When Linguistic and Internal Confidence Diverge in Large Language Models

Users often ask large language models (LLMs) to report how confident they are, but it is unclear whether such linguistic confidence tracks the model's internal confidence. We study this question across 8 classification tasks, 2 generation tasks and 30 models from three families. For classification, we compare linguistic confidence with logits-based confidence along three axes: association, magnitude agreement and calibration. For generation, we test whether linguistic confidence tracks semantic-entropy-based uncertainty. The axes frequently diverge. Instance-level association is weak on average, although it improves on easier items and for stronger base models. Instruction-tuned models often report higher confidence and sometimes show higher association, but they also have larger confidence gaps and worse calibration. Prompt design mostly changes the distribution of reported confidence. Attitude cues inflate confidence without improving alignment, while score exemplars can preserve rank-order signal when they avoid collapsed confidence values. Regression analyses show that distributional properties of confidence scores explain much of the observed alignment pattern, with model metadata playing a smaller role after controls. These results support a lossy-channel view of linguistic confidence. A more dispersed verbal confidence distribution can carry useful rank information, but it does not make the scores calibrated. Linguistic confidence should therefore be evaluated with multi-axis diagnostics before being used in downstream reliability pipelines.

Localize-Then-Decide Guarantees for LLM Judgments

Large language models (LLMs) are increasingly used as evaluators to assess output quality and preference alignment, yet providing reliable guarantees of agreement with human judgments remains challenging. Recent work introduces confidence-thresholding methods that provide such guarantees for pairwise comparisons, relying on the assumption that higher estimated confidence implies lower disagreement risk with humans. However, this assumption can break down when the number of candidate responses increases, since distributing probability mass across many alternatives can distort confidence estimates. To address this issue, we propose a Localize-Then-Decide framework. First, conformal prediction localizes a small shortlist that contains the human-preferred response with high probability. Then, a calibrated confidence-based rule selectively chooses a single response from this shortlist or abstains. This design restores the monotonic relationship between confidence and disagreement risk and enables high-probability agreement guarantees. Experiments with multiple candidate sizes across several datasets and judge LLMs demonstrate that our framework consistently achieves higher guarantee success rates and substantially higher coverage than single-stage baselines.

Claim-Level Confidence Calibration for Reliable Decision Making with Large Language Models

Large Language Models (LLMs) increasingly support decision-making in high-stakes domains, but they often hallucinate and express confidence that is misaligned with factual correctness. Response-level confidence is a coarse signal: a single generation can mix correct and incorrect statements, so a single number is not actionable for users that must accept, reject, or verify individual pieces of information. We study claim-level confidence calibration as a decision-relevant uncertainty signal: each response is decomposed into atomic, verifiable claims, and each claim is assigned a calibrated confidence using inference-time signals from consistency across samples and self-verification. Our framework operates in closed-box settings (no logits, no fine-tuning) and applies post-hoc calibration directly at the claim level, enabling selective intervention such as evidence retrieval or human review for low-confidence claims. Across TriviaQA and TruthfulQA we evaluate seven baselines on six recent models (Llama-3.1, Mistral, Qwen2.5, DeepSeek-R1, GPT-4, GPT-4o), and show that claim-level decomposition combined with post-hoc calibration reduces expected calibration error on factual questions while exposing failure modes on adversarial false-premise questions where decision-makers most need reliable uncertainty estimates.

DirEAG: Dirichlet Evidence Aggregation for Calibrating Verbalized Confidence in Mathematical Reasoning

Reliable confidence estimation is essential for using large language models in mathematical reasoning, but black-box verbalized confidence is difficult to calibrate. When the same problem is queried under multiple confidence-steering prompts, the resulting answer-confidence observations contain useful uncertainty information, yet their scales may shift across steering levels, models, and datasets. Existing black-box uncertainty methods often rely on answer agreement, sample consistency, or entropy, which describe output variation but do not model the numerical meaning of self-reported confidence. Conversely, direct averaging or heuristic aggregation of elicited confidence cannot learn prompt- and task-dependent bias. We propose DirEAG, a Dirichlet Evidence Aggregation method that converts each elicited answer-confidence observation into calibrated soft evidence over generated candidate answers and an additional null state, allowing the model to represent cases where none of the candidates is correct. Experiments on GSM8K, SVAMP, and GSM-Hard with Qwen, Mistral, and Gemma models show that, compared with direct confidence averaging and heuristic confidence-steering aggregation, DirEAG often achieves better calibration while maintaining competitive answer selection. Ablations further reveal that evidence aggregation and final binary calibration address distinct parts of the calibration problem.

Are You Sure You're Sure? On the Impact of Instruction Tuning on Confidence and Lexical Diversity

Instruction-tuned language models achieve strong performance across a range of generation tasks, but have also recently been shown to exhibit verbalized overconfidence. In question answering, verbalized model overconfidence may be associated with the consistency of the generated supporting rationales. In this paper, we study whether corresponding changes in the lexical diversity of generated answer rationales accompany changes in model confidence induced by instruction tuning. We evaluate three matched base and instruction-tuned models across question-answering benchmarks and find that instruction tuning consistently alters answer confidence, despite limited changes in predictive accuracy and decreases in likelihood-based calibration. Secondly, we observe a non-uniform effect of instruction tuning on rationale diversity: cross-rationale diversity consistently decreases, whereas surface-level lexical diversity varies in both direction and magnitude across models and benchmarks. Finally, we find that these differences persist after controlling for answer selection and rationale length, confirming that confidence and rationale diversity capture distinct effects of instruction tuning.

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

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

Reported Confidence in LLMs Tracks Commitment More Than Correctness

Confidence is an estimate of the probability that a chosen answer is correct. Verbal confidence reports are widely used as uncertainty measures in large language models, but whether they are best understood as estimates of correctness is unclear. We test this with a two-stage abstention paradigm from the neuroscience of perceptual decision making: a model first answers and reports its confidence, then decides whether to commit it to a user or abstain. Across four non-reasoning models, prompt framings, and confidence formats, verbal confidence predicted the commit/abstain decision substantially better than whether the answer was correct. Calibrated token log-probabilities showed the opposite profile, with abstention-prediction coupled to correctness discrimination, the signature of an answer-evidence signal. After removing the variance verbal confidence shared with log-probabilities, the residual stayed aligned with commitment while its link to correctness fell to near chance. The dissociation generalised to four reasoning models across four benchmarks of varying difficulty, from hard multiple-choice to frontier-level freeform questions. Mechanistic analyses in Gemma 3 and 4 were convergent: a post-answer state known to causally support verbal-confidence generation already encoded the future abstention decision before the abstention prompt, organised mainly by that decision rather than by correctness, the two lying in approximately orthogonal directions in activation space. Steering along a verbal-confidence-specific direction causally shifted abstention. Verbal and log-probability confidence are thus not interchangeable: log-probabilities track answer evidence and correctness, whereas verbal confidence is better understood as a behaviour-facing readout of an internal commit-readiness state, challenging the practice of treating verbal reports as proxies for reliability.

CALIBER: Calibrating Confidence Before and After Reasoning in Language Models

Reasoning language models are increasingly asked not only to answer difficult questions, but also to estimate their likelihood of success. Existing methods typically elicit confidence only once: either before thinking or after answering. We argue that confidence in reasoning models is state-dependent: before thinking, confidence should estimate the chance of the model correctly solving the prompt, while after thinking it should predict whether the realized answer is likely to be correct. This distinction determines the appropriate supervision target: prompt-level success should supervise confidence estimates made after seeing the prompt, while individual answer-level correctness should supervise confidence estimates made after answering. We introduce CALIBER (Calibration Before and After Reasoning), which elicits both estimates and supervises each with the target matched to its information state. Under this unified protocol, CALIBER reduces Expected Calibration Error (ECE) by 52.5% over the strongest single-confidence baseline on BigMathDigits for the 7B model, while achieving the best Brier score and AUROC, and remains within 2.1 points of the best accuracy. Further, on a larger 30B model, CALIBER achieves the best ECE on BigMathDigits while remaining competitive in Brier score and AUROC. Out of distribution, it achieves the best ECE and Brier score on GPQA and TriviaQA, and remains competitive on SimpleQA. Ablations further show that this position-target alignment is most beneficial under distribution shift where it consistently reduces calibration error across all out-of-distribution benchmarks.

When Confidence Takes the Wrong Path: Diagnosing Retrieval-State Lock-In in RAG

The trustworthiness of a retrieval-augmented generation (RAG) system depends on more than the answer it returns, yet many black-box uncertainty methods still read agreement among sampled answers as confidence. That inference fails when repeated samples condition on the same defective retrieval state. The state may be empty, with the model falling back on parametric memory, or populated by a coherent but wrong neighbourhood. In either case, the answers agree because the error is stable. The problem is recognised in deployed RAG, but it has lacked a name, a measurable signature, and a prevalence bound. We supply all three. We name the failure retrieval-state lock-in and diagnose it by separating the three objects a single confidence score conflates: the answer surface, the retrieved evidence, and the retrieval state itself. In an inspectable, ontology-guided knowledge-graph RAG (KG-RAG) system across six question-answering snapshots, we measure the agreement blind spot directly: at five samples per question, 42% of KG-RAG errors and 59% of dense-retrieval errors carry zero answer dispersion, so agreement has nothing to rank, while evidence- and retrieval-state checks still flag most of them. The decomposition supports an auditable decision rule: accepting an answer only when answer, evidence, and retrieval checks all agree that it is low-risk reaches 91.9% pooled precision against a 69.7% accept-all rate. The cost is coverage: it certifies only 7.7% of answers as low-risk. On the clinical calibration domain it reaches 100% precision under an automated judge; this is an in-domain automated-label upper bound, not a clinical safety claim, and still needs human validation. Confidence in RAG is object-specific: when answers agree, the useful question is which part of the pipeline to distrust.

Latent Confidence Alignment for LLM Self-Assessment

Confidence calibration in large language models (LLMs) is commonly evaluated by comparing predicted confidence with observed accuracy. However, such approaches do not model item difficulty, making it difficult to interpret discrepancies and to determine whether model confidence reflects genuine self-assessment or is merely a byproduct of the response generation process. To address this, we adopt a Rasch model-based latent ability framework and a metacognitive perspective, and propose Latent Confidence Alignment Error (LCAE) to measure the consistency between model self-assessment and the latent error probability implied by model ability and item difficulty. We further incorporate item difficulty as an external signal with a reasoning mechanism. Experiments on a medical-domain dataset with 20 models show that the proposed approach improves self-assessment quality without affecting model ability, and reveals an association between reliability and inference cost.

Can a Model Catch Its Own Hallucinations for Free?: Label-Free Doubt Signals Hold Their Own Against a Labelled Dataset for Abstention

Large language models state false facts as fluently as true ones, yet a model often "knows" internally when it is on shaky ground: the probability it assigns to its own answer tends to dip on the facts it gets wrong. The usual way to act on this, teaching a model to abstain rather than guess, requires a labelled dataset of right and wrong answers. We ask whether the model's own confidence, which is free and needs no labels, can do that job instead. We fine-tune each model (with LoRA) to answer when its frozen confidence is high and to say "I'm not sure" when it is low, using the signal alone and no correctness labels. Across six open-weights models (1B-8B, two families) on short-form factual question answering, with correctness adjudicated by an independent judge model, this label-free recipe holds its own against label-supervised abstention-tuning: at matched coverage we find no statistically detectable difference between the two. A control that drills hard examples instead of abstaining does not help, indicating the gain comes from calibration, not rote memorization. The signal's one blind spot is confidently wrong facts, which it cannot flag. A model's own doubt is thus a near-free substitute for a labelled dataset when teaching it when to abstain. Code and artifacts are available on request.

CoRA: Confidence-Rationale Alignment for Reliable Chain-of-Thought Reasoning

Chain-of-thought (CoT) reasoning can improve LLM performance, but high answer confidence may be misleading when the accompanying CoT rationale is plausible yet incomplete or poorly supported. We study confidence--rationale alignment: whether a model's confidence in its committed answer is justified by its generated rationale. We introduce a GRPO-based reinforcement learning framework that jointly rewards answer correctness, committed-answer probability, and rubric-based rationale support, where the rubric assesses grounding, coherence, task match, and connection to the selected answer without revealing the gold answer to the judge. Across MedQA, MathQA, and OpenBookQA using three open-weight LLMs, our method reduces the confidence--rationale alignment error by up to 26.51% compared with untuned checkpoints, SFT, and correctness-only GRPO, while maintaining competitive accuracy and often improving calibration. These results show that reliable CoT reasoning requires not only confident answers, but rationales that substantively support them.

Quantifying Faithful Confidence Expression in Large Reasoning Models

Reliable uncertainty communication is critical to the trustworthiness of LLMs, yet faithful calibration (FC)--the alignment between models' intrinsic and (linguistically) expressed confidence--is a persistent failure mode. This challenge is key for large reasoning models (LRMs), whose extended reasoning traces are often interpreted by users as evidence of deliberation, competence, and confidence. Despite the importance of FC and wide usage of LRMs, the extent to which LRMs can faithfully express their confidence remains poorly understood. Moreover, the prevailing paradigm to measure FC does not generalize well to the long chain-of-thought outputs generated by LRMs, which tend to lack clear step boundaries, involve inconsistent step structure, and encode complex conditional dependencies throughout the trace--complicating estimation of intrinsic confidence. To address this challenge, we introduce a novel framework to systematically quantify FC of LRMs. Our framework analyzes linguistic decisiveness relative to three sources of internal uncertainty, based on token probabilities, hidden states, and sampled response consistency. We also devise a prefix-conditioned sampling approach to control for conditional and structural variation across traces. Applying our framework to a diverse suite of leading models, datasets, and prompts, we find that faithful confidence expression is a significant challenge for LRMs. Reasoning behaviors do not automatically translate to improved FC, and prompt interventions for non-reasoning models do not improve faithfulness in the reasoning setting. Different confidence estimators further produce divergent assessments of the same traces, revealing fragility in prior evaluation methodologies. Taken together, our work establishes FC as a distinct reliability and alignment target for LRMs, particularly as such systems are increasingly deployed in high-stakes contexts.

Distilling Self-Consistency into Verbal Confidence: A Pre-Registered Negative Result and Post-Hoc Rescue on Gemma 3 4B

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.