Language Model Calibration

Small instruct-tuned LLMs produce degenerate verbal confidence under minimal elicitation: ceiling rates above 95%, near-chance Type-2 AUROC, and Invalid validity profiles. We test whether confidence-conditioned supervised fine-tuning (CSFT) with self-consistency-derived targets can close the gap between internal information and verbal readout. A pre-registered Phase 0 protocol on Gemma 3 4B-it with a modal filter restricting training to items with correct modal answers produced a negative result: AUROC2 dropped from 0.554 to 0.509 due to label-entropy collapse in the training targets. An exploratory rescue removed the filter, training on all 2,000 calibration items. This produced a binary verbal correctness discriminator with AUROC2 = 0.774 on held-out TriviaQA, compressing a 10-sample self-consistency signal (AUROC2 = 0.999) into a single-pass readout exceeding logit entropy (0.701). The shuffled-target control showed no improvement (0.501). On MMLU, accuracy improved from 54.2% to 77.4% with the shuffled model at baseline (56.1%), supporting a target-dependent interpretation. The result is exploratory, binary rather than continuously calibrated, and observed at a single scale. It identifies two design lessons: confidence training requires label entropy, and correct targets regularise output format.

Continual learning for large language models is typically evaluated through accuracy retention under sequential fine-tuning. We argue that this perspective is incomplete, because uncertainty reliability can degrade earlier and more sharply than top-1 performance. We study this empirically by measuring conformal coverage and calibration error on sequentially fine-tuned models across three model families and eight task sequences drawn primarily from classification and multiple-choice benchmarks. Across the classification-style settings we study, coverage loss exceeds accuracy loss by a factor of roughly $3.4\times \pm 0.5\times$ on average across seeds; in the most pronounced case, coverage drops from $0.92$ to $0.61$, while accuracy remains within three points of baseline. Standard continual-learning methods that preserve accuracy do not automatically preserve coverage, and naive calibration baselines recover only part of the gap. We propose calibration replay, a lightweight post-hoc procedure that maintains a task-specific held-out buffer and refits a task-specific conformal threshold under the current model after each update. It adds no training-time gradient cost, uses less than one percent of the memory of ordinary experience replay, and typically restores coverage to within two points of nominal at buffer size $m = 200$. We accompany the empirical study with a drift decomposition, a finite-sample recovery theorem showing exact conformal validity under exchangeability, and a mixture-validity proposition explaining why pooled thresholds do not suffice. Our guarantees are stated for classification-style tasks with task-specific buffers; extensions to open-ended generation are exploratory.

Stochastic sampling strategies are widely adopted in large language models (LLMs) to balance output coherence and diversity. These heuristics are often inherited in Multimodal LLMs (MLLMs) without task-specific justification. However, we contend that stochastic decoding can be suboptimal for Visual Question Answering (VQA). VQA is a closed-ended task with head-heavy answer distributions where uncertainty is usually epistemic, arising from missing or ambiguous visual evidence rather than plausible continuations. In this work, we provide a theoretical formalization of the relationship between model calibration and predictive accuracy, and derive the sufficient conditions for greedy decoding optimality. Extensive experiments provide empirical evidence for the superiority of greedy decoding over stochastic sampling across multiple benchmarks. Furthermore, we propose Greedy Decoding for Reasoning Models, which outperforms both stochastic sampling and standard greedy decoding in multimodal reasoning scenarios. Overall, our results caution against naively inheriting LLMs decoding heuristics in MLLMs and demonstrate that greedy decoding can be an efficient yet strong default for VQA.

Scaling test-time computation with reinforcement learning (RL) has emerged as a reliable path to improve large language models (LLM) reasoning ability. Yet, outcome-based reward often incentivizes models to be overconfident, leading to hallucinations, unreliable confidence-based control, and unnecessary compute allocation. We introduce Reinforcement Learning with Confidence Margin (RLCM), a calibration-aware RL framework that jointly optimizes correctness and confidence reliability via a margin-enhanced process reward over intermediate-budget completions. Rather than aligning confidence to correctness likelihoods, RLCM encourages to widen the confidence margin between correct and incorrect steps within a single reasoning trajectory. Across mathematical, code, logic and science benchmarks, our method substantially improves calibration while maintaining or improving accuracy. We further show that, with calibrated confidence signals, the resulting models enable more efficient conformal risk control and effective confidence-weighted aggregation.

The ability of large language models (LLMs) to express calibrated uncertainty is important for safe deployment. Chain-of-thought (CoT) reasoning is widely used to improve accuracy and reliability, but its effect on calibration is not fully understood. We show that this picture is incomplete: in some settings, increasing the reasoning budget beyond a task-specific threshold can cause models to become systematically overconfident, assigning high confidence to incorrect answers. We call this phenomenon Calibration Drift Under Reasoning (CDUR) and study it both theoretically and empirically. We define reasoning budget B and analyze conditions under which Expected Calibration Error ECE(B) follows a non-monotonic pattern: it first decreases as reasoning corrects errors, then increases as longer reasoning produces internally consistent but incorrect explanations. We propose a Hypothesis Lock-In model based on autoregressive generation to explain this behavior. We evaluate Llama-3.1-8B and Llama-3.3-70B on 47 reasoning-trap questions across four reasoning budgets and three seeds (1,368 API calls; 574 valid responses). The 8B model shows non-monotonic calibration behavior, while results for the 70B model are limited to baseline evaluation and are inconclusive for budget-dependent effects. We introduce CABStop, a calibration-aware stopping rule that halts reasoning when confidence diverges from an auxiliary accuracy estimate. These results suggest that increasing reasoning depth does not always improve reliability and should be monitored carefully.

Reasoning language models often lack the calibrated confidence needed for reliable deployment, particularly when correctness labels are unavailable and sampling budgets are limited. We introduce Binary Agreement for Self-consistency Calibration (BASC), which uses self-consistency as an unlabeled proxy for correctness without constructing costly self-consistency targets for each calibration query. Our key observation is that agreement between an anchor response and a single independent probe is a Bernoulli observation whose conditional mean is the anchor's latent self-consistency. Pooling these observations across unlabeled queries, BASC supports both recalibrating existing confidence scores and learning more discriminative scores before recalibration, using as few as two responses per calibration query and only one at deployment. The use of binary isotonic recalibration provides a distribution-free calibration guarantee with respect to latent self-consistency. Across 5 tasks and 9 reasoning models, BASC substantially improves calibration with respect to correctness.

Knowledge distillation (KD) transfers capabilities from large language models (LLMs) to smaller students, yet it can fail unpredictably and also underpins model leakage risks. Our analysis revealed several distillation traps: tail noise, off-policy instability, and, most fundamentally, the teacher-student gap, that distort training signals. These traps manifest as overconfident hallucinations, self-correction collapse, and local decoding degradation, causing distillation to fail. Motivated by these findings, we propose a post-hoc calibration method that, to the best of our knowledge, for the first time enables control over a teacher's distillability via reinforcement fine-tuning (RFT). Our objective combines task utility, KL anchor, and across-tokenizer calibration reward. This makes distillability a practical safety lever for foundation models, connecting robust teacher-student transfer with deployment-aware model protection. Experiments across math, knowledge QA, and instruction-following tasks show that students distilled from distillable calibrated teachers outperform SFT and KD baselines, while undistillable calibrated teachers retain their task performance but cause distilled students to collapse, offering a practical knob for both better KD and model IP protection.

Large language models are increasingly deployed to simulate patients for clinical training, research, and mental health tools, yet population-level validity remains largely untested. We introduce PsychBench, the first epidemiological audit of LLM patient simulation: 28,800 profiles from four frontier models (GPT-4o-mini, DeepSeek-V3, Gemini-3-Flash, GLM-4.7) evaluated against NHANES and NESARC-III baselines across 120 intersectional cohorts. The central finding is a coherence-fidelity dissociation: models produce clinically plausible individuals while misrepresenting the populations they are drawn from. Variance compression ranges from 14 percent (GLM-4.7) to 62 percent (DeepSeek-V3), eliminating the distributional tails of clinical reality. Despite test-retest correlations above r = 0.90, 36.66 percent of cases cross diagnostic thresholds between runs. Symptom correlation matrices diverge across demographic groups beyond split-half noise, with transgender populations diverging three to five times more than racial differences. Calibration bias is systematic and asymmetric. Models overestimate depression severity for most groups by 3.6 to 6.1 points (Cohen d = 1.13 to 1.91), consistent with training on clinical corpora with elevated base rates. For transgender women the direction inverts: models capture only 8 to 46 percent of documented minority stress elevation, yielding a -5.42 residual (d = -1.55). Models also attribute irritability to Black men and fatigue to women beyond matched controls, encoding racialized and gendered assumptions. Patterns replicate across US and Chinese architectures, indicating failures tied to current training paradigms rather than isolated implementations. For most users, LLM mental health tools risk pathologizing ordinary distress; for transgender users, algorithmic erasure of genuine need. The patients look right. They do not represent real populations.

Safe clinical deployment of Large Language Models (LLMs) requires not only high accuracy but also robust uncertainty calibration to ensure models defer to clinicians when appropriate. Our paper investigates how social descriptors of a patient (specifically sexual orientation and religious affiliation) distort these uncertainty signals and model accuracy. Evaluating nine general-purpose and biomedical LLMs on 2,364 medical questions and their counterfactual variants, we demonstrate that identity markers cause a "calibration crisis". "Homosexual" markers consistently trigger performance drops, and intersectional identities produce idiosyncratic, non-additive harms to calibration. Moreover, a clinician-validated case study in an open-ended generation setting confirms that these failures are not an artifact of the multiple-choice format. Our results demonstrate that the presence of social identity cues does not merely shift predictions; it affects the reliability of confidence signals, posing a significant risk to equitable care and safe deployment in confidence-based clinical workflows.

Multimodal Large Language Models (MLLMs) have demonstrated exceptional capabilities in various perception and reasoning tasks. Despite this success, ensuring their reliability in practical deployment necessitates robust confidence estimation. Prior works have predominantly focused on text-only LLMs, often relying on computationally expensive self-consistency sampling. In this paper, we extend this to multimodal settings and conduct a comprehensive evaluation of MLLMs' response confidence estimation. Our analysis reveals a significant instinct-reflection misalignment: the model's implicit token-level support frequently diverges from its verbal self-assessment confidence. To address this misalignment, we propose a monotone confidence fusion framework to merge dual-channel signals and cross-channel consistency to estimate correctness. Subsequently, an order-preserving mean alignment step is applied to correct global bias, which improves calibration while preserving the risk-coverage trade-off for selective prediction. Experiments on diverse open-source and closed-source MLLMs show that our method consistently yields more reliable confidence estimates and improves both calibration and failure prediction. Code will be available at https://github.com/Yunkaidang/Instinct-vs.-Reflection.

Recent advances in summary evaluation are based on model-based metrics to assess quality dimensions, such as completeness, conciseness, and faithfulness. However, these methods often require large language models, and predicted scores are frequently miscalibrated, limiting their reliability. Moreover, evaluating the average quality across different summaries for a single document typically requires access to multiple reference summaries. Here, we propose a general framework that generates individual and average proxy scores without relying on reference summaries, human annotations, or expensive model-based metrics. We also propose group isotonic regression binning (GIRB), a calibration method that adjusts the raw predictions to better align with ground-truth evaluation metrics. While we focus on continuous-value scenarios, such as summarization, the method is applicable to discrete-value tasks, such as question answering. Experiments on seven datasets demonstrate that our approach consistently outperforms existing baselines.

On-policy distillation (OPD) is an increasingly important paradigm for post-training language models. However, we identify a pervasive Scaling Law of Miscalibration: while OPD effectively improves task accuracy, it systematically traps models in severe overconfidence. We trace this failure to an information mismatch: teacher supervision is formed under privileged context available during training, whereas the deployed model must report confidence using only deployment-time information. We formalize this perspective theoretically, showing that teacher-conditioned success is generally not a valid target for deployment-time confidence and that helpful privileged context induces entropy collapse and a systematic optimism bias. To address this, we propose a calibration-aware OPD framework, CaOPD, that estimates empirical confidence from model rollouts, replaces self-reported confidence with this student-grounded target, and distills the revised response through the same self-distillation pipeline. Experiments across various models and domains show that CaOPD achieves Pareto-optimal calibration while maintaining competitive capability, generalizing robustly under out-of-distribution and continual learning. Our findings highlight that capability distillation does not imply calibrated confidence, and that confidence should be treated as an essential objective in post-training. Code: https://github.com/SalesforceAIResearch/CaOPD

Large language models are increasingly deployed in settings where reliability matters, yet output-level uncertainty signals such as token probabilities, entropy, and self-consistency can become brittle under calibration--deployment mismatch. Conformal prediction provides finite-sample validity under exchangeability, but its practical usefulness depends on the quality of the nonconformity score. We propose a conformal framework for LLM question answering that uses internal representations rather than output-facing statistics: specifically, we introduce Layer-Wise Information (LI) scores, which measure how conditioning on the input reshapes predictive entropy across model depth, and use them as nonconformity scores within a standard split conformal pipeline. Across closed-ended and open-domain QA benchmarks, with the clearest gains under cross-domain shift, our method achieves a better validity--efficiency trade-off than strong text-level baselines while maintaining competitive in-domain reliability at the same nominal risk level. These results suggest that internal representations can provide more informative conformal scores when surface-level uncertainty is unstable under distribution shift.

We introduce a cross-domain behavioural assay of monitoring-control coupling in LLMs, grounded in the Nelson and Narens (1990) metacognitive framework and applying human psychometric methodology to LLM evaluation. The battery comprises 524 items across six cognitive domains (learning, metacognitive calibration, social cognition, attention, executive function, prospective regulation), each grounded in an established experimental paradigm. Tasks T1-T5 were pre-registered on OSF prior to data collection; T6 was added as an exploratory extension. After every forced-choice response, dual probes adapted from Koriat and Goldsmith (1996) ask the model to KEEP or WITHDRAW its answer and to BET or decline. The critical metric is the withdraw delta: the difference in withdrawal rate between incorrect and correct items. Applied to 20 frontier LLMs (10,480 evaluations), the battery discriminates three profiles consistent with the Nelson-Narens architecture: blanket confidence, blanket withdrawal, and selective sensitivity. Accuracy rank and metacognitive sensitivity rank are largely inverted. Retrospective monitoring and prospective regulation appear dissociable (r = .17, 95% CI wide given n=20; exemplar-based evidence is the primary support). Scaling on metacognitive calibration is architecture-dependent: monotonically decreasing (Qwen), monotonically increasing (GPT-5.4), or flat (Gemma). Behavioural findings converge structurally with an independent Type-2 SDT approach, providing preliminary cross-method construct validity. All items, data, and code: https://github.com/synthiumjp/metacognitive-monitoring-battery.

Clinical language models (LMs) are increasingly applied to support clinical risk prediction from free-text notes, yet their uncertainty estimates often remain poorly calibrated and clinically unreliable. In this work, we propose Clinical Uncertainty Risk Alignment (CURA), a framework that aligns clinical LM-based risk estimates and uncertainty with both individual error likelihoods and cohort-level ambiguities. CURA first fine-tunes domain-specific clinical LMs to obtain task-adapted patient embeddings, and then performs uncertainty fine-tuning of a multi-head classifier using a bi-level uncertainty objective. Specifically, an individual-level calibration term aligns predictive uncertainty with each patient's likelihood of error, while a cohort-aware regularizer pulls risk estimates toward event rates in their local neighborhoods in the embedding space and places extra weight on ambiguous cohorts near the decision boundary. We further show that this cohort-aware term can be interpreted as a cross-entropy loss with neighborhood-informed soft labels, providing a label-smoothing view of our method. Extensive experiments on MIMIC-IV clinical risk prediction tasks across various clinical LMs show that CURA consistently improves calibration metrics without substantially compromising discrimination. Further analysis illustrates that CURA reduces overconfident false reassurance and yields more trustworthy uncertainty estimates for downstream clinical decision support.

Large language models (LLMs) are prone to generating factually incorrect outputs. Recent work has applied conformal prediction to provide uncertainty estimates and statistical guarantees for the factuality of LLM generations. However, existing approaches are typically not prompt-adaptive, limiting their ability to capture input-dependent variability. As a result, they may filter out too few items (leading to over-coverage) or too many (under-coverage) for a given task or prompt. We propose an adaptive conformal prediction approach that extends conformal score transformation methods to LLMs, with applications to long-form generation and multiple-choice question answering. This enables prompt-dependent calibration, retaining marginal coverage guarantees while improving conditional coverage. In addition, the approach naturally supports selective prediction, allowing unreliable claims or answer choices to be filtered out in downstream applications. We evaluate our approach on multiple white-box models across diverse domains and show that it significantly outperforms existing baselines in terms of conditional coverage.

Large Language Models (LLMs) are widely used across many domains, but their scale makes deployment challenging. Post-Training Quantization (PTQ) reduces memory footprint without retraining by leveraging a small calibration set. Recent Hessian-based PTQ methods compensate quantization error via cross-channel dependencies, but such approaches degrade at low bit-widths due to noisy curvature estimates from limited calibration data. We propose DASH-Q, a robust PTQ framework using diagonal Hessian approximation and iterative weighted least squares. By discarding noise-prone dependencies, DASH-Q filters sampling noise while prioritizing the preservation of salient feature power. We outperform other PTQ baselines in ultra low-bit regime, improving zero-shot accuracy by 7.01% on average and up to 14.01% over the strongest baselines across five baseline LLM models, while showing robust and stable performance with very small calibration data.

We introduce MIRROR, a benchmark comprising eight experiments across four metacognitive levels that evaluates whether large language models can use self-knowledge to make better decisions. We evaluate 16 models from 8 labs across approximately 250,000 evaluation instances using five independent behavioral measurement channels. Core experiments are run across the full model roster; experiments with specialized infrastructure requirements report explicitly marked model subsets. We find two phenomena with direct implications for agentic deployment: (1) compositional self-prediction fails universally -- the Compositional Calibration Error ranges from 0.500 to 0.943 on the original 15-model Exp3-v1 set (and 0.434 to 0.758 on the balanced 16-model Exp3-v2 expansion), indicating that models cannot predict their own performance on multi-domain tasks, and (2) models exhibit above-chance but imperfect domain-specific self-knowledge yet systematically fail to translate even this partial awareness into appropriate agentic action-selection -- external metacognitive control reduces the Confident Failure Rate from 0.600 to 0.143 (76% reduction at temperature 0; mean 70% at temperature 0.7 across 5 models from 4 labs). Providing models with their own calibration scores produces no significant improvement (p > 0.05); only architectural constraint is effective. This suggests that external metacognitive scaffolding -- not improved self-knowledge -- is the path to safer autonomous AI systems. Code, data, and Croissant metadata will be released publicly with the benchmark.

Large Language Models (LLMs) are increasingly applied to complex telecommunications tasks, including 3GPP specification analysis and O-RAN network troubleshooting. However, a critical limitation remains: LLM-generated confidence scores are often biased and unreliable, frequently exhibiting systematic overconfidence. This lack of trustworthy self-assessment makes it difficult to verify model outputs and safely rely on them in practice. In this paper, we study confidence calibration in telecom-domain LLMs using the representative Gemma-3 model family (4B, 12B, and 27B parameters), evaluated on TeleQnA, ORANBench, and srsRANBench. We show that standard single-pass, verbalized confidence estimates fail to reflect true correctness, often assigning high confidence to incorrect predictions. To address this, we propose a novel Twin-Pass Chain of Thought (CoT)-Ensembling methodology for improving confidence estimation by leveraging multiple independent reasoning evaluations and aggregating their assessments into a calibrated confidence score. Our approach reduces Expected Calibration Error (ECE) by up to 88% across benchmarks, significantly improving the reliability of model self-assessment. These results highlight the limitations of current confidence estimation practices and demonstrate a practical path toward more trustworthy evaluation of LLM outputs in telecommunications.

The most cited calibration result in deep learning -- post-temperature-scaling ECE of 0.012 on CIFAR-100 (Guo et al., 2017) -- is below the statistical noise floor. We prove this is not a failure of the experiment but a law: the minimax rate for estimating calibration error with model error rate epsilon is Theta((Lepsilon/m)^{1/3}), and no estimator can beat it. This "verification tax" implies that as AI models improve, verifying their calibration becomes fundamentally harder -- with the same exponent in opposite directions. We establish four results that contradict standard evaluation practice: (1) self-evaluation without labels provides exactly zero information about calibration, bounded by a constant independent of compute; (2) a sharp phase transition at mepsilon approx 1 below which miscalibration is undetectable; (3) active querying eliminates the Lipschitz constant, collapsing estimation to detection; (4) verification cost grows exponentially with pipeline depth at rate L^K. We validate across five benchmarks (MMLU, TruthfulQA, ARC-Challenge, HellaSwag, WinoGrande; ~27,000 items) with 6 LLMs from 5 families (8B-405B parameters, 27 benchmark-model pairs with logprob-based confidence), 95% bootstrap CIs, and permutation tests. Self-evaluation non-significance holds in 80% of pairs. Across frontier models, 23% of pairwise comparisons are indistinguishable from noise, implying that credible calibration claims must report verification floors and prioritize active querying once gains approach benchmark resolution.

Group Relative Policy Optimization (GRPO) enhances LLM reasoning but often induces overconfidence, where incorrect responses yield lower perplexity than correct ones, degrading relative calibration as described by the Area Under the Curve (AUC). Existing approaches either yield limited improvements in calibration or sacrifice gains in reasoning accuracy. We first prove that this degradation in GRPO-style algorithms stems from their uncertainty-agnostic advantage estimation, which inevitably misaligns optimization gradients with calibration. This leads to improved accuracy at the expense of degraded calibration. We then propose Calibration-Aware Policy Optimization (CAPO). It adopts a logistic AUC surrogate loss that is theoretically consistent and admits regret bound, enabling uncertainty-aware advantage estimation. By further incorporating a noise masking mechanism, CAPO achieves stable learning dynamics that jointly optimize calibration and accuracy. Experiments on multiple mathematical reasoning benchmarks show that CAPO-1.5B significantly improves calibration by up to 15% while achieving accuracy comparable to or better than GRPO, and further boosts accuracy on downstream inference-time scaling tasks by up to 5%. Moreover, when allowed to abstain under low-confidence conditions, CAPO achieves a Pareto-optimal precision-coverage trade-off, highlighting its practical value for hallucination mitigation.

Large Language Models are increasingly deployed for decision-making, yet their adoption in high-stakes domains remains limited by miscalibrated probabilities, unfaithful explanations, and inability to incorporate expert knowledge precisely. We propose IDEA, a framework that extracts LLM decision knowledge into an interpretable parametric model over semantically meaningful factors. Through joint learning of verbal-to-numerical mappings and decision parameters via EM, correlated sampling that preserves factor dependencies, and direct parameter editing with mathematical guarantees, IDEA produces calibrated probabilities while enabling quantitative human-AI collaboration. Experiments across five datasets show IDEA with Qwen-3-32B (78.6%) outperforms DeepSeek R1 (68.1%) and GPT-5.2 (77.9%), achieving perfect factor exclusion and exact calibration -- precision unattainable through prompting alone. The implementation is publicly available at https://github.com/leonbig/IDEA.

We study whether a variational language model can support a minimal and measurable form of agentic control grounded in its own internal evidence. Our model combines local variational hidden computation (EVE), a homeostatic latent regulator, structurally aware checkpoint retention and a calibrated uncertainty-aware controller operating on top of the retained model. Rather than treating uncertainty as a passive diagnostic measured after prediction, we treat it as an operational signal that can regulate training, support checkpoint retention and guide inference-time intervention. The resulting framework is deliberately focused. It studies a closed-loop form of internal control in which structural and predictive signals become actionable. Empirically, the variational backbone improves over a matched deterministic reference on the language-modeling task while also exhibiting a richer and more usable uncertainty profile. On top of this backbone, the calibrated controller remains active, uses multiple actions under a full agentic evaluation and yields a positive quality-cost trade-off. These results support a precise claim: internal uncertainty can serve not only as a descriptive property of a variational language model, but also as a practical control interface for regulation, checkpoint retention and minimal agentic routing.

Large language models (LLMs) are increasingly deployed for tabular question answering, yet calibration on structured data is largely unstudied. This paper presents the first systematic comparison of five confidence estimation methods across five frontier LLMs and two tabular QA benchmarks. All models are severely overconfident (smooth ECE 0.35-0.64 versus 0.10-0.15 reported for textual QA). A consistent self-evaluation versus perturbation dichotomy replicates across both benchmarks and all four fully-covered models: self-evaluation methods (verbalized, P(True)) achieve AUROC 0.42-0.76, while perturbation methods (semantic entropy, self-consistency, and our Multi-Format Agreement) achieve AUROC 0.78-0.86. Per-model paired bootstrap tests reject the null at p<0.001 after Holm-Bonferroni correction, and a 3-seed check on GPT-4o-mini gives a per-seed standard deviation of only 0.006. The paper proposes Multi-Format Agreement (MFA), which exploits the lossless and deterministic serialization variation unique to structured data (Markdown, HTML, JSON, CSV) to estimate confidence at 20% lower API cost than sampling baselines. MFA reduces ECE by 44-63%, generalizes across all four models on TableBench (mean AUROC 0.80), and combines complementarily with sampling: an MFA + self-consistency ensemble lifts AUROC from 0.74 to 0.82. A secondary contribution, structure-aware recalibration, improves AUROC by +10 percentage points over standard post-hoc methods.

Large language models (LLMs) often hallucinate in long-form generation. Existing approaches mainly improve factuality through post-hoc revision or reinforcement learning (RL) with correctness-based rewards, but they do not teach the model to estimate which parts of its generation are reliable. As a result, models may still state incorrect claims confidently in their responses. Recent advances in reasoning have significantly improved LLM performance, and have been leveraged to estimate confidence by incorporating calibration into RL objectives. However, existing approaches remain limited to a single scalar confidence for the entire response, which is insufficient for long-form generation where uncertainty varies across individual claims. To mitigate this problem, we propose CURE, a framework that improves long-form factuality by teaching LLMs to reason about uncertainty at the claim level. We first introduce a Claim-Aware Reasoning Protocol, which structures outputs into atomic claims paired with explicit confidence estimates. We then develop a multi-stage training pipeline that aligns model confidence with claims' correctness and then optimizes on factuality. The resulting calibrated confidence further enables selective prediction, allowing the model to abstain from uncertain claims at inference time. Experiments on four long-form factuality benchmarks show that CURE consistently improves factual accuracy over competitive supervised and RL baselines, while maintaining factual recall. In particular, it improves claim-level accuracy by up to 39.9% on Biography generation. These gains are accompanied by improved calibration, as reflected by a 16.0% increase in AUROC on FactBench.

Agentic data science (ADS) pipelines have grown rapidly in both capability and adoption, with systems such as OpenAI Codex now able to directly analyze datasets and produce answers to statistical questions. However, these systems can reach falsely optimistic conclusions that are difficult for users to detect. To address this, we propose a pair of lightweight sanity checks grounded in the Predictability-Computability-Stability (PCS) framework for veridical data science. These checks use reasonable perturbations to screen whether an agent can reliably distinguish signal from noise, acting as a falsifiability constraint that can expose affirmative conclusions as unsupported. Together, the two checks characterize the trustworthiness of an ADS output, e.g. whether it has found stable signal, is responding to noise, or is sensitive to incidental aspects of the input. We validate the approach on synthetic data with controlled signal-to-noise ratios, confirming that the sanity checks track ground-truth signal strength. We then demonstrate the checks on 11 real-world datasets using OpenAI Codex, characterizing the trustworthiness of each conclusion and finding that in 6 of the datasets an affirmative conclusion is not well-supported, even though a single ADS run may support one. We further analyze failure modes of ADS systems and find that ADS self-reported confidence is poorly calibrated to the empirical stability of its conclusions.

Modern large language models (LLMs) are increasingly fine-tuned via reinforcement learning from human feedback (RLHF) or related reward optimisation schemes. While such procedures improve perceived helpfulness, we investigate whether sycophantic reward signals degrade calibration -- a property essential for reliable uncertainty quantification. We fine-tune Qwen3-8B under three regimes: no fine-tuning (base), neutral supervised fine-tuning (SFT) on TriviaQA, and sycophancy-inducing Group Relative Policy Optimisation (GRPO) that rewards agreement with planted wrong answers. Evaluating on $1{,}000$ MMLU items across five subject domains with bootstrap confidence intervals and permutation testing, we find that sycophantic GRPO produces consistent directional calibration degradation -- ECE rises by $+0.006$ relative to the base model and MCE increases by $+0.010$ relative to neutral SFT -- though the effect does not reach statistical significance ($p = 0.41$) at this training budget. Post-hoc matrix scaling applied to all three models reduces ECE by $40$--$64\%$ and improves accuracy by $1.5$--$3.0$ percentage points. However, the sycophantic model retains the highest post-scaling ECE relative to the neutral SFT control ($0.042$ vs.\ $0.037$), suggesting that reward-induced miscalibration leaves a structured residual even after affine correction. These findings establish a methodology for evaluating the calibration impact of reward hacking and motivate calibration-aware training objectives.

Generative listwise reranking leverages global context for superior retrieval but is plagued by intrinsic position bias, where models exhibit structural sensitivity to input order independent of relevance. Existing mitigations present a dilemma: inference-time aggregation incurs prohibitive latency, while training-based methods often fail to eradicate ingrained priors, particularly in compact models. To resolve this dilemma, we propose CapCal (Content-Agnostic Probability Calibration), a training-free framework that mechanically decouples positional bias from ranking decisions. By estimating the bias distribution via content-free placeholders, CapCal rectifies output logits through an entropy-adaptive contrastive mechanism. Evaluations across 10 benchmarks confirm that CapCal achieves superior performance among training-free methods while preserving single-pass efficiency. Notably, it unlocks the latent potential of lightweight models (e.g., 0.6B), delivering absolute NDCG gains exceeding 10 points and outperforming both permutation-based aggregation and data-augmentation baselines.

Uncertainty quantification techniques measure confidence in language model outputs to support critical applications like hallucination detection and selective prediction. While prior work has developed various confidence metrics and demonstrated their calibration for classification tasks or using verbalized confidence, the robustness of probability-based and self-consistency-based UQ metrics for natural language generation remains underexplored particularly under model adaptation. Since practitioners routinely apply supervised fine-tuning to adapt models to new tasks, a key question arises: do confidence metrics maintain their calibration when models are fine-tuned? We investigate this question across NLG tasks including translation, question answering, and mathematical reasoning. We find that calibration shifts substantially after SFT: across 216 configurations, it degrades in 112 cases and improves in 104, with confidence scores shifting due to factors beyond output quality, such as proximity to the training distribution. Degradation is therefore neither universal nor rare, and its direction cannot be anticipated from the pre-SFT model. Through a downstream task evaluation, we show that this miscalibration substantially reduces the practical utility of confidence scores for identifying correct answers. Our findings reveal that existing confidence metrics for NLG cannot be reliably deployed off-the-shelf after fine-tuning, highlighting the need for calibration-robust UQ methods under model adaptation.

Transformers have had a profound impact on the field of artificial intelligence, especially on large language models and their variants. However, as was the case with neural networks, their black-box nature limits trust and deployment in high-stakes settings. For models to be genuinely useful and trustworthy in critical applications, they must provide more than just predictions: they must supply users with a clear understanding of the reasoning that underpins their decisions. This article presents an uncertainty quantification framework for transformer-based language models. This framework, called CONFIDE (CONformal prediction for FIne-tuned DEep language models), applies conformal prediction to the internal embeddings of encoder-only architectures, like BERT and RoBERTa, while enabling hyperparameter tuning. CONFIDE uses either [CLS] token embeddings or flattened hidden states to construct class-conditional nonconformity scores, enabling statistically valid prediction sets with instance-level explanations. Empirically, CONFIDE improves test accuracy by up to 4.09% on BERT-tiny and achieves greater correct efficiency (i.e., the expected size of the prediction set conditioned on it containing the true label) compared to prior methods, including NM2 and VanillaNN. We show that early and intermediate transformer layers often yield better-calibrated and more semantically meaningful representations for conformal prediction. In resource-constrained models and high-stakes tasks with ambiguous labels, CONFIDE offers robustness and interpretability where softmax-based uncertainty fails. We position CONFIDE as a framework for practical diagnostic and efficiency/robustness improvement over prior conformal baselines.