: [27%, 35%]) at micro-F1 = 0.91 while reducing ECE from 0.12 to 0.03. At the same operating point, UCCI beats entropy thresholding, split-conformal routing, and a FrugalGPT-style learned threshold. All cascade results use end-to-end routing on actual model outputs and measured H100 latency, not simulated routing from global accuracies or nominal API prices.

Varun Kotte

Independent Researcher.

Cost-Aware Inference Language Model Calibration LLM Uncertainty Estimation LLM Routing

May 11, 2026cs.AI

The Metacognitive Probe: Five Behavioural Calibration Diagnostics for LLMs

The Metacognitive Probe is an exploratory five-task, 15-slot diagnostic that decomposes an LLM's confidence behaviour into five behaviourally-distinct dimensions: confidence calibration (T1-CC), epistemic vigilance (T2-EV), knowledge boundary (T3-KB), calibration range (T4-CR), and reasoning-chain validation (T5-RCV). It is evaluated on N=8 frontier models and N=69 humans. The instrument is motivated by Flavell (1979) and Nelson and Narens (1990) but operates on observable confidence-correctness alignment; it is not a validated cross-species metacognition scale, and the pre-specified human developmental hypothesis was falsified. Composite benchmarks (MMLU, BIG-Bench, HELM, GPQA) ask whether a model produces a correct response. They are silent on whether the model knows when its response is wrong. A model can score 80 on a composite calibration benchmark and still be wildly overconfident in narrow pockets the aggregate cannot surface. The Metacognitive Probe surfaces those pockets. Our headline is a 47-point within-model dissociation in Gemini 2.5 Flash: panel-best within-task calibration (T1-CC = 88; Spearman rho = +0.551, 95% CI [+0.14, +0.80], p = 0.005) and panel-worst cross-task difficulty prediction (T4-CR = 41; sigma_conf = 1.4 across twelve factoids).

Rafael C. T. Oliveira

Independent Researcher

Language Model Calibration LLM Uncertainty Estimation Metacognition in Language Models Language Model Probing

May 10, 2026cs.CL

The Silent Vote: Improving Zero-Shot LLM Reliability by Aggregating Semantic Neighborhoods

Large Language Models are increasingly used as zero-shot classifiers in complex reasoning tasks. However, standard constrained decoding suffers from a phenomenon we define as Renormalization Bias. When a model is restricted to a small set of target labels, the standard softmax operation discards the probability mass assigned to semantic synonyms in the original distribution. This loss of information, which we call the Silent Vote, results in artificial overconfidence and poor calibration. We propose Semantic Softmax, an inference-time layer that recovers this lost information by aggregating the scores of the semantic neighborhood surrounding each target label. We evaluate this approach on Qwen-3 and Phi-4-mini models using GoEmotions and Civil Comments datasets. Our results demonstrate consistent improvements across all evaluation metrics: Semantic Softmax substantially reduces Expected Calibration Error (ECE) and Brier Score, while simultaneously enhancing discriminative performance in terms of AUROC and Macro-F1. By accounting for linguistic nuances, our method provides a more calibrated and accurate alternative for zero-shot classification.

Sanket Badhe, Priyanka Tiwari, Deep Shah

Google

Constrained Decoding Zero-Shot Text Classification Language Model Calibration

May 10, 2026stat.ME

Calibrate, Don't Curate: Label-Efficient Estimation from Noisy LLM Judges

Multi-judge evaluation is increasingly used to assess LLMs and reward models, and the prevailing heuristic is to curate: keep the most accurate judges and discard weaker ones. We show that this heuristic can reverse when the target is not point accuracy, but calibrated probabilistic evaluation from a labeled calibration set. Holding the aggregation and calibration procedures fixed, we compare accuracy-ranked top-

k

judge selection with using the full judge panel. Across four labeled pairwise-evaluation benchmarks spanning LLM-as-judge and reward-model settings, the calibrated full panel consistently outperforms accuracy-based selection. On RewardBench2, retaining all judges achieves negative log-likelihood (NLL) of

0.006

versus

0.013

under top-5 selection, halving the calibration error. This advantage persists after judge-family deduplication and against stronger same-pipeline subset search. We explain this reversal with oracle analyses showing that the optimal calibrated risk under proper scoring rules cannot increase when additional judge signals are made available, and that even below-chance judges can be useful when their biases are learnable and their signals are non-redundant. The resulting operating principle is simple: in multi-judge evaluation with labeled calibration data, do not discard weak judges by accuracy alone; keep them when they are parseable, non-redundant, and calibratable.

Yanran Li

Department of Biostatistics Columbia University

LLM Evaluation LLM-as-a-Judge Pairwise Preference Evaluation Language Model Calibration Language Model Ensembles

May 8, 2026cs.CV

NICE FACT: Diagnosing and Calibrating VLMs in Quantitative Reasoning for Kinematic Physics

The ability to derive precise spatial and physical insights is a cornerstone of vision-language models (VLMs), yet their poor performances in related spatial intelligence tasks such as physical reasoning remain a fundamental barrier. The community critically lacks a scientific analysis revealing whether VLMs faithfully reach answers or plausibly make guesses. This work aims to provide a fundamental understanding of how VLMs perceive the physical world, and utilize physical laws, while assessing the reliability of model confidence. We propose NICE and FACT, a dual-diagnostic paradigm that explicitly decomposes quantitative reasoning for kinematic physics: FACT diagnoses visual fidelity, physical law comprehension, and temporal grounding. NICE studies our novel neighborhood-informed calibration method and novel metrics to evaluate and calibrate confidence reliability. Evaluated across 6 latest state-of-the-art VLMs, we uncover that models fail to identify visual preconditions or utilize necessary physical laws to reach answers. This work highlights and establishes a standardized diagnostic paradigm to guide the development of faithful, physically-grounded VLMs.

Jian Lan, Zhicheng Liu, Xinpeng Wang +5

University of Munich (LMU), Germany 2Munich Center of Machine Learning3 Sichuan University

VLM Evaluation Physical Reasoning Language Model Calibration Physical Reasoning in Video

May 8, 2026cs.CL

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

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

_1

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

_2

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

_2

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

Zhanliang Wang, Jiancong Xiao, Ruochen Jin +3

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

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

May 8, 2026cs.CL

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

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

Sree Bhattacharyya, Samarth Khanna, Leona Chen +3

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

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

May 8, 2026cs.LG

Bayesian Fine-tuning in Projected Subspaces

Low-Rank Adaptation (LoRA) enables parameter-efficient fine-tuning of large models by decomposing weight updates into low-rank matrices, significantly reducing storage and computational overhead. While effective, standard LoRA lacks mechanisms for uncertainty quantification, leading to overconfident and poorly calibrated models. Bayesian variants of LoRA address this limitation, but at the cost of a significantly increased number of trainable parameters, partially offsetting the original efficiency gains. Additionally, these models are harder to train and may suffer from unstable convergence. In this work, we propose a novel framework for parameter-efficient Bayesian fine-tuning, demonstrating that effective uncertainty quantification can be achieved in very low-dimensional parameter spaces. The proposed method achieves strong performance with improved calibration and generalization while maintaining computational efficiency. Our empirical findings show that, with the appropriate projection of the weight space uncertainty can be effectively modeled in a low-dimensional space, and weight covariances exhibit low ranks.

Viktar Dubovik, Patryk Marszałek, Jacek Tabor +1

Jagiellonian University, Kraków, Poland · Doctoral School of Exact and Natural Sciences, Jagiellonian University, Kraków, Poland

Bayesian Neural Networks Fine-Tuning Low-Rank Adaptation Language Model Calibration Bayesian LoRA Parameter-Efficient Fine-Tuning

May 8, 2026cs.AI

Confidence-Aware Alignment Makes Reasoning LLMs More Reliable

Large reasoning models often reach correct answers through flawed intermediate steps, creating a gap between final accuracy and reasoning reliability. Existing alignment strategies address this with external verifiers or massive sampling, limiting scalability. In this work, we introduce CASPO (Confidence-Aware Step-wise Preference Optimization), a framework that aligns token-level confidence with step-wise logical correctness through iterative Direct Preference Optimization, without training a separate reward model. During inference, we propose Confidence-aware Thought (CaT), which leverages this calibrated confidence to dynamically prune uncertain reasoning branches with negligible O(V) latency. Experiments across ten benchmarks and multiple model families show that CASPO consistently improves reasoning reliability and inference efficiency. CASPO scales to Qwen3-8B-Base and surpasses tree-search baselines on AIME'24 and AIME'25 without using reward-model data. We also release a step-wise dataset with confidence annotations to support fine-grained analysis of reasoning reliability. Code is available at https://github.com/Thecommonirin/CASPO.

Kejia Chen, Jiawen Zhang, Yihong Wu +5

Zhejiang University · Université de Montréal · Sun Yat-sen University +1

LLM Alignment Direct Preference Optimization Efficient Language Model Reasoning Language Model Calibration LLM Reliability LLM Uncertainty Estimation+2

May 7, 2026cs.LG

Bias and Uncertainty in LLM-as-a-Judge Estimation

LLM-as-a-Judge evaluation has become a standard tool for assessing base model performance. However, characterizing performance via the naive estimator, i.e., raw judge outputs, is systematically biased. Recent work has proposed estimators to correct this bias, but their reliability depends critically on judge quality and, for model comparisons, on calibration stability. Sharing calibration across compared models is practically attractive but can introduce severe bias, including cases where the comparison estimate points in the wrong direction with high apparent confidence. We study these failure modes through analytical results, simulations over judge quality (

J

) and cross-model calibration instability (

ΔJ

), and a real-data MMLU-Pro case study with sign reversal. We propose

J

and

ΔJ

as diagnostics for when corrected estimates, especially shared-calibration comparisons, are likely unreliable, and provide reporting guidance for LaaJ evaluation.

James Fiedler

Indeed Inc.

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

May 7, 2026cs.LG

A Reproducible Optimisation Protocol for Calibrating Prompt-Based Large Language Model Workflows in Evidence Synthesis

This methods article presents a reproducible calibration workflow for prompt-based large language models (LLMs) in structured evidence-synthesis tasks. The method separates the rules that define the scientific task from the mutable prompt harness that frames and applies them. It optimises that harness against labelled or reference examples and an explicit task metric, then preserves the calibrated workflow as an inspectable artefact with its specification, metric, settings, and evaluation traces. The example code instantiates the protocol with DSPy and GEPA tools, but the underlying logic can transfer to other prompt-optimisation frameworks that support structured task definitions, metric-guided search, and artefact reuse. Title and abstract screening is the worked validation case because it provides labelled benchmark data and clear evaluation metrics. The demonstrated workflow uses a smaller student LLM for performing the scientific task execution and a larger reflection LLM to steer the prompt optimisation process during calibration. This work shows compilation, artefact round-tripping, and how optimisation budget affects a smaller student model.

Teo Susnjak

School of Mathematical and Computational Sciences Massey University, Auckland, New Zealand

Large Language Model-Guided Optimization Language Model Calibration Automatic Prompt Optimization

May 7, 2026cs.CL

Log-Likelihood, Simpson's Paradox, and the Detection of Machine-Generated Text

The ability to reliably distinguish human-written text from that generated by large language models is of profound societal importance. The dominant approach to this problem exploits the likelihood hypothesis: that machine-generated text should appear more probable to a detector language model than human-written text. However, we demonstrate that the token-level signal distinguishing human and machine text is non-uniform across the hidden space of the detector model, and naively averaging likelihood-based token scores across regions with fundamentally different statistical structure, as most detectors do, causes a form of Simpson's paradox: a strong local signal is destroyed by inappropriate aggregation. To correct for this, we introduce a learned local calibration step grounded in Bayesian decision theory. Rather than aggregating raw token scores, we first learn lightweight predictors of the score distributions conditioned on position in hidden space, and aggregate calibrated log-likelihood ratios instead. This single intervention dramatically and consistently improves detection performance across all baseline detectors and all datasets we consider. For example, our calibrated variant of Fast-DetectGPT improves AUROC from

0.63

to

0.85

on GPT-5.4 text, and a locally-calibrated DMAP detector we introduce achieves state-of-the-art performance across the board. That said, our central contribution is not a new detector, but a precise diagnosis of a significant cause of under-performance of existing detectors and a principled, modular remedy compatible with any token-averaging pipeline. This will serve as a foundation for the community to build upon, with natural avenues including richer distributional models, improved calibration strategies, and principled ensembling with hidden-space geometry signals via the full Bayes-optimal decision rule.

Tom Kempton, Viktor Drobnyi, Maeve Madigan +1

Department of Mathematics University of Manchester · Risk and Security AI Lab Visa Inc.

AI-Generated Text Detection Language Model Calibration Model Calibration

May 7, 2026cs.AI

Saliency-Aware Regularized Quantization Calibration for Large Language Models

Post-training quantization (PTQ) is an effective approach for deploying large language models (LLMs) under memory and latency constraints. Most existing PTQ methods determine quantization parameters by minimizing a layer-wise reconstruction error on a predetermined calibration dataset, typically optimized via either scale search or Gram-based methods. However, from the perspective of generalization risk, existing PTQ calibration objectives based solely on empirical reconstruction error over limited or unrepresentative calibration data may move the quantized weights away from the original floating-point weights, potentially degrading downstream performance. To address this issue, we propose \emph{Regularized Quantization Calibration} (RQC), a unified framework that augments standard PTQ objectives with a regularizer that explicitly controls weight deviation from the original weights. We further generalize this framework to incorporate a saliency-aware regularizer, resulting in \emph{Saliency-Aware Regularized Quantization Calibration} (SARQC). The proposed regularization encourages quantized weights to remain close to the original weights during calibration, leading to improved generalization at inference time. SARQC integrates seamlessly into existing PTQ pipelines and enhances both scale-search-based and Gram-based methods under a unified formulation. Extensive experiments on dense and Mixture-of-Experts LLMs demonstrate consistent improvements in perplexity and zero-shot accuracy, without introducing additional inference overhead.

Yanlong Zhao, Xiaoyuan Cheng, Huihang Liu +6

University of Science and Technology of China · University College London · 3Shanghai University of Finance and Economics +5

LLM Quantization Language Model Calibration Post-Training Quantization Neural Network Quantization

May 7, 2026cs.AI

BitCal-TTS: Bit-Calibrated Test-Time Scaling for Quantized Reasoning Models

Post-training quantization makes large reasoning models practical under tight memory and latency budgets, but it can distort the online signals that drive adaptive test-time compute allocation. Under a fixed cap on the number of newly generated tokens, miscalibrated confidence can lead to harmful early halting: the model may surface a plausible final line while the underlying reasoning is still wrong, or the controller may stop before the trace has stabilized. We study this interaction for greedy 4-bit inference and propose BitCal-TTS, a lightweight runtime controller that combines (i) inexpensive online proxies for token-level uncertainty and reasoning-trace stability, (ii) a bit-conditioned confidence rescaling that is conservative at low nominal precision, and (iii) a bit-aware post-marker confirmation horizon designed for GSM8K-style structured outputs. The method requires no fine-tuning of the base model and integrates with standard Hugging Face 4-bit inference using forward hooks for logits and last-layer hidden states. On small evaluation shards of GSM8K with Qwen2.5 Instruct models, BitCal-TTS improves exact-match accuracy over a non-bit-aware adaptive baseline at the 7B and 14B scales while preserving substantial token savings relative to fixed-budget decoding. At a token cap of B=512, on the evaluation shards we report (N=54 for 7B and N=35 for 14B; not the full GSM8K test set), accuracy gains are +3.7 points (7B) and +2.8 points (14B), with the premature-stop rate falling from 14.8% to 11.1% on 7B and from 17.1% to 11.4% on 14B. We report Wilson 95% confidence intervals throughout and explicitly discuss the limited statistical power of the partial-shard comparisons. We release code and figure-generation scripts to support full reproduction.

Sai Babu Patarlapalli, Surya Teja Avvaru

LLM Inference 4-Bit Quantization Test-Time Scaling Language Model Calibration Inference-Time Compute Allocation

May 6, 2026cs.CL

Distilling Bayesian Belief States into Language Models for Auditable Negotiation

Negotiation agents must infer what their counterpart values, update those beliefs over dialogue turns, and choose actions under uncertainty. End-to-end large language models (LLMs) can imitate negotiation dialogue, but their opponent beliefs are usually implicit and difficult to inspect. We propose BOND (Bayesian Opponent-belief Negotiation Distillation), a framework for auditable negotiation. BOND consists of an LLM-based Bayesian teacher that scores dialogue contexts against the six possible opponent priority orderings, updates a posterior over those orderings, and uses the posterior for menu-based decision making, as well as a smaller 8B student language model that emits both negotiation actions and normalized posterior beliefs as tagged text. In the CaSiNo negotiation dataset, BOND outperforms the state-of-the-art and achieves mean Brier score 0.085 over opponent-priority posteriors. The distilled student preserves much of this belief signal, achieving Brier 0.114, below the uniform six-ordering reference of 5/36, approximately 0.139. Compared with a 70B structured-CoT baseline, the significantly smaller 8B student model yields substantially better elicited posterior calibration. We further showcase auditability through posterior trajectories, belief-versus-policy error decomposition, and posterior-prefix interventions. These diagnostics reveal that distillation preserves a scoreable belief report more strongly than causal belief-conditioned control, making weak belief-action coupling visible, not hidden.

Zongqi Cui, Baihan Lin

Emory University · Icahn School of Medicine at Mount Sinai

Multi-Agent Negotiation Opponent Modeling Automated Negotiation LLM Auditing Language Model Calibration Language Model Distillation+1

May 5, 2026cs.CL

EQUITRIAGE: A Fairness Audit of Gender Bias in LLM-Based Emergency Department Triage

Emergency department triage assigns patients an acuity score that determines treatment priority, and clinical evidence documents persistent gender disparities in human acuity assessment. As hospitals pilot large language models (LLMs) as triage decision support, a critical question is whether these models reproduce or mitigate known biases. We present EQUITRIAGE, a fairness audit of LLM-based ESI assignment evaluating five models (Gemini-3-Flash, Nemotron-3-Super, DeepSeek-V3.1, Mistral-Small-3.2, GPT-4.1-Nano) across 374,275 evaluations on 18,714 MIMIC-IV-ED vignettes under four prompt strategies. Of 9,368 originals, 9,346 are paired with a gender-swapped counterfactual. All five models produced flip rates above a pre-registered 5% threshold (9.9% to 43.8%). Two showed directional female undertriage (DeepSeek F/M 2.15:1, Gemini 1.34:1); two were near-parity; one had high sensitivity with weak male-direction asymmetry. DeepSeek's directional bias coexisted with a low outcome-linked calibration gap (0.013 against MIMIC-IV admission), a Chouldechova-style dissociation between within-group calibration and between-pair counterfactual invariance. Demographic blinding reduced Gemini's flip rate to 0.5%; an age-preserving blind variant left DeepSeek with residual F/M 1.25, implicating age as a residual channel. Chain-of-thought prompting degraded accuracy for all five models. A two-model ablation reveals opposite underlying mechanisms for the same directional phenotype: in Gemini the signal is emergent in the combined name+gender swap, while in DeepSeek the gender token alone carries it. EQUITRIAGE shows that group parity, counterfactual invariance, and gender calibration are distinct fairness properties, that intervention effectiveness is model-dependent, and that per-model counterfactual auditing should precede clinical deployment.

Richard J. Young, Alice M. Matthews

University of Nevada, Las Vegas, Lee Business School, Las Vegas, NV, USA · DeepNeuro AI, Las Vegas, NV, USA · Concorde Career Colleges, Dept. of Cardiovascular and Medical Diagnostic Sonography

Gender Bias in Language Models Clinical Triage Social Bias in Language Models Clinical Decision-Making Language Model Calibration Language Model Bias Evaluation+1