Confidence Estimation in Language Models

Visual token pruning speeds up multimodal large language models (MLLMs) by keeping a small subset of the visual tokens, and pruning methods are compared by the accuracy they retain. We study what pruning does to the confidence of these models, across common selectors, several MLLMs, and different output formats. Pruning errors concentrate on questions whose evidence the selector removed, and confidence does not register the removal. When the queried object loses all of its tokens, accuracy on these questions drops from 59% to 17%, while confidence stays at the unpruned level. Returning a few object tokens to the kept set recovers most of the lost accuracy. Selectors that keep the most attended tokens remove such evidence most often and produce confident errors, which temperature scaling cannot re-rank. Selectors that avoid keeping redundant tokens stay close to the calibration of the unpruned model. We then use the confidence of the pruned model to set a per-question token budget. The model answers with few tokens first and again with all tokens when its confidence is low. Conformal risk control sets the threshold to bound the expected deviation from the unpruned model. With coverage-based selection, this cascade needs about a third of the prefill tokens of the unpruned model, while with FastV it needs more than the unpruned model. The savings come mainly from how well the confidence ranks the answers that differ from the unpruned ones.

Large language models are increasingly deployed in high-stakes domains, where confident yet incorrect inferences may cause severe real-world harm, bringing the long-overlooked issue of confidence faithfulness to the forefront. A promising solution jointly optimizes unsupervised Reinforcement Learning from Internal Feedback (RLIF) with reasoning-trace-guided Reasoning Distillation (RD), yet it faces three persistent challenges, namely the scarcity of high-quality training corpora, factually unwarranted overconfidence, and erroneous updates amplified by indiscriminate fusion. Inspired by how human confidence accumulates from uncertainty to certainty, we propose Progressive Reasoning Gain (PRG) to measure whether reasoning steps progressively strengthen confidence in the final answer. Building on PRG, we introduce HyTuning, a hybrid post-training framework that adaptively reweights RD and RLIF, using scarce supervised reasoning traces as a stable anchor while exploiting abundant unlabeled queries for scalability. Experiments on several domain-specific and general benchmarks demonstrate that HyTuning improves accuracy while achieving confidence faithfulness under limited supervision, supporting a practical ``Less Data Approximates More'' effect. Our code will be released upon acceptance.

Standard evaluation of LLM confidence relies on calibration metrics (ECE, Brier score) that conflate how much a model knows (Type-1 accuracy) with how well its confidence signal tracks that knowledge (Type-2 metacognitive sensitivity). We apply Signal Detection Theory (SDT) to decompose these capacities, treating token-level normalised log-probability as a graded confidence variable and answer correctness as the state to be discriminated. We characterise the Type-2 ROC of this signal, including its unequal-variance structure via z-ROC analysis, and -- because the meta-d' efficiency ratio is not well defined for open-ended QA, which lacks a two-alternative Type-1 decision -- quantify metacognitive efficiency with a model-free information measure, normalised metacognitive information (meta-I_2r). Applied to four LLMs (Llama-3-8B-Instruct, Mistral-7B-Instruct-v0.3, Llama-3-8B-Base, Gemma-2-9B-Instruct) across 224,000 factual QA trials, we find: (1) metacognitive information varies more than two-fold across models and co-varies inversely with accuracy -- the least accurate model has the most informative confidence -- though with four models this ordering cannot be separated from an error-difficulty confound, so we report it as coupling, not decoupling; (2) the confidence signal has model-specific unequal-variance structure (z-ROC slopes 0.81 to 1.18) invisible to calibration metrics; (3) metacognitive information is domain-specific, strongest in Arts & Literature for every model; (4) temperature dissociates Type-1 accuracy from metacognitive information, which stays stable while accuracy shifts. All estimates carry permutation nulls and bootstrap confidence intervals. Pre-registered; code and data public.

Accurate confidence estimation is critical for reliable use of large language models (LLMs). Prior work on LLM calibration largely focuses on response-level confidence, which estimates the correctness of a single generated output. However, this formulation is misaligned with many practical settings where the central question is how likely a model is to solve a query overall. We show that this mismatch results from the stochastic nature of modern LLM decoding, under which single-response correctness fails to reflect underlying model capability. To address this issue, we introduce capability calibration, a new evaluation framework for measuring how well query-level confidence aligns with a model's expected accuracy on individual queries. We formally distinguish capability calibration (CC) from response calibration (RC) and show that the two differ both theoretically and empirically. We further show that CC is better suited than RC to applications like pass@k prediction and inference budget allocation. Finally, we evaluate common confidence estimation methods to understand the practical feasibility of CC.

Large language models present challenges for principled uncertainty quantification, in part due to their complexity and the diversity of their outputs. Semantic dispersion, or the variance in the meaning of sampled answers, has been proposed as a useful proxy for model uncertainty, but the associated computational cost prohibits its use in latency-critical applications. We show that sampled semantic distributions can be distilled into lightweight student models which estimate a prompt-conditioned density before the language model generates an answer token. The student model predicts a semantic distribution over possible answers; the entropy of this distribution provides a prompt-level uncertainty signal, and the probability density allows answer-level reliability evaluation. Across experiments on TriviaQA and MMLU, we find our student models perform competitively relative to the teacher's sampled semantic dispersion on a hallucination prediction task, whilst offering additional uncertainty primitives for out-of-domain detection and multiple-choice answer selection. We term this technique Semantic Self-Distillation (SSD), which can serve as a general framework for distilling predictive uncertainty in complex output spaces beyond language.

Large Language Models usually put more emphasis on accuracy and therefore, will guess even when not certain about the prediction, which is especially severe when fine-tuned on small datasets due to the inherent tendency toward miscalibration. In this work, we introduce Bayesian-LoRA, which reformulates the deterministic LoRA update as a probabilistic low-rank representation inspired by Sparse Gaussian Processes. We identify a structural isomorphism between LoRA's factorization and Kronecker-factored SGP posteriors, and show that LoRA emerges as a limiting case when posterior uncertainty collapses. We conduct extensive experiments on various LLM architectures across commonsense reasoning benchmarks. With only approximately 0.42M additional parameters and ${\approx}1.2{\times}$ training cost relative to standard LoRA, Bayesian-LoRA significantly improves calibration across models up to 30B, achieving up to 84% ECE reduction and 76% NLL reduction while maintaining competitive accuracy for both in-distribution and out-of-distribution (OoD) evaluations.

Accurately assessing model confidence is essential for deploying large language models (LLMs) in mission-critical factual domains. While retrieval-augmented generation (RAG) is widely adopted to improve grounding, confidence calibration in RAG settings remains poorly understood. We conduct a systematic study across four benchmarks, revealing that LLMs exhibit poor calibration performance especially when noisy contexts are retrieved. Specifically, contradictory or irrelevant evidence tends to exacerbate the model's overconfidence issue. To address this, we propose NOVA Rules (NOise-Aware Verbal Confidence CAlibration Rules) to provide a principled foundation for resolving overconfidence under noise. We further design NOVA, a noise-aware calibration framework that synthesizes supervision from ~2K HotpotQA examples guided by these rules. By performing supervised fine-tuning (SFT) with this data, NOVA equips models with intrinsic noise awareness without relying on stronger teacher models. Empirical results show that NOVA yields substantial gains, improving ECE scores by 10.9% in-domain and 8.0% out-of-domain. By bridging the gap between retrieval noise and verbal calibration, NOVA paves the way for both accurate and epistemically reliable LLMs.

Confidence estimation (CE) indicates how reliable the answers of large language models are and impacts user trust and decision-making. Existing evaluations mainly concern the alignment between confidence and correctness, but ignore the variability of language: confidence estimates should remain consistent under semantically equivalent prompts or answer variations, while changing when answer meaning differs, as this may indicate a change in correctness. Therefore, we introduce a novel evaluation framework based on three complementary properties: \textbf{robustness} to prompt perturbations, \textbf{stability} across semantically equivalent answers, and \textbf{sensitivity} to semantically different answers. We show that these metrics are largely independent from existing CE metrics, and that common CE methods often fail on them: while most methods achieve high robustness and stability, they struggle to distinguish semantically different answers, potentially because they do not effectively leverage generation-side information. Overall, our framework exposes overlooked limitations of current CE evaluations and provides guidance for selecting confidence estimators for real-world applications.

When a model knows when it does not know, many possibilities emerge. The first question is how to enable a model to recognize that it does not know. A promising approach is to use confidence, computed from the model's internal signals, to reflect its ignorance. Prior work in specific domains has shown that calibration can provide reliable confidence estimates. In this work, we propose a simple, effective, and universal training-free method that applies to both vision and language models, performing model calibration, cascading, and data cleaning to better exploit a model's ability to recognize when it does not know. We first highlight two key empirical observations: higher confidence corresponds to higher accuracy within a single model, and models calibrated on the validation set remain calibrated on a held-out test set. These findings empirically establish the reliability and comparability of calibrated confidence. Building on this, we introduce two applications: (1) model cascading with calibrated advantage routing and (2) data cleaning based on model ensemble. Using the routing signal derived from the comparability of calibrated confidences, we cascade large and small models to improve efficiency with almost no compromise in accuracy, and we further cascade two models of comparable scale to achieve performance beyond either model alone. Leveraging multiple experts and their calibrated confidences, we design a simple yet effective data-cleaning method that balances precision and detection rate to identify mislabeled samples in ImageNet and Massive Multitask Language Understanding (MMLU) datasets. Our results demonstrate that enabling models to recognize when they do not know is a practical step toward more efficient, reliable, and trustworthy AI.

Confidence calibration, the alignment of a model's predicted confidence with its actual accuracy, is crucial for the reliable deployment of Large Language Models (LLMs). However, this critical property remains largely under-explored in multilingual contexts. In this work, we conduct the first large-scale, systematic studies of multilingual calibration across six model families and over 100 languages, revealing that non-English languages suffer from systematically worse calibration. To diagnose this, we investigate the model's internal representations and find that the final layer, biased by English-centric training, provides a poor signal for multilingual confidence. In contrast, our layer-wise analysis uncovers a key insight that late-intermediate layers consistently offer a more reliable and better-calibrated signal. Building on this, we introduce a suite of training-free methods, including Language-Aware Confidence Ensemble (LACE), which adaptively selects an optimal ensemble of layers for each specific language. Our study highlights the hidden costs of English-centric alignment and offer a new path toward building more globally equitable and trustworthy LLMs by looking beyond the final layer.

Best-of-n sampling improves the accuracy of large language models (LLMs) and large reasoning models (LRMs) by generating multiple candidate solutions and selecting the one with the highest reward. The key challenge for reasoning tasks is designing a scoring function that can identify correct reasoning chains without access to ground-truth answers. We propose Probabilistic Confidence Selection And Ranking (PiCSAR): a simple, training-free method that scores each candidate generation using the joint log-likelihood of the reasoning and final answer. The joint log-likelihood of the reasoning and final answer naturally decomposes into reasoning confidence and answer confidence. PiCSAR achieves substantial gains across diverse benchmarks (+10.18 on MATH500, +9.81 on AIME2025), outperforming baselines with at least 2x fewer samples in 16 out of 20 comparisons. Our analysis reveals that correct reasoning chains exhibit significantly higher reasoning and answer confidence, justifying the effectiveness of PiCSAR.

Large language models (LLMs) often produce incorrect answers with high confidence, yet the factors associated with such overconfidence remain insufficiently understood. We study this problem through the lens of knowledge popularity. Using entity-centric factual QA derived from Wikidata triplets, we characterize popularity through question entity popularity, answer popularity, and question-answer co-occurrence. We find two consistent patterns. First, hallucinated answers are far from random: compared with ground-truth answers, they tend to be more popular or more frequently associated with the question entity. Second, confidence is strongly tied to the popularity of generated answers: even among incorrect predictions, more popular answers or those with higher question-answer co-occurrence receive higher confidence. Together, these findings suggest that popular but wrong alternatives may contribute to overconfidence. We further show that popularity-related signals can mitigate overconfidence and improve overall confidence estimation. Across six models and three datasets, incorporating knowledge popularity reduces average confidence on incorrect answers from 0.765 to 0.254 and overall ECE from 0.356 to 0.050, while improving Alignment from 77.08% to 83.72%.

Verbalized confidence, in which LLMs report a numerical certainty score, is widely used to estimate uncertainty in black-box settings, yet the confidence scale itself (typically 0--100) is rarely examined. We show that this design choice is not neutral. Across six LLMs and three datasets, verbalized confidence is heavily discretized, with more than 78% of responses concentrating on just three round-number values. To investigate this phenomenon, we systematically manipulate confidence scales along three dimensions: granularity, boundary placement, and range regularity, and evaluate metacognitive sensitivity using $meta\text{-}d'$. We find that a 0--20 scale consistently improves metacognitive efficiency over the standard 0--100 format, while boundary compression degrades performance and round-number preferences persist even under irregular ranges. These results demonstrate that confidence scale design directly affects the quality of verbalized uncertainty and should be treated as a first-class experimental variable in LLM evaluation.

Practical uncertainty quantification (UQ) for large language models must decide, from a single generation, whether a specific answer should be trusted. Existing methods either sample multiple generations, read only output-token probabilities, or reduce the model's internal computation to a single hidden state. We introduce ActMap, a white-box representation that compresses the generation-time hidden-state trajectory (every layer, every generated token) into a fixed $12\times32\times128$ tensor of temporal-statistic channels that preserves structure across transformer depth and pooled hidden coordinates. The map is captured during the generation pass with no measurable overhead, has a fixed shape across model depths and hidden sizes, and occupies 96 KiB: a compact artifact that can be retained for audit-relevant generations and probed directly, with occlusion analysis localizing the classifier's signal to mid-depth regions of the map. A lightweight classifier, instantiated as a compact Vision Transformer, reads an estimated correctness probability from each map in a fraction of a millisecond; capacity-matched MLPs perform comparably, indicating the representation itself carries the result. Trained and evaluated in-domain on short-answer QA, direct-answer math, and summarization factuality with three instruction-tuned 7-8B models, ActMap consistently outperforms sampling, token-probability, attention, and embedding baselines, and matches ACT-ViT, a detector trained on dense activation tensors $67\times$ larger, at essentially the same mean AUROC with lower calibration error on ten of twelve pairs. The resulting score supports abstention, routing, and selective verification from a single generation, making it a practical primitive for scalable oversight of deployed models.