Daily Papers

We introduce a simple, yet novel entropy-based framework to drive token efficiency in large language models during reasoning tasks. Our approach uses Shannon entropy from token-level logprobs as a confidence signal to enable early stopping, achieving 25-50% computational savings while maintaining task accuracy. Crucially, we demonstrate that entropy-based confidence calibration represents an emergent property of advanced post-training optimization present in modern reasoning models but notably absent in standard instruction-tuned and pre-trained models (Llama 3.3 70B). We show that the entropy threshold to stop reasoning varies from model to model but can be calculated easily in one shot using only a few examples from existing reasoning datasets. Our results indicate that advanced reasoning models often know that they've gotten a correct answer early on, and that this emergent confidence awareness can be exploited to save tokens and reduce latency. The framework demonstrates consistent performance across reasoning-optimized model families with 25-50% computational cost reduction while preserving accuracy, revealing that confidence mechanisms represent a distinguishing characteristic of modern post-trained reasoning systems versus their predecessors.

Confidence calibration -- the problem of predicting probability estimates representative of the true correctness likelihood -- is important for classification models in many applications. We discover that modern neural networks, unlike those from a decade ago, are poorly calibrated. Through extensive experiments, we observe that depth, width, weight decay, and Batch Normalization are important factors influencing calibration. We evaluate the performance of various post-processing calibration methods on state-of-the-art architectures with image and document classification datasets. Our analysis and experiments not only offer insights into neural network learning, but also provide a simple and straightforward recipe for practical settings: on most datasets, temperature scaling -- a single-parameter variant of Platt Scaling -- is surprisingly effective at calibrating predictions.

The partial label challenge in Multi-Label Class-Incremental Learning (MLCIL) arises when only the new classes are labeled during training, while past and future labels remain unavailable. This issue leads to a proliferation of false-positive errors due to erroneously high confidence multi-label predictions, exacerbating catastrophic forgetting within the disjoint label space. In this paper, we aim to refine multi-label confidence calibration in MLCIL and propose a Confidence Self-Calibration (CSC) approach. Firstly, for label relationship calibration, we introduce a class-incremental graph convolutional network that bridges the isolated label spaces by constructing learnable, dynamically extended label relationship graph. Then, for confidence calibration, we present a max-entropy regularization for each multi-label increment, facilitating confidence self-calibration through the penalization of over-confident output distributions. Our approach attains new state-of-the-art results in MLCIL tasks on both MS-COCO and PASCAL VOC datasets, with the calibration of label confidences confirmed through our methodology.

Accurate confidence estimation is essential for trustworthy large language models (LLMs) systems, as it empowers the user to determine when to trust outputs and enables reliable deployment in safety-critical applications. Current confidence estimation methods for LLMs neglect the relevance between responses and contextual information, a crucial factor in output quality evaluation, particularly in scenarios where background knowledge is provided. To bridge this gap, we propose CRUX (Context-aware entropy Reduction and Unified consistency eXamination), the first framework that integrates context faithfulness and consistency for confidence estimation via two novel metrics. First, contextual entropy reduction represents data uncertainty with the information gain through contrastive sampling with and without context. Second, unified consistency examination captures potential model uncertainty through the global consistency of the generated answers with and without context. Experiments across three benchmark datasets (CoQA, SQuAD, QuAC) and two domain-specific datasets (BioASQ, EduQG) demonstrate CRUX's effectiveness, achieving the highest AUROC than existing baselines.

Wild Test-Time Adaptation (WTTA) is proposed to adapt a source model to unseen domains under extreme data scarcity and multiple shifts. Previous approaches mainly focused on sample selection strategies, while overlooking the fundamental problem on underlying optimization. Initially, we critically analyze the widely-adopted entropy minimization framework in WTTA and uncover its significant limitations in noisy optimization dynamics that substantially hinder adaptation efficiency. Through our analysis, we identify region confidence as a superior alternative to traditional entropy, however, its direct optimization remains computationally prohibitive for real-time applications. In this paper, we introduce a novel region-integrated method ReCAP that bypasses the lengthy process. Specifically, we propose a probabilistic region modeling scheme that flexibly captures semantic changes in embedding space. Subsequently, we develop a finite-to-infinite asymptotic approximation that transforms the intractable region confidence into a tractable and upper-bounded proxy. These innovations significantly unlock the overlooked potential dynamics in local region in a concise solution. Our extensive experiments demonstrate the consistent superiority of ReCAP over existing methods across various datasets and wild scenarios.

We study how to characterize and predict the truthfulness of texts generated from large language models (LLMs), which serves as a crucial step in building trust between humans and LLMs. Although several approaches based on entropy or verbalized uncertainty have been proposed to calibrate model predictions, these methods are often intractable, sensitive to hyperparameters, and less reliable when applied in generative tasks with LLMs. In this paper, we suggest investigating internal activations and quantifying LLM's truthfulness using the local intrinsic dimension (LID) of model activations. Through experiments on four question answering (QA) datasets, we demonstrate the effectiveness ohttps://info.arxiv.org/help/prep#abstractsf our proposed method. Additionally, we study intrinsic dimensions in LLMs and their relations with model layers, autoregressive language modeling, and the training of LLMs, revealing that intrinsic dimensions can be a powerful approach to understanding LLMs.

For safety-related applications, it is crucial to produce trustworthy deep neural networks whose prediction is associated with confidence that can represent the likelihood of correctness for subsequent decision-making. Existing dense binary classification models are prone to being over-confident. To improve model calibration, we propose Adaptive Stochastic Label Perturbation (ASLP) which learns a unique label perturbation level for each training image. ASLP employs our proposed Self-Calibrating Binary Cross Entropy (SC-BCE) loss, which unifies label perturbation processes including stochastic approaches (like DisturbLabel), and label smoothing, to correct calibration while maintaining classification rates. ASLP follows Maximum Entropy Inference of classic statistical mechanics to maximise prediction entropy with respect to missing information. It performs this while: (1) preserving classification accuracy on known data as a conservative solution, or (2) specifically improves model calibration degree by minimising the gap between the prediction accuracy and expected confidence of the target training label. Extensive results demonstrate that ASLP can significantly improve calibration degrees of dense binary classification models on both in-distribution and out-of-distribution data. The code is available on https://github.com/Carlisle-Liu/ASLP.

Quantifying the uncertainty of predictions made by large language models (LLMs) in binary text classification tasks remains a challenge. Calibration, in the context of LLMs, refers to the alignment between the model's predicted probabilities and the actual correctness of its predictions. A well-calibrated model should produce probabilities that accurately reflect the likelihood of its predictions being correct. We propose a novel approach that utilizes the inductive Venn--Abers predictor (IVAP) to calibrate the probabilities associated with the output tokens corresponding to the binary labels. Our experiments on the BoolQ dataset using the Llama 2 model demonstrate that IVAP consistently outperforms the commonly used temperature scaling method for various label token choices, achieving well-calibrated probabilities while maintaining high predictive quality. Our findings contribute to the understanding of calibration techniques for LLMs and provide a practical solution for obtaining reliable uncertainty estimates in binary question answering tasks, enhancing the interpretability and trustworthiness of LLM predictions.

Estimating uncertainty or confidence in the responses of a model can be significant in evaluating trust not only in the responses, but also in the model as a whole. In this paper, we explore the problem of estimating confidence for responses of large language models (LLMs) with simply black-box or query access to them. We propose a simple and extensible framework where, we engineer novel features and train a (interpretable) model (viz. logistic regression) on these features to estimate the confidence. We empirically demonstrate that our simple framework is effective in estimating confidence of flan-ul2, llama-13b and mistral-7b with it consistently outperforming existing black-box confidence estimation approaches on benchmark datasets such as TriviaQA, SQuAD, CoQA and Natural Questions by even over 10% (on AUROC) in some cases. Additionally, our interpretable approach provides insight into features that are predictive of confidence, leading to the interesting and useful discovery that our confidence models built for one LLM generalize zero-shot across others on a given dataset.

Test-time adaptation (TTA) methods, which generally rely on the model's predictions (e.g., entropy minimization) to adapt the source pretrained model to the unlabeled target domain, suffer from noisy signals originating from 1) incorrect or 2) open-set predictions. Long-term stable adaptation is hampered by such noisy signals, so training models without such error accumulation is crucial for practical TTA. To address these issues, including open-set TTA, we propose a simple yet effective sample selection method inspired by the following crucial empirical finding. While entropy minimization compels the model to increase the probability of its predicted label (i.e., confidence values), we found that noisy samples rather show decreased confidence values. To be more specific, entropy minimization attempts to raise the confidence values of an individual sample's prediction, but individual confidence values may rise or fall due to the influence of signals from numerous other predictions (i.e., wisdom of crowds). Due to this fact, noisy signals misaligned with such 'wisdom of crowds', generally found in the correct signals, fail to raise the individual confidence values of wrong samples, despite attempts to increase them. Based on such findings, we filter out the samples whose confidence values are lower in the adapted model than in the original model, as they are likely to be noisy. Our method is widely applicable to existing TTA methods and improves their long-term adaptation performance in both image classification (e.g., 49.4% reduced error rates with TENT) and semantic segmentation (e.g., 11.7% gain in mIoU with TENT).

In this work, we explore uncertainty estimation as a proxy for correctness in LLM-generated code. To this end, we adapt two state-of-the-art techniques from natural language generation -- one based on entropy and another on mutual information -- to the domain of code generation. Given the distinct semantic properties of code, we introduce modifications, including a semantic equivalence check based on symbolic execution. Our findings indicate a strong correlation between the uncertainty computed through these techniques and correctness, highlighting the potential of uncertainty estimation for quality assessment. Additionally, we propose a simplified version of the entropy-based method that assumes a uniform distribution over the LLM's responses, demonstrating comparable effectiveness. Using these techniques, we develop an abstention policy that prevents the model from making predictions when uncertainty is high, reducing incorrect outputs to near zero. Our evaluation on the LiveCodeBench shows that our approach significantly outperforms a baseline relying solely on LLM-reported log-probabilities.

Retrieval Augmented Generation (RAG) complements the knowledge of Large Language Models (LLMs) by leveraging external information to enhance response accuracy for queries. This approach is widely applied in several fields by taking its advantage of injecting the most up-to-date information, and researchers are focusing on understanding and improving this aspect to unlock the full potential of RAG in such high-stakes applications. However, despite the potential of RAG to address these needs, the mechanisms behind the confidence levels of its outputs remain underexplored, although the confidence of information is very critical in some domains, such as finance, healthcare, and medicine. Our study focuses the impact of RAG on confidence within the medical domain under various configurations and models. We evaluate confidence by treating the model's predicted probability as its output and calculating Expected Calibration Error (ECE) and Adaptive Calibration Error (ACE) scores based on the probabilities and accuracy. In addition, we analyze whether the order of retrieved documents within prompts calibrates the confidence. Our findings reveal large variation in confidence and accuracy depending on the model, settings, and the format of input prompts. These results underscore the necessity of optimizing configurations based on the specific model and conditions.

Empowering large language models to accurately express confidence in their answers is essential for trustworthy decision-making. Previous confidence elicitation methods, which primarily rely on white-box access to internal model information or model fine-tuning, have become less suitable for LLMs, especially closed-source commercial APIs. This leads to a growing need to explore the untapped area of black-box approaches for LLM uncertainty estimation. To better break down the problem, we define a systematic framework with three components: prompting strategies for eliciting verbalized confidence, sampling methods for generating multiple responses, and aggregation techniques for computing consistency. We then benchmark these methods on two key tasks-confidence calibration and failure prediction-across five types of datasets (e.g., commonsense and arithmetic reasoning) and five widely-used LLMs including GPT-4 and LLaMA 2 Chat. Our analysis uncovers several key insights: 1) LLMs, when verbalizing their confidence, tend to be overconfident, potentially imitating human patterns of expressing confidence. 2) As model capability scales up, both calibration and failure prediction performance improve. 3) Employing our proposed strategies, such as human-inspired prompts, consistency among multiple responses, and better aggregation strategies can help mitigate this overconfidence from various perspectives. 4) Comparisons with white-box methods indicate that while white-box methods perform better, the gap is narrow, e.g., 0.522 to 0.605 in AUROC. Despite these advancements, none of these techniques consistently outperform others, and all investigated methods struggle in challenging tasks, such as those requiring professional knowledge, indicating significant scope for improvement. We believe this study can serve as a strong baseline and provide insights for eliciting confidence in black-box LLMs.

Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes error, and epistemic uncertainty via the size of the set. In this paper, we extend the notion of calibration, which is commonly used to evaluate the validity of the aleatoric uncertainty representation of a single probabilistic classifier, to assess the validity of an epistemic uncertainty representation obtained by sets of probabilistic classifiers. Broadly speaking, we call a set of probabilistic classifiers calibrated if one can find a calibrated convex combination of these classifiers. To evaluate this notion of calibration, we propose a novel nonparametric calibration test that generalizes an existing test for single probabilistic classifiers to the case of sets of probabilistic classifiers. Making use of this test, we empirically show that ensembles of deep neural networks are often not well calibrated.

Test-time adaptation (TTA) fine-tunes pre-trained deep neural networks for unseen test data. The primary challenge of TTA is limited access to the entire test dataset during online updates, causing error accumulation. To mitigate it, TTA methods have utilized the model output's entropy as a confidence metric that aims to determine which samples have a lower likelihood of causing error. Through experimental studies, however, we observed the unreliability of entropy as a confidence metric for TTA under biased scenarios and theoretically revealed that it stems from the neglect of the influence of latent disentangled factors of data on predictions. Building upon these findings, we introduce a novel TTA method named Destroy Your Object (DeYO), which leverages a newly proposed confidence metric named Pseudo-Label Probability Difference (PLPD). PLPD quantifies the influence of the shape of an object on prediction by measuring the difference between predictions before and after applying an object-destructive transformation. DeYO consists of sample selection and sample weighting, which employ entropy and PLPD concurrently. For robust adaptation, DeYO prioritizes samples that dominantly incorporate shape information when making predictions. Our extensive experiments demonstrate the consistent superiority of DeYO over baseline methods across various scenarios, including biased and wild. Project page is publicly available at https://whitesnowdrop.github.io/DeYO/.

Recent advances in machine learning have significantly improved prediction accuracy in various applications. However, ensuring the calibration of probabilistic predictions remains a significant challenge. Despite efforts to enhance model calibration, the rigorous statistical evaluation of model calibration remains less explored. In this work, we develop confidence intervals the ell_2 Expected Calibration Error (ECE). We consider top-1-to-k calibration, which includes both the popular notion of confidence calibration as well as full calibration. For a debiased estimator of the ECE, we show asymptotic normality, but with different convergence rates and asymptotic variances for calibrated and miscalibrated models. We develop methods to construct asymptotically valid confidence intervals for the ECE, accounting for this behavior as well as non-negativity. Our theoretical findings are supported through extensive experiments, showing that our methods produce valid confidence intervals with shorter lengths compared to those obtained by resampling-based methods.

The ability to acknowledge the inevitable uncertainty in their knowledge and reasoning is a prerequisite for AI systems to be truly truthful and reliable. In this paper, we present a taxonomy of uncertainty specific to vision-language AI systems, distinguishing between epistemic uncertainty (arising from a lack of information) and aleatoric uncertainty (due to inherent unpredictability), and further explore finer categories within. Based on this taxonomy, we synthesize a benchmark dataset, CertainlyUncertain, featuring 178K visual question answering (VQA) samples as contrastive pairs. This is achieved by 1) inpainting images to make previously answerable questions into unanswerable ones; and 2) using image captions to prompt large language models for both answerable and unanswerable questions. Additionally, we introduce a new metric confidence-weighted accuracy, that is well correlated with both accuracy and calibration error, to address the shortcomings of existing metrics.

Large language models (LLMs) produce outputs with varying levels of uncertainty, and, just as often, varying levels of correctness; making their practical reliability far from guaranteed. To quantify this uncertainty, we systematically evaluate four approaches for confidence estimation in LLM outputs: VCE, MSP, Sample Consistency, and CoCoA (Vashurin et al., 2025). For the evaluation of the approaches, we conduct experiments on four question-answering tasks using a state-of-the-art open-source LLM. Our results show that each uncertainty metric captures a different facet of model confidence and that the hybrid CoCoA approach yields the best reliability overall, improving both calibration and discrimination of correct answers. We discuss the trade-offs of each method and provide recommendations for selecting uncertainty measures in LLM applications.

A model must adapt itself to generalize to new and different data during testing. In this setting of fully test-time adaptation the model has only the test data and its own parameters. We propose to adapt by test entropy minimization (tent): we optimize the model for confidence as measured by the entropy of its predictions. Our method estimates normalization statistics and optimizes channel-wise affine transformations to update online on each batch. Tent reduces generalization error for image classification on corrupted ImageNet and CIFAR-10/100 and reaches a new state-of-the-art error on ImageNet-C. Tent handles source-free domain adaptation on digit recognition from SVHN to MNIST/MNIST-M/USPS, on semantic segmentation from GTA to Cityscapes, and on the VisDA-C benchmark. These results are achieved in one epoch of test-time optimization without altering training.

Generating accurate and calibrated confidence estimates is critical for deploying LLMs in high-stakes or user-facing applications, and remains an open challenge. Prior research has often framed confidence as a problem of eliciting a model's "self-knowledge", i.e., the ability of an LLM to judge whether its own answers are correct; this approach implicitly assumes that there is some privileged information about the answer's correctness that is accessible to the model itself. However, our experiments reveal that an LLM attempting to predict the correctness of its own outputs generally performs no better than an unrelated LLM. Moreover, we hypothesize that a key factor in building a "Correctness Model" (CM) is exposure to a target model's historical predictions. We propose multiple methods to inject this historical correctness information, creating a Generalized Correctness Model (GCM). We first show that GCMs can be trained on the correctness data from many LLMs and learn patterns for correctness prediction applicable across datasets and models. We then use CMs as a lens for studying the source of correctness prediction ability and its generalization, systematically controlling their training data and finding that answer phrasing is a strong predictor for correctness. We further explore alternative methods of injecting history without training an LLM, finding that including history as in-context examples can help improve correctness prediction, and post-hoc calibration can provide complementary reductions in calibration error. We evaluate GCMs based on Qwen3-8B across 5 model families and the MMLU and TriviaQA datasets, as well as on a downstream selective prediction task, finding that reliable LLM confidence estimation is a generalizable and model-agnostic skill learned by systematically encoding correctness history rather than a model-specific skill reliant on self-introspection.

Uncertainty quantification (UQ) is vital for trustworthy deep learning, yet existing methods are either computationally intensive, such as Bayesian or ensemble methods, or provide only partial, task-specific estimates, such as single-forward-pass techniques. In this paper, we propose a post-hoc single-forward-pass framework that jointly captures aleatoric and epistemic uncertainty without modifying or retraining pretrained models. Our method applies Split-Point Analysis (SPA) to decompose predictive residuals into upper and lower subsets, computing Mean Absolute Residuals (MARs) on each side. We prove that, under ideal conditions, the total MAR equals the harmonic mean of subset MARs; deviations define a novel Self-consistency Discrepancy Score (SDS) for fine-grained epistemic estimation across regression and classification. For regression, side-specific quantile regression yields prediction intervals with improved empirical coverage, which are further calibrated via SDS. For classification, when calibration data are available, we apply SPA-based calibration identities to adjust the softmax outputs and then compute predictive entropy on these calibrated probabilities. Extensive experiments on diverse regression and classification benchmarks demonstrate that our framework matches or exceeds several state-of-the-art UQ methods while incurring minimal overhead. Our source code is available at https://github.com/zzz0527/SPC-UQ.

We address the neural network robustness problem by adding Similarity (i.e., correctly predicted depth-matches into training)-awareness and Distance-to-training-distribution-awareness to the existing output Magnitude (i.e., decision-boundary)-awareness of the softmax function. The resulting SDM activation function provides strong signals of the relative epistemic (reducible) predictive uncertainty. We use this novel behavior to further address the complementary HCI problem of mapping the output to human-interpretable summary statistics over relevant partitions of a held-out calibration set. Estimates of prediction-conditional uncertainty are obtained via a parsimonious learned transform over the class-conditional empirical CDFs of the output of a final-layer SDM activation function. For decision-making and as an intrinsic model check, estimates of class-conditional accuracy are obtained by further partitioning the high-probability regions of this calibrated output into class-conditional, region-specific CDFs. The uncertainty estimates from SDM calibration are remarkably robust to test-time distribution shifts and out-of-distribution inputs; incorporate awareness of the effective sample size; provide estimates of uncertainty from the learning and data splitting processes; and are well-suited for selective classification and conditional branching for additional test-time compute based on the predictive uncertainty, as for selective LLM generation, routing, and composition over multiple models and retrieval. Finally, we construct SDM networks, LLMs with uncertainty-aware verification and interpretability-by-exemplar as intrinsic properties. We provide open-source software implementing these results.

Large language models (LLMs) often generate inaccurate or fabricated information and generally fail to indicate their confidence, which limits their broader applications. Previous work elicits confidence from LLMs by direct or self-consistency prompting, or constructing specific datasets for supervised finetuning. The prompting-based approaches have inferior performance, and the training-based approaches are limited to binary or inaccurate group-level confidence estimates. In this work, we present the advanced SaySelf, a training framework that teaches LLMs to express more accurate fine-grained confidence estimates. In addition, beyond the confidence scores, SaySelf initiates the process of directing LLMs to produce self-reflective rationales that clearly identify gaps in their parametric knowledge and explain their uncertainty. This is achieved by using an LLM to automatically summarize the uncertainties in specific knowledge via natural language. The summarization is based on the analysis of the inconsistency in multiple sampled reasoning chains, and the resulting data is utilized for supervised fine-tuning. Moreover, we utilize reinforcement learning with a meticulously crafted reward function to calibrate the confidence estimates, motivating LLMs to deliver accurate, high-confidence predictions and to penalize overconfidence in erroneous outputs. Experimental results in both in-distribution and out-of-distribution datasets demonstrate the effectiveness of SaySelf in reducing the confidence calibration error and maintaining the task performance. We show that the generated self-reflective rationales are reasonable and can further contribute to the calibration. The code is made public at https://github.com/xu1868/SaySelf.

Self-training is a well-known approach for semi-supervised learning. It consists of iteratively assigning pseudo-labels to unlabeled data for which the model is confident and treating them as labeled examples. For neural networks, softmax prediction probabilities are often used as a confidence measure, although they are known to be overconfident, even for wrong predictions. This phenomenon is particularly intensified in the presence of sample selection bias, i.e., when data labeling is subject to some constraint. To address this issue, we propose a novel confidence measure, called T-similarity, built upon the prediction diversity of an ensemble of linear classifiers. We provide the theoretical analysis of our approach by studying stationary points and describing the relationship between the diversity of the individual members and their performance. We empirically demonstrate the benefit of our confidence measure for three different pseudo-labeling policies on classification datasets of various data modalities. The code is available at https://github.com/ambroiseodt/tsim.

A critical component in the trustworthiness of LLMs is reliable uncertainty communication, yet LLMs often use assertive language when conveying false claims, leading to over-reliance and eroded trust. We present the first systematic study of faithful confidence calibration of LLMs, benchmarking models' ability to use linguistic expressions of uncertainty that faithfully reflect their intrinsic uncertainty, across a comprehensive array of models, datasets, and prompting strategies. Our results demonstrate that LLMs largely fail at this task, and that existing interventions are insufficient: standard prompt approaches provide only marginal gains, and existing, factuality-based calibration techniques can even harm faithful calibration. To address this critical gap, we introduce MetaFaith, a novel prompt-based calibration approach inspired by human metacognition. We show that MetaFaith robustly improves faithful calibration across diverse models and task domains, enabling up to 61% improvement in faithfulness and achieving an 83% win rate over original generations as judged by humans.

A probabilistic classifier with reliable predictive uncertainties i) fits successfully to the target domain data, ii) provides calibrated class probabilities in difficult regions of the target domain (e.g.\ class overlap), and iii) accurately identifies queries coming out of the target domain and rejects them. We introduce an original combination of Evidential Deep Learning, Neural Processes, and Neural Turing Machines capable of providing all three essential properties mentioned above for total uncertainty quantification. We observe our method on five classification tasks to be the only one that can excel all three aspects of total calibration with a single standalone predictor. Our unified solution delivers an implementation-friendly and compute efficient recipe for safety clearance and provides intellectual economy to an investigation of algorithmic roots of epistemic awareness in deep neural nets.

Increasing test-time computation is a straightforward approach to enhancing the quality of responses in Large Language Models (LLMs). While Best-of-N sampling and Self-Consistency with majority voting are simple and effective, they require a fixed number of sampling responses for each query, regardless of its complexity. This could result in wasted computation for simpler questions and insufficient exploration for more challenging ones. In this work, we argue that model confidence of responses can be used for improving the efficiency of test-time scaling. Unfortunately, LLMs are known to be overconfident and provide unreliable confidence estimation. To address this limitation, we introduce Self-Calibration by distilling Self-Consistency-derived confidence into the model itself. This enables reliable confidence estimation at test time with one forward pass. We then design confidence-based efficient test-time scaling methods to handle queries of various difficulty, such as Early-Stopping for Best-of-N and Self-Consistency with calibrated confidence. Experiments on three LLMs across six datasets demonstrate the effectiveness of our approach. Specifically, applying confidence-based Early Stopping to Best-of-N improves MathQA accuracy from 81.0 to 83.6 with a sample budget of 16 responses, indicating the efficacy of confidence-based sampling strategy at inference time.

We investigate the problem of determining the predictive confidence (or, conversely, uncertainty) of a neural classifier through the lens of low-resource languages. By training models on sub-sampled datasets in three different languages, we assess the quality of estimates from a wide array of approaches and their dependence on the amount of available data. We find that while approaches based on pre-trained models and ensembles achieve the best results overall, the quality of uncertainty estimates can surprisingly suffer with more data. We also perform a qualitative analysis of uncertainties on sequences, discovering that a model's total uncertainty seems to be influenced to a large degree by its data uncertainty, not model uncertainty. All model implementations are open-sourced in a software package.

Misclassification detection is an important problem in machine learning, as it allows for the identification of instances where the model's predictions are unreliable. However, conventional uncertainty measures such as Shannon entropy do not provide an effective way to infer the real uncertainty associated with the model's predictions. In this paper, we introduce a novel data-driven measure of uncertainty relative to an observer for misclassification detection. By learning patterns in the distribution of soft-predictions, our uncertainty measure can identify misclassified samples based on the predicted class probabilities. Interestingly, according to the proposed measure, soft-predictions corresponding to misclassified instances can carry a large amount of uncertainty, even though they may have low Shannon entropy. We demonstrate empirical improvements over multiple image classification tasks, outperforming state-of-the-art misclassification detection methods.

Deep neural networks have demonstrated remarkable performance across numerous learning tasks but often suffer from miscalibration, resulting in unreliable probability outputs. This has inspired many recent works on mitigating miscalibration, particularly through post-hoc recalibration methods that aim to obtain calibrated probabilities without sacrificing the classification performance of pre-trained models. In this study, we summarize and categorize previous works into three general strategies: intuitively designed methods, binning-based methods, and methods based on formulations of ideal calibration. Through theoretical and practical analysis, we highlight ten common limitations in previous approaches. To address these limitations, we propose a probabilistic learning framework for calibration called h-calibration, which theoretically constructs an equivalent learning formulation for canonical calibration with boundedness. On this basis, we design a simple yet effective post-hoc calibration algorithm. Our method not only overcomes the ten identified limitations but also achieves markedly better performance than traditional methods, as validated by extensive experiments. We further analyze, both theoretically and experimentally, the relationship and advantages of our learning objective compared to traditional proper scoring rule. In summary, our probabilistic framework derives an approximately equivalent differentiable objective for learning error-bounded calibrated probabilities, elucidating the correspondence and convergence properties of computational statistics with respect to theoretical bounds in canonical calibration. The theoretical effectiveness is verified on standard post-hoc calibration benchmarks by achieving state-of-the-art performance. This research offers valuable reference for learning reliable likelihood in related fields.

Ensuring reliable confidence scores from deep neural networks is of paramount significance in critical decision-making systems, particularly in real-world domains such as healthcare. Recent literature on calibrating deep segmentation networks has resulted in substantial progress. Nevertheless, these approaches are strongly inspired by the advancements in classification tasks, and thus their uncertainty is usually modeled by leveraging the information of individual pixels, disregarding the local structure of the object of interest. Indeed, only the recent Spatially Varying Label Smoothing (SVLS) approach considers pixel spatial relationships across classes, by softening the pixel label assignments with a discrete spatial Gaussian kernel. In this work, we first present a constrained optimization perspective of SVLS and demonstrate that it enforces an implicit constraint on soft class proportions of surrounding pixels. Furthermore, our analysis shows that SVLS lacks a mechanism to balance the contribution of the constraint with the primary objective, potentially hindering the optimization process. Based on these observations, we propose NACL (Neighbor Aware CaLibration), a principled and simple solution based on equality constraints on the logit values, which enables to control explicitly both the enforced constraint and the weight of the penalty, offering more flexibility. Comprehensive experiments on a wide variety of well-known segmentation benchmarks demonstrate the superior calibration performance of the proposed approach, without affecting its discriminative power. Furthermore, ablation studies empirically show the model agnostic nature of our approach, which can be used to train a wide span of deep segmentation networks.

Numerous crucial tasks in real-world decision-making rely on machine learning algorithms with calibrated uncertainty estimates. However, modern methods often yield overconfident and uncalibrated predictions. Various approaches involve training an ensemble of separate models to quantify the uncertainty related to the model itself, known as epistemic uncertainty. In an explicit implementation, the ensemble approach has high computational cost and high memory requirements. This particular challenge is evident in state-of-the-art neural networks such as transformers, where even a single network is already demanding in terms of compute and memory. Consequently, efforts are made to emulate the ensemble model without actually instantiating separate ensemble members, referred to as implicit ensembling. We introduce LoRA-Ensemble, a parameter-efficient deep ensemble method for self-attention networks, which is based on Low-Rank Adaptation (LoRA). Initially developed for efficient LLM fine-tuning, we extend LoRA to an implicit ensembling approach. By employing a single pre-trained self-attention network with weights shared across all members, we train member-specific low-rank matrices for the attention projections. Our method exhibits superior calibration compared to explicit ensembles and achieves similar or better accuracy across various prediction tasks and datasets.

Accurate confidence calibration in Large Language Models (LLMs) is critical for safe use in high-stakes domains, where clear verbalized confidence enhances user trust. Traditional methods that mimic reference confidence expressions often fail to capture the reasoning needed for accurate confidence assessment. We propose natural language critiques as a solution, ideally suited for confidence calibration, as precise gold confidence labels are hard to obtain and often require multiple generations. This paper studies how natural language critiques can enhance verbalized confidence, addressing: (1) What to critique: uncertainty (question-focused) or confidence (answer-specific)? Analysis shows confidence suits multiple-choice tasks, while uncertainty excels in open-ended scenarios. (2) How to critique: self-critique or critique calibration training? We propose Self-Critique, enabling LLMs to critique and optimize their confidence beyond mere accuracy, and CritiCal, a novel Critique Calibration training method that leverages natural language critiques to improve confidence calibration, moving beyond direct numerical optimization. Experiments show that CritiCal significantly outperforms Self-Critique and other competitive baselines, even surpassing its teacher model, GPT-4o, in complex reasoning tasks. CritiCal also shows robust generalization in out-of-distribution settings, advancing LLM's reliability.

This paper presents a novel technique for accelerating inference in large, pre-trained language models (LLMs) by introducing early exits during inference. The computational demands of these models, used across a wide range of applications, can be substantial. By capitalizing on the inherent variability in token complexity, our approach enables selective acceleration of the inference process. Specifically, we propose the integration of early exit ''heads'' atop existing transformer layers, which facilitate conditional terminations based on a confidence metric. These heads are trained in a self-supervised manner using the model's own predictions as training data, thereby eliminating the need for additional annotated data. The confidence metric, established using a calibration set, ensures a desired level of accuracy while enabling early termination when confidence exceeds a predetermined threshold. Notably, our method preserves the original accuracy and reduces computational time on certain tasks, leveraging the existing knowledge of pre-trained LLMs without requiring extensive retraining. This lightweight, modular modification has the potential to greatly enhance the practical usability of LLMs, particularly in applications like real-time language processing in resource-constrained environments.

Honesty alignment-the ability of large language models (LLMs) to recognize their knowledge boundaries and express calibrated confidence-is essential for trustworthy deployment. Existing methods either rely on training-free confidence estimation (e.g., token probabilities, self-consistency) or training-based calibration with correctness annotations. While effective, achieving universal honesty alignment with training-based calibration requires costly, large-scale labeling. To support annotation-efficient training, we introduce Elicitation-Then-Calibration (EliCal), a two-stage framework that first elicits internal confidence using inexpensive self-consistency supervision, then calibrates this confidence with a small set of correctness annotations. To support a large-scale study, we release HonestyBench, a benchmark covering ten free-form QA datasets with 560k training and 70k evaluation instances annotated with correctness and self-consistency signals. Experiments show that EliCal achieves near-optimal alignment with only 1k correctness annotations (0.18% of full supervision) and better alignment performance on unseen MMLU tasks than the calibration-only baseline, offering a scalable solution toward universal honesty alignment in LLMs.

In this paper, we uncover a systematic bias in the evaluation paradigm of adopting large language models~(LLMs), e.g., GPT-4, as a referee to score and compare the quality of responses generated by candidate models. We find that the quality ranking of candidate responses can be easily hacked by simply altering their order of appearance in the context. This manipulation allows us to skew the evaluation result, making one model appear considerably superior to the other, e.g., Vicuna-13B could beat ChatGPT on 66 over 80 tested queries with ChatGPT as an evaluator. To address this issue, we propose a calibration framework with three simple yet effective strategies: 1) Multiple Evidence Calibration, which requires the evaluator model to generate multiple evaluation evidence before assigning ratings; 2) Balanced Position Calibration, which aggregates results across various orders to determine the final score; 3) Human-in-the-Loop Calibration, which introduces a balanced position diversity entropy to measure the difficulty of each example and seeks human assistance when needed. We also manually annotate the "win/tie/lose" outcomes of responses from ChatGPT and Vicuna-13B in the Vicuna Benchmark's question prompt, and extensive experiments demonstrate that our approach successfully mitigates evaluation bias, resulting in closer alignment with human judgments. We release our code and human annotation at https://github.com/i-Eval/FairEval to facilitate future research.

Hallucination in large language models (LLMs) can be detected by assessing the uncertainty of model outputs, typically measured using entropy. Semantic entropy (SE) enhances traditional entropy estimation by quantifying uncertainty at the semantic cluster level. However, as modern LLMs generate longer one-sentence responses, SE becomes less effective because it overlooks two crucial factors: intra-cluster similarity (the spread within a cluster) and inter-cluster similarity (the distance between clusters). To address these limitations, we propose a simple black-box uncertainty quantification method inspired by nearest neighbor estimates of entropy. Our approach can also be easily extended to white-box settings by incorporating token probabilities. Additionally, we provide theoretical results showing that our method generalizes semantic entropy. Extensive empirical results demonstrate its effectiveness compared to semantic entropy across two recent LLMs (Phi3 and Llama3) and three common text generation tasks: question answering, text summarization, and machine translation. Our code is available at https://github.com/BigML-CS-UCLA/SNNE.

Large language models (LLMs) have demonstrated remarkable capabilities across a wide range of tasks in various domains. Despite their impressive performance, they can be unreliable due to factual errors in their generations. Assessing their confidence and calibrating them across different tasks can help mitigate risks and enable LLMs to produce better generations. There has been a lot of recent research aiming to address this, but there has been no comprehensive overview to organize it and outline the main lessons learned. The present survey aims to bridge this gap. In particular, we outline the challenges and we summarize recent technical advancements for LLM confidence estimation and calibration. We further discuss their applications and suggest promising directions for future work.

Model calibration aims to align confidence with prediction correctness. The Cross-Entropy (CE) loss is widely used for calibrator training, which enforces the model to increase confidence on the ground truth class. However, we find the CE loss has intrinsic limitations. For example, for a narrow misclassification, a calibrator trained by the CE loss often produces high confidence on the wrongly predicted class (e.g., a test sample is wrongly classified and its softmax score on the ground truth class is around 0.4), which is undesirable. In this paper, we propose a new post-hoc calibration objective derived from the aim of calibration. Intuitively, the proposed objective function asks that the calibrator decrease model confidence on wrongly predicted samples and increase confidence on correctly predicted samples. Because a sample itself has insufficient ability to indicate correctness, we use its transformed versions (e.g., rotated, greyscaled and color-jittered) during calibrator training. Trained on an in-distribution validation set and tested with isolated, individual test samples, our method achieves competitive calibration performance on both in-distribution and out-of-distribution test sets compared with the state of the art. Further, our analysis points out the difference between our method and commonly used objectives such as CE loss and mean square error loss, where the latters sometimes deviates from the calibration aim.

When using large language models (LLMs) in high-stakes applications, we need to know when we can trust their predictions. Some works argue that prompting high-performance LLMs is sufficient to produce calibrated uncertainties, while others introduce sampling methods that can be prohibitively expensive. In this work, we first argue that prompting on its own is insufficient to achieve good calibration and then show that fine-tuning on a small dataset of correct and incorrect answers can create an uncertainty estimate with good generalization and small computational overhead. We show that a thousand graded examples are sufficient to outperform baseline methods and that training through the features of a model is necessary for good performance and tractable for large open-source models when using LoRA. We also investigate the mechanisms that enable reliable LLM uncertainty estimation, finding that many models can be used as general-purpose uncertainty estimators, applicable not just to their own uncertainties but also the uncertainty of other models. Lastly, we show that uncertainty estimates inform human use of LLMs in human-AI collaborative settings through a user study.

Tool-using agents that act in the world need to be both useful and safe. Well-calibrated model confidences can be used to weigh the risk versus reward of potential actions, but prior work shows that many models are poorly calibrated. Inspired by interpretability literature exploring the internals of models, we propose a novel class of model-internal confidence estimators (MICE) to better assess confidence when calling tools. MICE first decodes from each intermediate layer of the language model using logitLens and then computes similarity scores between each layer's generation and the final output. These features are fed into a learned probabilistic classifier to assess confidence in the decoded output. On the simulated trial and error (STE) tool-calling dataset using Llama3 models, we find that MICE beats or matches the baselines on smoothed expected calibration error. Using MICE confidences to determine whether to call a tool significantly improves over strong baselines on a new metric, expected tool-calling utility. Further experiments show that MICE is sample-efficient, can generalize zero-shot to unseen APIs, and results in higher tool-calling utility in scenarios with varying risk levels. Our code is open source, available at https://github.com/microsoft/mice_for_cats.

Retrieval-Augmented Generation (RAG) mitigates hallucinations in Large Language Models (LLMs) by integrating external knowledge. However, conflicts between parametric knowledge and retrieved context pose challenges, particularly when retrieved information is unreliable or the model's internal knowledge is outdated. In such cases, LLMs struggle to determine whether to rely more on their own parameters or the conflicted context. To address this, we propose **CK-PLUG**, a plug-and-play method for controlling LLMs' reliance on parametric and contextual knowledge. We introduce a novel knowledge consistency metric, Confidence Gain, which detects knowledge conflicts by measuring entropy shifts in token probability distributions after context insertion. CK-PLUG then enables fine-grained control over knowledge preference by adjusting the probability distribution of tokens with negative confidence gain through a single tuning parameter. Experiments demonstrate CK-PLUG's ability to significantly regulate knowledge reliance in counterfactual RAG scenarios while maintaining generation fluency and knowledge accuracy. For instance, on Llama3-8B, memory recall (MR) of RAG response can be adjusted within a broad range (9.9%-71.9%), compared to the baseline of 42.1%. Moreover, CK-PLUG supports adaptive control based on the model's confidence in both internal and external knowledge, achieving consistent performance improvements across various general RAG tasks. Our code is available at: https://github.com/byronBBL/CK-PLUG{this https URL}.

A trustworthy real-world prediction system should produce well-calibrated confidence scores; that is, its confidence in an answer should be indicative of the likelihood that the answer is correct, enabling deferral to an expert in cases of low-confidence predictions. Recent studies have shown that unsupervised pre-training produces large language models (LMs) whose conditional probabilities are remarkably well-calibrated. However, the most widely-used LMs are fine-tuned with reinforcement learning from human feedback (RLHF-LMs), and some studies have suggested that RLHF-LMs produce conditional probabilities that are very poorly calibrated. In light of this perceived weakness, we conduct a broad evaluation of methods for extracting confidence scores from RLHF-LMs. For RLHF-LMs such as ChatGPT, GPT-4, and Claude, we find that verbalized confidences emitted as output tokens are typically better-calibrated than the model's conditional probabilities on the TriviaQA, SciQ, and TruthfulQA benchmarks, often reducing the expected calibration error by a relative 50%.

We present a principled approach to provide LLM-based evaluation with a rigorous guarantee of human agreement. We first propose that a reliable evaluation method should not uncritically rely on model preferences for pairwise evaluation, but rather assess the confidence of judge models and selectively decide when to trust its judgement. We then show that under this selective evaluation framework, human agreement can be provably guaranteed -- such that the model evaluation aligns with that of humans to a user-specified agreement level. As part of our framework, we also introduce Simulated Annotators, a novel confidence estimation method that significantly improves judge calibration and thus enables high coverage of evaluated instances. Finally, we propose Cascaded Selective Evaluation, where we use cheaper models as initial judges and escalate to stronger models only when necessary -- again, while still providing a provable guarantee of human agreement. Experimental results show that Cascaded Selective Evaluation guarantees strong alignment with humans, far beyond what LLM judges could achieve without selective evaluation. For example, on a subset of Chatbot Arena where GPT-4 almost never achieves 80% human agreement, our method, even while employing substantially cost-effective models such as Mistral-7B, guarantees over 80% human agreement with almost 80% test coverage.

In any ranking system, the retrieval model outputs a single score for a document based on its belief on how relevant it is to a given search query. While retrieval models have continued to improve with the introduction of increasingly complex architectures, few works have investigated a retrieval model's belief in the score beyond the scope of a single value. We argue that capturing the model's uncertainty with respect to its own scoring of a document is a critical aspect of retrieval that allows for greater use of current models across new document distributions, collections, or even improving effectiveness for down-stream tasks. In this paper, we address this problem via an efficient Bayesian framework for retrieval models which captures the model's belief in the relevance score through a stochastic process while adding only negligible computational overhead. We evaluate this belief via a ranking based calibration metric showing that our approximate Bayesian framework significantly improves a retrieval model's ranking effectiveness through a risk aware reranking as well as its confidence calibration. Lastly, we demonstrate that this additional uncertainty information is actionable and reliable on down-stream tasks represented via cutoff prediction.

Large language models (LLMs) are increasingly used in high-stakes settings, where overconfident responses can mislead users. Reliable confidence estimation has been shown to enhance trust and task accuracy. Yet existing methods face practical barriers: logits are often hidden, multi-sampling is computationally expensive, and verbalized numerical uncertainty (e.g., giving a 0-100 score) deviates from natural communication. We revisit linguistic confidence (LC), where models express uncertainty through hedging language (e.g., probably, might), offering a lightweight and human-centered alternative. To advance this direction, we (1) release the first diverse, large-scale dataset of hedging expressions with human-annotated confidence scores, and (2) propose a lightweight mapper that converts hedges into confidence scores at near-zero cost. Building on these resources, we (3) conduct the first systematic study of LC across modern LLMs and QA benchmarks, revealing that while most LLMs underperform in expressing reliable LC, carefully designed prompting achieves competitive calibration and discriminability. Finally, we (4) introduce a fine-tuning framework that further improves LC reliability. Taken together, our work positions linguistic confidence as a scalable, efficient, and human-aligned approach to LLM uncertainty estimation, and calls for deeper exploration of this promising yet underexplored direction.

Miscalibration in Large Language Models (LLMs) undermines their reliability, highlighting the need for accurate confidence estimation. We introduce CCPS (Calibrating LLM Confidence by Probing Perturbed Representation Stability), a novel method analyzing internal representational stability in LLMs. CCPS applies targeted adversarial perturbations to final hidden states, extracts features reflecting the model's response to these perturbations, and uses a lightweight classifier to predict answer correctness. CCPS was evaluated on LLMs from 8B to 32B parameters (covering Llama, Qwen, and Mistral architectures) using MMLU and MMLU-Pro benchmarks in both multiple-choice and open-ended formats. Our results show that CCPS significantly outperforms current approaches. Across four LLMs and three MMLU variants, CCPS reduces Expected Calibration Error by approximately 55% and Brier score by 21%, while increasing accuracy by 5 percentage points, Area Under the Precision-Recall Curve by 4 percentage points, and Area Under the Receiver Operating Characteristic Curve by 6 percentage points, all relative to the strongest prior method. CCPS delivers an efficient, broadly applicable, and more accurate solution for estimating LLM confidence, thereby improving their trustworthiness.

We introduce a method to measure uncertainty in large language models. For tasks like question answering, it is essential to know when we can trust the natural language outputs of foundation models. We show that measuring uncertainty in natural language is challenging because of "semantic equivalence" -- different sentences can mean the same thing. To overcome these challenges we introduce semantic entropy -- an entropy which incorporates linguistic invariances created by shared meanings. Our method is unsupervised, uses only a single model, and requires no modifications to off-the-shelf language models. In comprehensive ablation studies we show that the semantic entropy is more predictive of model accuracy on question answering data sets than comparable baselines.

Uncertainty estimation is crucial for evaluating Large Language Models (LLMs), particularly in high-stakes domains where incorrect answers result in significant consequences. Numerous approaches consider this problem, while focusing on a specific type of uncertainty, ignoring others. We investigate what estimates, specifically token-wise entropy and model-as-judge (MASJ), would work for multiple-choice question-answering tasks for different question topics. Our experiments consider three LLMs: Phi-4, Mistral, and Qwen of different sizes from 1.5B to 72B and 14 topics. While MASJ performs similarly to a random error predictor, the response entropy predicts model error in knowledge-dependent domains and serves as an effective indicator of question difficulty: for biology ROC AUC is 0.73. This correlation vanishes for the reasoning-dependent domain: for math questions ROC-AUC is 0.55. More principally, we found out that the entropy measure required a reasoning amount. Thus, data-uncertainty related entropy should be integrated within uncertainty estimates frameworks, while MASJ requires refinement. Moreover, existing MMLU-Pro samples are biased, and should balance required amount of reasoning for different subdomains to provide a more fair assessment of LLMs performance.

Multimodal machine learning has achieved remarkable progress in a wide range of scenarios. However, the reliability of multimodal learning remains largely unexplored. In this paper, through extensive empirical studies, we identify current multimodal classification methods suffer from unreliable predictive confidence that tend to rely on partial modalities when estimating confidence. Specifically, we find that the confidence estimated by current models could even increase when some modalities are corrupted. To address the issue, we introduce an intuitive principle for multimodal learning, i.e., the confidence should not increase when one modality is removed. Accordingly, we propose a novel regularization technique, i.e., Calibrating Multimodal Learning (CML) regularization, to calibrate the predictive confidence of previous methods. This technique could be flexibly equipped by existing models and improve the performance in terms of confidence calibration, classification accuracy, and model robustness.

When language models (LMs) are trained via reinforcement learning (RL) to generate natural language "reasoning chains", their performance improves on a variety of difficult question answering tasks. Today, almost all successful applications of RL for reasoning use binary reward functions that evaluate the correctness of LM outputs. Because such reward functions do not penalize guessing or low-confidence outputs, they often have the unintended side-effect of degrading calibration and increasing the rate at which LMs generate incorrect responses (or "hallucinate") in other problem domains. This paper describes RLCR (Reinforcement Learning with Calibration Rewards), an approach to training reasoning models that jointly improves accuracy and calibrated confidence estimation. During RLCR, LMs generate both predictions and numerical confidence estimates after reasoning. They are trained to optimize a reward function that augments a binary correctness score with a Brier score -- a scoring rule for confidence estimates that incentivizes calibrated prediction. We first prove that this reward function (or any analogous reward function that uses a bounded, proper scoring rule) yields models whose predictions are both accurate and well-calibrated. We next show that across diverse datasets, RLCR substantially improves calibration with no loss in accuracy, on both in-domain and out-of-domain evaluations -- outperforming both ordinary RL training and classifiers trained to assign post-hoc confidence scores. While ordinary RL hurts calibration, RLCR improves it. Finally, we demonstrate that verbalized confidence can be leveraged at test time to improve accuracy and calibration via confidence-weighted scaling methods. Our results show that explicitly optimizing for calibration can produce more generally reliable reasoning models.

We consider the problem of ranking n experts based on their performances on d tasks. We make a monotonicity assumption stating that for each pair of experts, one outperforms the other on all tasks. We consider the sequential setting where in each round, the learner has access to noisy evaluations of actively chosen pair of expert-task, given the information available up to the actual round. Given a confidence parameter delta in (0, 1), we provide strategies allowing to recover the correct ranking of experts and develop a bound on the total number of queries made by our algorithm that hold with probability at least 1 -- delta. We show that our strategy is adaptive to the complexity of the problem (our bounds are instance dependent), and develop matching lower bounds up to a poly-logarithmic factor. Finally, we adapt our strategy to the relaxed problem of best expert identification and provide numerical simulation consistent with our theoretical results.

While large language models (LLMs) have demonstrated remarkable performance across diverse tasks, they fundamentally lack self-awareness and frequently exhibit overconfidence, assigning high confidence scores to incorrect predictions. Accurate confidence estimation is therefore critical for enhancing the trustworthiness and reliability of LLM-generated outputs. However, existing approaches suffer from coarse-grained scoring mechanisms that fail to provide fine-grained, continuous confidence estimates throughout the generation process. To address these limitations, we introduce FineCE, a novel confidence estimation method that delivers accurate, fine-grained confidence scores during text generation. Specifically, we first develop a comprehensive pipeline for constructing training data that effectively captures the underlying probabilistic distribution of LLM responses, and then train a model to predict confidence scores for arbitrary text sequences in a supervised manner. Furthermore, we propose a Backward Confidence Integration (BCI) strategy that leverages information from the subsequent text to enhance confidence estimation for the current sequence during inference. We also introduce three strategies for identifying optimal positions to perform confidence estimation within the generation process. Extensive experiments on multiple benchmark datasets demonstrate that FineCE consistently outperforms existing classical confidence estimation methods. Our code and all baselines used in the paper are available on GitHub.

Uncertainty quantification is essential for assessing the reliability and trustworthiness of modern AI systems. Among existing approaches, verbalized uncertainty, where models express their confidence through natural language, has emerged as a lightweight and interpretable solution in large language models (LLMs). However, its effectiveness in vision-language models (VLMs) remains insufficiently studied. In this work, we conduct a comprehensive evaluation of verbalized confidence in VLMs, spanning three model categories, four task domains, and three evaluation scenarios. Our results show that current VLMs often display notable miscalibration across diverse tasks and settings. Notably, visual reasoning models (i.e., thinking with images) consistently exhibit better calibration, suggesting that modality-specific reasoning is critical for reliable uncertainty estimation. To further address calibration challenges, we introduce Visual Confidence-Aware Prompting, a two-stage prompting strategy that improves confidence alignment in multimodal settings. Overall, our study highlights the inherent miscalibration in VLMs across modalities. More broadly, our findings underscore the fundamental importance of modality alignment and model faithfulness in advancing reliable multimodal systems.

Large Language Models deployed as question answering tools require robust calibration to avoid overconfidence. We systematically evaluate how reasoning capabilities and budget affect confidence assessment accuracy, using the ClimateX dataset (Lacombe et al., 2023) and expanding it to human and planetary health. Our key finding challenges the "test-time scaling" paradigm: while recent reasoning LLMs achieve 48.7% accuracy in assessing expert confidence, increasing reasoning budgets consistently impairs rather than improves calibration. Extended reasoning leads to systematic overconfidence that worsens with longer thinking budgets, producing diminishing and negative returns beyond modest computational investments. Conversely, search-augmented generation dramatically outperforms pure reasoning, achieving 89.3% accuracy by retrieving relevant evidence. Our results suggest that information access, rather than reasoning depth or inference budget, may be the critical bottleneck for improved confidence calibration of knowledge-intensive tasks.

When answering questions, LLMs can convey not only an answer, but a level of confidence about the answer being correct. This includes explicit confidence markers (e.g. giving a numeric score) as well as implicit markers, like an authoritative tone or elaborating with additional knowledge. For LLMs to be trustworthy knowledge sources, the confidence they convey should match their actual expertise; however, most current models tend towards overconfidence. To calibrate both implicit and explicit confidence markers, we introduce a pragmatic, listener-aware finetuning method (LACIE) that models the listener, considering not only whether an answer is right, but whether it will be accepted by a listener. We cast calibration as preference optimization, creating data via a two-agent game, where a speaker model's outputs are judged by a simulated listener. We then finetune three LLMs (Mistral-7B, Llama3-8B, Llama3-70B) with LACIE, and show that the resulting models are better calibrated w.r.t. a simulated listener. Crucially, these trends transfer to human listeners, helping them correctly predict model correctness: we conduct a human evaluation where annotators accept or reject an LLM's answers, finding that training with LACIE results in 47% fewer incorrect answers being accepted while maintaining the same level of acceptance for correct answers. Furthermore, LACIE generalizes to another dataset, resulting in a large increase in truthfulness on TruthfulQA when trained on TriviaQA. Our analysis indicates that LACIE leads to a better confidence separation between correct and incorrect examples. Qualitatively, we find that a LACIE-trained model hedges more and implicitly signals certainty when it is correct by using an authoritative tone or including details. Finally, LACIE finetuning leads to an emergent increase in model abstention (e.g. saying "I don't know") for answers that are likely wrong.

Applying a machine learning model for decision-making in the real world requires to distinguish what the model knows from what it does not. A critical factor in assessing the knowledge of a model is to quantify its predictive uncertainty. Predictive uncertainty is commonly measured by the entropy of the Bayesian model average (BMA) predictive distribution. Yet, the properness of this current measure of predictive uncertainty was recently questioned. We provide new insights regarding those limitations. Our analyses show that the current measure erroneously assumes that the BMA predictive distribution is equivalent to the predictive distribution of the true model that generated the dataset. Consequently, we introduce a theoretically grounded measure to overcome these limitations. We experimentally verify the benefits of our introduced measure of predictive uncertainty. We find that our introduced measure behaves more reasonably in controlled synthetic tasks. Moreover, our evaluations on ImageNet demonstrate that our introduced measure is advantageous in real-world applications utilizing predictive uncertainty.

Knowledge distillation (KD) has gained a lot of attention in the field of model compression for edge devices thanks to its effectiveness in compressing large powerful networks into smaller lower-capacity models. Online distillation, in which both the teacher and the student are learning collaboratively, has also gained much interest due to its ability to improve on the performance of the networks involved. The Kullback-Leibler (KL) divergence ensures the proper knowledge transfer between the teacher and student. However, most online KD techniques present some bottlenecks under the network capacity gap. By cooperatively and simultaneously training, the models the KL distance becomes incapable of properly minimizing the teacher's and student's distributions. Alongside accuracy, critical edge device applications are in need of well-calibrated compact networks. Confidence calibration provides a sensible way of getting trustworthy predictions. We propose BD-KD: Balancing of Divergences for online Knowledge Distillation. We show that adaptively balancing between the reverse and forward divergences shifts the focus of the training strategy to the compact student network without limiting the teacher network's learning process. We demonstrate that, by performing this balancing design at the level of the student distillation loss, we improve upon both performance accuracy and calibration of the compact student network. We conducted extensive experiments using a variety of network architectures and show improvements on multiple datasets including CIFAR-10, CIFAR-100, Tiny-ImageNet, and ImageNet. We illustrate the effectiveness of our approach through comprehensive comparisons and ablations with current state-of-the-art online and offline KD techniques.

A significant use case of instruction-finetuned Large Language Models (LLMs) is to solve question-answering tasks interactively. In this setting, an LLM agent is tasked with making a prediction by sequentially querying relevant information from the user, as opposed to a single-turn conversation. This paper explores sequential querying strategies that aim to minimize the expected number of queries. One such strategy is Information Pursuit (IP), a greedy algorithm that at each iteration selects the query that maximizes information gain or equivalently minimizes uncertainty. However, obtaining accurate estimates of mutual information or conditional entropy for LLMs is very difficult in practice due to over- or under-confident LLM probabilities, which leads to suboptimal query selection and predictive performance. To better estimate the uncertainty at each iteration, we propose Conformal Information Pursuit (C-IP), an alternative approach to sequential information gain based on conformal prediction sets. More specifically, C-IP leverages a relationship between prediction sets and conditional entropy at each iteration to estimate uncertainty based on the average size of conformal prediction sets. In contrast to conditional entropy, we find that conformal prediction sets are a distribution-free and robust method of measuring uncertainty. Experiments with 20 Questions show that C-IP obtains better predictive performance and shorter query-answer chains compared to previous approaches to IP and uncertainty-based chain-of-thought methods. Furthermore, extending to an interactive medical setting between a doctor and a patient on the MediQ dataset, C-IP achieves competitive performance with direct single-turn prediction while offering greater interpretability.

Uncertainty estimation is a significant issue for current large language models (LLMs) that are generally poorly calibrated and over-confident, especially with reinforcement learning from human feedback (RLHF). Unlike humans, whose decisions and confidences not only stem from intrinsic beliefs but can also be adjusted through daily observations, existing calibration methods for LLMs focus on estimating or eliciting individual confidence without taking full advantage of the "Collective Wisdom": the interaction among multiple LLMs that can collectively improve both accuracy and calibration. In this work, we propose Collaborative Calibration, a post-hoc training-free calibration strategy that leverages the collaborative and expressive capabilities of multiple tool-augmented LLM agents in a simulated group deliberation process. We demonstrate the effectiveness of Collaborative Calibration on generative QA tasks across various domains, showing its potential in harnessing the rationalization of collectively calibrated confidence assessments and improving the reliability of model predictions.

We show that a GPT-3 model can learn to express uncertainty about its own answers in natural language -- without use of model logits. When given a question, the model generates both an answer and a level of confidence (e.g. "90% confidence" or "high confidence"). These levels map to probabilities that are well calibrated. The model also remains moderately calibrated under distribution shift, and is sensitive to uncertainty in its own answers, rather than imitating human examples. To our knowledge, this is the first time a model has been shown to express calibrated uncertainty about its own answers in natural language. For testing calibration, we introduce the CalibratedMath suite of tasks. We compare the calibration of uncertainty expressed in words ("verbalized probability") to uncertainty extracted from model logits. Both kinds of uncertainty are capable of generalizing calibration under distribution shift. We also provide evidence that GPT-3's ability to generalize calibration depends on pre-trained latent representations that correlate with epistemic uncertainty over its answers.

Semi-supervised learning is attracting blooming attention, due to its success in combining unlabeled data. To mitigate potentially incorrect pseudo labels, recent frameworks mostly set a fixed confidence threshold to discard uncertain samples. This practice ensures high-quality pseudo labels, but incurs a relatively low utilization of the whole unlabeled set. In this work, our key insight is that these uncertain samples can be turned into certain ones, as long as the confusion classes for the top-1 class are detected and removed. Invoked by this, we propose a novel method dubbed ShrinkMatch to learn uncertain samples. For each uncertain sample, it adaptively seeks a shrunk class space, which merely contains the original top-1 class, as well as remaining less likely classes. Since the confusion ones are removed in this space, the re-calculated top-1 confidence can satisfy the pre-defined threshold. We then impose a consistency regularization between a pair of strongly and weakly augmented samples in the shrunk space to strive for discriminative representations. Furthermore, considering the varied reliability among uncertain samples and the gradually improved model during training, we correspondingly design two reweighting principles for our uncertain loss. Our method exhibits impressive performance on widely adopted benchmarks. Code is available at https://github.com/LiheYoung/ShrinkMatch.

As large language models (LLMs) are increasingly deployed in user-facing applications, building trust and maintaining safety by accurately quantifying a model's confidence in its prediction becomes even more important. However, finding effective ways to calibrate LLMs - especially when the only interface to the models is their generated text - remains a challenge. We propose APRICOT (auxiliary prediction of confidence targets): A method to set confidence targets and train an additional model that predicts an LLM's confidence based on its textual input and output alone. This approach has several advantages: It is conceptually simple, does not require access to the target model beyond its output, does not interfere with the language generation, and has a multitude of potential usages, for instance by verbalizing the predicted confidence or adjusting the given answer based on the confidence. We show how our approach performs competitively in terms of calibration error for white-box and black-box LLMs on closed-book question-answering to detect incorrect LLM answers.

Although large language models (LLMs) are capable of performing various tasks, they still suffer from producing plausible but incorrect responses. To improve the reliability of LLMs, recent research has focused on uncertainty quantification to predict whether a response is correct or not. However, most uncertainty quantification methods have been evaluated on questions requiring a single clear answer, ignoring the existence of data uncertainty that arises from irreducible randomness. Instead, these methods only consider model uncertainty, which arises from a lack of knowledge. In this paper, we investigate previous uncertainty quantification methods under the presence of data uncertainty. Our contributions are two-fold: 1) proposing a new Multi-Answer Question Answering dataset, MAQA, consisting of world knowledge, mathematical reasoning, and commonsense reasoning tasks to evaluate uncertainty quantification regarding data uncertainty, and 2) assessing 5 uncertainty quantification methods of diverse white- and black-box LLMs. Our findings show that entropy and consistency-based methods estimate the model uncertainty well even under data uncertainty, while other methods for white- and black-box LLMs struggle depending on the tasks. Additionally, methods designed for white-box LLMs suffer from overconfidence in reasoning tasks compared to simple knowledge queries. We believe our observations will pave the way for future work on uncertainty quantification in realistic setting.

The Optical Character Recognition (OCR) task is important for evaluating Vision-Language Models (VLMs) and providing high-quality data sources for LLM training data. While state-of-the-art VLMs show improved average OCR accuracy, they still struggle with sample-level quality degradation and lack reliable automatic detection of low-quality outputs. We introduce Consensus Entropy (CE), a training-free post-inference method that quantifies OCR uncertainty by aggregating outputs from multiple VLMs. Our approach exploits a key insight: correct VLM OCR predictions converge in output space while errors diverge. We develop a lightweight multi-model framework that effectively identifies problematic samples, selects the best outputs and combines model strengths. Experiments across multiple OCR benchmarks and VLMs demonstrate that CE outperforms VLM-as-judge approaches and single-model baselines at the same cost and achieves state-of-the-art results across multiple metrics. For instance, our solution demonstrates: achieving 15.2% higher F1 scores than VLM-as-judge methods in quality verification, delivering 6.0% accuracy gains on mathematical calculation tasks, and requiring rephrasing only 7.3% of inputs while maintaining overall performance. Notably, the entire process requires neither training nor supervision while maintaining plug-and-play functionality throughout.

Predicting not only the target but also an accurate measure of uncertainty is important for many machine learning applications and in particular safety-critical ones. In this work we study the calibration of uncertainty prediction for regression tasks which often arise in real-world systems. We show that the existing definition for calibration of a regression uncertainty [Kuleshov et al. 2018] has severe limitations in distinguishing informative from non-informative uncertainty predictions. We propose a new definition that escapes this caveat and an evaluation method using a simple histogram-based approach. Our method clusters examples with similar uncertainty prediction and compares the prediction with the empirical uncertainty on these examples. We also propose a simple, scaling-based calibration method that preforms as well as much more complex ones. We show results on both a synthetic, controlled problem and on the object detection bounding-box regression task using the COCO and KITTI datasets.

Language models (LMs) should provide reliable confidence estimates to help users detect mistakes in their outputs and defer to human experts when necessary. Asking a language model to assess its confidence ("Score your confidence from 0-1.") is a natural way of evaluating its uncertainty. However, models struggle to provide absolute assessments of confidence (i.e. judging confidence in answering a question independent of other questions) and the coarse-grained scores they produce are not useful for evaluating the correctness of their answers. We propose relative confidence estimation, where we match up questions against each other and ask the model to make relative judgments of confidence ("Which question are you more confident in answering correctly?"). Treating each question as a "player" in a series of matchups against other questions and the model's preferences as match outcomes, we can use rank aggregation methods like Elo rating and Bradley-Terry to translate the model's confidence preferences into confidence scores. We evaluate relative confidence estimation against absolute confidence estimation and self-consistency confidence methods on five state-of-the-art LMs -- GPT-4, GPT-4o, Gemini 1.5 Pro, Claude 3.5 Sonnet, and Llama 3.1 405B -- across 14 challenging STEM, social science, and commonsense reasoning question answering tasks. Our results demonstrate that relative confidence estimation consistently provides more reliable confidence scores than absolute confidence estimation, with average gains of 3.5% in selective classification AUC over direct absolute confidence estimation methods and 1.7% over self-consistency approaches across all models and datasets.

Assessing the quality of Large Language Model (LLM) outputs presents a critical challenge. Previous methods either rely on text-level information (e.g., reward models, majority voting), which can overfit to superficial cues, or on calibrated confidence from token probabilities, which would fail on less-calibrated models. Yet both of these signals are, in fact, partial projections of a richer source of information: the model's internal hidden states. Early layers, closer to token embeddings, preserve semantic and lexical features that underpin text-based judgments, while later layers increasingly align with output logits, embedding confidence-related information. This paper explores hidden states directly as a unified foundation for verification. We show that the correctness of a solution is encoded as a geometrically separable signature within the trajectory of hidden activations. To validate this, we present Clue (Clustering and Experience-based Verification), a deliberately minimalist, non-parametric verifier. With no trainable parameters, CLUE only summarizes each reasoning trace by an hidden state delta and classifies correctness via nearest-centroid distance to ``success'' and ``failure'' clusters formed from past experience. The simplicity of this method highlights the strength of the underlying signal. Empirically, CLUE consistently outperforms LLM-as-a-judge baselines and matches or exceeds modern confidence-based methods in reranking candidates, improving both top-1 and majority-vote accuracy across AIME 24/25 and GPQA. As a highlight, on AIME 24 with a 1.5B model, CLUE boosts accuracy from 56.7% (majority@64) to 70.0% (top-maj@16).

Autonomous Graphical User Interface (GUI) agents rely on accurate GUI grounding, which maps language instructions to on-screen coordinates, to execute user commands. However, current models, whether trained via supervised fine-tuning (SFT) or reinforcement fine-tuning (RFT), lack self-awareness of their capability boundaries, leading to overconfidence and unreliable predictions. We first systematically evaluate probabilistic and verbalized confidence in general and GUI-specific models, revealing a misalignment between confidence and actual accuracy, which is particularly critical in dynamic GUI automation tasks, where single errors can cause task failure. To address this, we propose HyperClick, a novel framework that enhances reliable GUI grounding through uncertainty calibration. HyperClick introduces a dual reward mechanism, combining a binary reward for correct actions with a truncated Gaussian-based spatial confidence modeling, calibrated using the Brier score. This approach jointly optimizes grounding accuracy and confidence reliability, fostering introspective self-criticism. Extensive experiments on seven challenge benchmarks show that HyperClick achieves state-of-the-art performance while providing well-calibrated confidence. By enabling explicit confidence calibration and introspective self-criticism, HyperClick reduces overconfidence and supports more reliable GUI automation.

Multimodal large language models (MLLMs) hold considerable promise for applications in healthcare. However, their deployment in safety-critical settings is hindered by two key limitations: (i) sensitivity to prompt design, and (ii) a tendency to generate incorrect responses with high confidence. As clinicians may rely on a model's stated confidence to gauge the reliability of its predictions, it is especially important that when a model expresses high confidence, it is also highly accurate. We introduce Prompt4Trust, the first reinforcement learning (RL) framework for prompt augmentation targeting confidence calibration in MLLMs. A lightweight LLM is trained to produce context-aware auxiliary prompts that guide a downstream task MLLM to generate responses in which the expressed confidence more accurately reflects predictive accuracy. Unlike conventional calibration techniques, Prompt4Trust specifically prioritizes aspects of calibration most critical for safe and trustworthy clinical decision-making. Beyond improvements driven by this clinically motivated calibration objective, our proposed method also improves task accuracy, achieving state-of-the-art medical visual question answering (VQA) performance on the PMC-VQA benchmark, which is composed of multiple-choice questions spanning diverse medical imaging modalities. Moreover, our framework trained with a small downstream task MLLM showed promising zero-shot generalization to larger MLLMs in our experiments, suggesting the potential for scalable calibration without the associated computational costs. This work demonstrates the potential of automated yet human-aligned prompt engineering for improving the the trustworthiness of MLLMs in safety critical settings. Our codebase can be found at https://github.com/xingbpshen/prompt4trust.

Process reward models (PRMs) play a central role in guiding inference-time scaling algorithms for large language models (LLMs). However, we observe that even state-of-the-art PRMs can be poorly calibrated and often overestimate success probabilities. To address this, we present a calibration approach, performed via quantile regression, that adjusts PRM outputs to better align with true success probabilities. Leveraging these calibrated success estimates and their associated confidence bounds, we introduce an instance-adaptive scaling (IAS) framework that dynamically adjusts the inference budget based on the estimated likelihood that a partial reasoning trajectory will yield a correct final answer. Unlike conventional methods that allocate a fixed number of reasoning trajectories per query, this approach successfully adapts to each instance and reasoning step when using our calibrated PRMs. Experiments on mathematical reasoning benchmarks show that (i) our PRM calibration method successfully achieves small calibration error, outperforming the baseline methods, (ii) calibration is crucial for enabling effective adaptive scaling, and (iii) the proposed IAS strategy reduces inference costs while maintaining final answer accuracy, utilizing less compute on more confident problems as desired.

Major cloud providers have employed advanced AI-based solutions like large language models to aid humans in identifying the root causes of cloud incidents. Despite the growing prevalence of AI-driven assistants in the root cause analysis process, their effectiveness in assisting on-call engineers is constrained by low accuracy due to the intrinsic difficulty of the task, a propensity for LLM-based approaches to hallucinate, and difficulties in distinguishing these well-disguised hallucinations. To address this challenge, we propose to perform confidence estimation for the predictions to help on-call engineers make decisions on whether to adopt the model prediction. Considering the black-box nature of many LLM-based root cause predictors, fine-tuning or temperature-scaling-based approaches are inapplicable. We therefore design an innovative confidence estimation framework based on prompting retrieval-augmented large language models (LLMs) that demand a minimal amount of information from the root cause predictor. This approach consists of two scoring phases: the LLM-based confidence estimator first evaluates its confidence in making judgments in the face of the current incident that reflects its ``grounded-ness" level in reference data, then rates the root cause prediction based on historical references. An optimization step combines these two scores for a final confidence assignment. We show that our method is able to produce calibrated confidence estimates for predicted root causes, validate the usefulness of retrieved historical data and the prompting strategy as well as the generalizability across different root cause prediction models. Our study takes an important move towards reliably and effectively embedding LLMs into cloud incident management systems.

In question-answering tasks, determining when to trust the outputs is crucial to the alignment of large language models (LLMs). Kuhn et al. (2023) introduces semantic entropy as a measure of uncertainty, by incorporating linguistic invariances from the same meaning. It primarily relies on setting threshold to measure the level of semantic equivalence relation. We propose a more nuanced framework that extends beyond such thresholding by developing a Shapley-based uncertainty metric that captures the continuous nature of semantic relationships. We establish three fundamental properties that characterize valid uncertainty metrics and prove that our Shapley uncertainty satisfies these criteria. Through extensive experiments, we demonstrate that our Shapley uncertainty more accurately predicts LLM performance in question-answering and other datasets, compared to similar baseline measures.

Traditional evaluations of multimodal large language models (LLMs) have been limited by their focus on single-image reasoning, failing to assess crucial aspects like contextual understanding, reasoning stability, and uncertainty calibration. This study addresses these limitations by introducing a novel benchmark that integrates multi-image reasoning tasks with rejection-based evaluation and positional bias detection. To evaluate these dimensions, we further introduce entropy as a novel metric for quantifying reasoning consistency across reordered answer variants. We applied this benchmark to assess Grok 3, ChatGPT-4o, ChatGPT-o1, Gemini 2.0 Flash Experimental, DeepSeek Janus models, Qwen2.5-VL-72B-Instruct, QVQ-72B-Preview, and Pixtral 12B across eight visual reasoning tasks, including difference spotting and diagram interpretation. Our findings reveal ChatGPT-o1 leading in overall accuracy (82.5\%) and rejection accuracy (70.0\%), closely followed by Gemini 2.0 Flash Experimental (70.8\%). QVQ-72B-Preview demonstrated superior rejection accuracy (85.5\%). Notably, Pixtral 12B (51.7\%) showed promise in specific domains, while Janus models exhibited challenges in bias and uncertainty calibration, reflected in low rejection accuracies and high entropy scores. High entropy scores in Janus models (Janus 7B: 0.8392, Janus 1B: 0.787) underscore their susceptibility to positional bias and unstable reasoning, contrasting with the low entropy and robust reasoning of ChatGPT models. The study further demonstrates that model size is not the sole determinant of performance, as evidenced by Grok 3 underperformance despite its substantial parameter count. By employing multi-image contexts, rejection mechanisms, and entropy-based consistency metrics, this benchmark sets a new standard for evaluating multimodal LLMs, enabling a more robust and reliable assessment of next-generation AI systems.

Quality estimation is omnipresent in machine translation, for both evaluation and generation. Unfortunately, quality estimation models are often opaque and computationally expensive, making them impractical to be part of large-scale pipelines. In this work, we tackle two connected challenges: (1) reducing the cost of quality estimation at scale, and (2) developing an inexpensive uncertainty estimation method for quality estimation. To address the latter, we introduce Instant Confidence COMET, an uncertainty-aware quality estimation model that matches the performance of previous approaches at a fraction of their costs. We extend this to Early-Exit COMET, a quality estimation model that can compute quality scores and associated confidences already at early model layers, allowing us to early-exit computations and reduce evaluation costs. We also apply our model to machine translation reranking. We combine Early-Exit COMET with an upper confidence bound bandit algorithm to find the best candidate from a large pool without having to run the full evaluation model on all candidates. In both cases (evaluation and reranking) our methods reduce the required compute by 50% with very little degradation in performance.

Uncertainty quantification (UQ) for open-ended language generation remains a critical yet underexplored challenge, especially under black-box constraints where internal model signals are inaccessible. In this paper, we introduce Token-Entropy Conformal Prediction (TECP), a novel framework that leverages token-level entropy as a logit-free, reference-free uncertainty measure and integrates it into a split conformal prediction (CP) pipeline to construct prediction sets with formal coverage guarantees. Unlike existing approaches that rely on semantic consistency heuristics or white-box features, TECP directly estimates epistemic uncertainty from the token entropy structure of sampled generations and calibrates uncertainty thresholds via CP quantiles to ensure provable error control. Empirical evaluations across six large language models and two benchmarks (CoQA and TriviaQA) demonstrate that TECP consistently achieves reliable coverage and compact prediction sets, outperforming prior self-consistency-based UQ methods. Our method provides a principled and efficient solution for trustworthy generation in black-box LLM settings.

It is important for Large Language Models to be aware of the boundary of their knowledge, the mechanism of identifying known and unknown queries. This type of awareness can help models perform adaptive inference, such as invoking RAG, engaging in slow and deep thinking, or adopting the abstention mechanism, which is beneficial to the development of efficient and trustworthy AI. In this work, we propose a method to detect knowledge boundaries via Query-Level Uncertainty, which aims to determine if the model is able to address a given query without generating any tokens. To this end, we introduce a novel and training-free method called Internal Confidence, which leverages self-evaluations across layers and tokens. Empirical results on both factual QA and mathematical reasoning tasks demonstrate that our internal confidence can outperform several baselines. Furthermore, we showcase that our proposed method can be used for efficient RAG and model cascading, which is able to reduce inference costs while maintaining performance.

We introduce BSDetector, a method for detecting bad and speculative answers from a pretrained Large Language Model by estimating a numeric confidence score for any output it generated. Our uncertainty quantification technique works for any LLM accessible only via a black-box API, whose training data remains unknown. By expending a bit of extra computation, users of any LLM API can now get the same response as they would ordinarily, as well as a confidence estimate that cautions when not to trust this response. Experiments on both closed and open-form Question-Answer benchmarks reveal that BSDetector more accurately identifies incorrect LLM responses than alternative uncertainty estimation procedures (for both GPT-3 and ChatGPT). By sampling multiple responses from the LLM and considering the one with the highest confidence score, we can additionally obtain more accurate responses from the same LLM, without any extra training steps. In applications involving automated evaluation with LLMs, accounting for our confidence scores leads to more reliable evaluation in both human-in-the-loop and fully-automated settings (across both GPT 3.5 and 4).

Large language models (LLMs) have transformed natural language processing, but their reliable deployment requires effective uncertainty quantification (UQ). Existing UQ methods are often heuristic and lack a probabilistic foundation. This paper begins by providing a theoretical justification for the role of perturbations in UQ for LLMs. We then introduce a dual random walk perspective, modeling input-output pairs as two Markov chains with transition probabilities defined by semantic similarity. Building on this, we propose a fully probabilistic framework based on an inverse model, which quantifies uncertainty by evaluating the diversity of the input space conditioned on a given output through systematic perturbations. Within this framework, we define a new uncertainty measure, Inv-Entropy. A key strength of our framework is its flexibility: it supports various definitions of uncertainty measures, embeddings, perturbation strategies, and similarity metrics. We also propose GAAP, a perturbation algorithm based on genetic algorithms, which enhances the diversity of sampled inputs. In addition, we introduce a new evaluation metric, Temperature Sensitivity of Uncertainty (TSU), which directly assesses uncertainty without relying on correctness as a proxy. Extensive experiments demonstrate that Inv-Entropy outperforms existing semantic UQ methods. The code to reproduce the results can be found at https://github.com/UMDataScienceLab/Uncertainty-Quantification-for-LLMs.

Large language models (LLMs) have demonstrated remarkable capabilities out of box for a wide range of applications, yet accuracy still remains a major growth area, especially in mission-critical domains such as biomedicine. An effective method to calibrate the confidence level on LLM responses is essential to automatically detect errors and facilitate human-in-the-loop verification. An important source of calibration signals stems from expert-stipulated programmatic supervision, which is often available at low cost but has its own limitations such as noise and coverage. In this paper, we introduce a Pareto optimal self-supervision framework that can leverage available programmatic supervision to systematically calibrate LLM responses by producing a risk score for every response, without any additional manual efforts. This is accomplished by learning a harmonizer model to align LLM output with other available supervision sources, which would assign higher risk scores to more uncertain LLM responses and facilitate error correction. Experiments on standard relation extraction tasks in biomedical and general domains demonstrate the promise of this approach, with our proposed risk scores highly correlated with the real error rate of LLMs. For the most uncertain test instances, dynamic prompting based on our proposed risk scores results in significant accuracy improvement for off-the-shelf LLMs, boosting GPT-3 results past state-of-the-art (SOTA) weak supervision and GPT-4 results past SOTA supervised results on challenging evaluation datasets.

Generative video models demonstrate impressive text-to-video capabilities, spurring widespread adoption in many real-world applications. However, like large language models (LLMs), video generation models tend to hallucinate, producing plausible videos even when they are factually wrong. Although uncertainty quantification (UQ) of LLMs has been extensively studied in prior work, no UQ method for video models exists, raising critical safety concerns. To our knowledge, this paper represents the first work towards quantifying the uncertainty of video models. We present a framework for uncertainty quantification of generative video models, consisting of: (i) a metric for evaluating the calibration of video models based on robust rank correlation estimation with no stringent modeling assumptions; (ii) a black-box UQ method for video models (termed S-QUBED), which leverages latent modeling to rigorously decompose predictive uncertainty into its aleatoric and epistemic components; and (iii) a UQ dataset to facilitate benchmarking calibration in video models. By conditioning the generation task in the latent space, we disentangle uncertainty arising due to vague task specifications from that arising from lack of knowledge. Through extensive experiments on benchmark video datasets, we demonstrate that S-QUBED computes calibrated total uncertainty estimates that are negatively correlated with the task accuracy and effectively computes the aleatoric and epistemic constituents.

We explore uncertainty quantification in large language models (LLMs), with the goal to identify when uncertainty in responses given a query is large. We simultaneously consider both epistemic and aleatoric uncertainties, where the former comes from the lack of knowledge about the ground truth (such as about facts or the language), and the latter comes from irreducible randomness (such as multiple possible answers). In particular, we derive an information-theoretic metric that allows to reliably detect when only epistemic uncertainty is large, in which case the output of the model is unreliable. This condition can be computed based solely on the output of the model obtained simply by some special iterative prompting based on the previous responses. Such quantification, for instance, allows to detect hallucinations (cases when epistemic uncertainty is high) in both single- and multi-answer responses. This is in contrast to many standard uncertainty quantification strategies (such as thresholding the log-likelihood of a response) where hallucinations in the multi-answer case cannot be detected. We conduct a series of experiments which demonstrate the advantage of our formulation. Further, our investigations shed some light on how the probabilities assigned to a given output by an LLM can be amplified by iterative prompting, which might be of independent interest.

Calibrating deep learning models to yield uncertainty-aware predictions is crucial as deep neural networks get increasingly deployed in safety-critical applications. While existing post-hoc calibration methods achieve impressive results on in-domain test datasets, they are limited by their inability to yield reliable uncertainty estimates in domain-shift and out-of-domain (OOD) scenarios. We aim to bridge this gap by proposing DAC, an accuracy-preserving as well as Density-Aware Calibration method based on k-nearest-neighbors (KNN). In contrast to existing post-hoc methods, we utilize hidden layers of classifiers as a source for uncertainty-related information and study their importance. We show that DAC is a generic method that can readily be combined with state-of-the-art post-hoc methods. DAC boosts the robustness of calibration performance in domain-shift and OOD, while maintaining excellent in-domain predictive uncertainty estimates. We demonstrate that DAC leads to consistently better calibration across a large number of model architectures, datasets, and metrics. Additionally, we show that DAC improves calibration substantially on recent large-scale neural networks pre-trained on vast amounts of data.

Expressing confidence is challenging for embodied agents navigating dynamic multimodal environments, where uncertainty arises from both perception and decision-making processes. We present the first work investigating embodied confidence elicitation in open-ended multimodal environments. We introduce Elicitation Policies, which structure confidence assessment across inductive, deductive, and abductive reasoning, along with Execution Policies, which enhance confidence calibration through scenario reinterpretation, action sampling, and hypothetical reasoning. Evaluating agents in calibration and failure prediction tasks within the Minecraft environment, we show that structured reasoning approaches, such as Chain-of-Thoughts, improve confidence calibration. However, our findings also reveal persistent challenges in distinguishing uncertainty, particularly under abductive settings, underscoring the need for more sophisticated embodied confidence elicitation methods.

Safe deployment of graph neural networks (GNNs) under distribution shift requires models to provide accurate confidence indicators (CI). However, while it is well-known in computer vision that CI quality diminishes under distribution shift, this behavior remains understudied for GNNs. Hence, we begin with a case study on CI calibration under controlled structural and feature distribution shifts and demonstrate that increased expressivity or model size do not always lead to improved CI performance. Consequently, we instead advocate for the use of epistemic uncertainty quantification (UQ) methods to modulate CIs. To this end, we propose G-DeltaUQ, a new single model UQ method that extends the recently proposed stochastic centering framework to support structured data and partial stochasticity. Evaluated across covariate, concept, and graph size shifts, G-DeltaUQ not only outperforms several popular UQ methods in obtaining calibrated CIs, but also outperforms alternatives when CIs are used for generalization gap prediction or OOD detection. Overall, our work not only introduces a new, flexible GNN UQ method, but also provides novel insights into GNN CIs on safety-critical tasks.

Accurate probabilistic predictions are essential for optimal decision making. While neural network miscalibration has been studied primarily in classification, we investigate this in the less-explored domain of regression. We conduct the largest empirical study to date to assess the probabilistic calibration of neural networks. We also analyze the performance of recalibration, conformal, and regularization methods to enhance probabilistic calibration. Additionally, we introduce novel differentiable recalibration and regularization methods, uncovering new insights into their effectiveness. Our findings reveal that regularization methods offer a favorable tradeoff between calibration and sharpness. Post-hoc methods exhibit superior probabilistic calibration, which we attribute to the finite-sample coverage guarantee of conformal prediction. Furthermore, we demonstrate that quantile recalibration can be considered as a specific case of conformal prediction. Our study is fully reproducible and implemented in a common code base for fair comparisons.

In long-horizon tasks, recent agents based on Large Language Models (LLMs) face a significant challenge that sparse, outcome-based rewards make it difficult to assign credit to intermediate steps. Previous methods mainly focus on creating dense reward signals to guide learning, either through traditional reinforcement learning techniques like inverse reinforcement learning or by using Process Reward Models for step-by-step feedback. In this paper, we identify a fundamental problem in the learning dynamics of LLMs: the magnitude of policy gradients is inherently coupled with the entropy, which leads to inefficient small updates for confident correct actions and potentially destabilizes large updates for uncertain ones. To resolve this, we propose Entropy-Modulated Policy Gradients (EMPG), a framework that re-calibrates the learning signal based on step-wise uncertainty and the final task outcome. EMPG amplifies updates for confident correct actions, penalizes confident errors, and attenuates updates from uncertain steps to stabilize exploration. We further introduce a bonus term for future clarity that encourages agents to find more predictable solution paths. Through comprehensive experiments on three challenging agent tasks, WebShop, ALFWorld, and Deep Search, we demonstrate that EMPG achieves substantial performance gains and significantly outperforms strong policy gradient baselines. Project page is at https://empgseed-seed.github.io/

Calibration measures and reliability diagrams are two fundamental tools for measuring and interpreting the calibration of probabilistic predictors. Calibration measures quantify the degree of miscalibration, and reliability diagrams visualize the structure of this miscalibration. However, the most common constructions of reliability diagrams and calibration measures -- binning and ECE -- both suffer from well-known flaws (e.g. discontinuity). We show that a simple modification fixes both constructions: first smooth the observations using an RBF kernel, then compute the Expected Calibration Error (ECE) of this smoothed function. We prove that with a careful choice of bandwidth, this method yields a calibration measure that is well-behaved in the sense of (B{\l}asiok, Gopalan, Hu, and Nakkiran 2023a) -- a consistent calibration measure. We call this measure the SmoothECE. Moreover, the reliability diagram obtained from this smoothed function visually encodes the SmoothECE, just as binned reliability diagrams encode the BinnedECE. We also provide a Python package with simple, hyperparameter-free methods for measuring and plotting calibration: `pip install relplot\`.

Calibrated uncertainty estimates in machine learning are crucial to many fields such as autonomous vehicles, medicine, and weather and climate forecasting. While there is extensive literature on uncertainty calibration for classification, the classification findings do not always translate to regression. As a result, modern models for predicting uncertainty in regression settings typically produce uncalibrated and overconfident estimates. To address these gaps, we present a calibration method for regression settings that does not assume a particular uncertainty distribution over the error: Calibrating Regression Uncertainty Distributions Empirically (CRUDE). CRUDE makes the weaker assumption that error distributions have a constant arbitrary shape across the output space, shifted by predicted mean and scaled by predicted standard deviation. We detail a theoretical connection between CRUDE and conformal inference. Across an extensive set of regression tasks, CRUDE demonstrates consistently sharper, better calibrated, and more accurate uncertainty estimates than state-of-the-art techniques.

In real-world scenarios, typical visual recognition systems could fail under two major causes, i.e., the misclassification between known classes and the excusable misbehavior on unknown-class images. To tackle these deficiencies, flexible visual recognition should dynamically predict multiple classes when they are unconfident between choices and reject making predictions when the input is entirely out of the training distribution. Two challenges emerge along with this novel task. First, prediction uncertainty should be separately quantified as confusion depicting inter-class uncertainties and ignorance identifying out-of-distribution samples. Second, both confusion and ignorance should be comparable between samples to enable effective decision-making. In this paper, we propose to model these two sources of uncertainty explicitly with the theory of Subjective Logic. Regarding recognition as an evidence-collecting process, confusion is then defined as conflicting evidence, while ignorance is the absence of evidence. By predicting Dirichlet concentration parameters for singletons, comprehensive subjective opinions, including confusion and ignorance, could be achieved via further evidence combinations. Through a series of experiments on synthetic data analysis, visual recognition, and open-set detection, we demonstrate the effectiveness of our methods in quantifying two sources of uncertainties and dealing with flexible recognition.

Network calibration aims to accurately estimate the level of confidences, which is particularly important for employing deep neural networks in real-world systems. Recent approaches leverage mixup to calibrate the network's predictions during training. However, they do not consider the problem that mixtures of labels in mixup may not accurately represent the actual distribution of augmented samples. In this paper, we present RankMixup, a novel mixup-based framework alleviating the problem of the mixture of labels for network calibration. To this end, we propose to use an ordinal ranking relationship between raw and mixup-augmented samples as an alternative supervisory signal to the label mixtures for network calibration. We hypothesize that the network should estimate a higher level of confidence for the raw samples than the augmented ones (Fig.1). To implement this idea, we introduce a mixup-based ranking loss (MRL) that encourages lower confidences for augmented samples compared to raw ones, maintaining the ranking relationship. We also propose to leverage the ranking relationship among multiple mixup-augmented samples to further improve the calibration capability. Augmented samples with larger mixing coefficients are expected to have higher confidences and vice versa (Fig.1). That is, the order of confidences should be aligned with that of mixing coefficients. To this end, we introduce a novel loss, M-NDCG, in order to reduce the number of misaligned pairs of the coefficients and confidences. Extensive experimental results on standard benchmarks for network calibration demonstrate the effectiveness of RankMixup.

Large language models demonstrate remarkable in-context learning capabilities, adapting to new tasks without parameter updates. While this phenomenon has been successfully modeled as implicit Bayesian inference, recent empirical findings reveal a fundamental contradiction: transformers systematically violate the martingale property, a cornerstone requirement of Bayesian updating on exchangeable data. This violation challenges the theoretical foundations underlying uncertainty quantification in critical applications. Our theoretical analysis establishes four key results: (1) positional encodings induce martingale violations of order Theta(log n / n); (2) transformers achieve information-theoretic optimality with excess risk O(n^{-1/2}) in expectation over orderings; (3) the implicit posterior representation converges to the true Bayesian posterior in the space of sufficient statistics; and (4) we derive the optimal chain-of-thought length as k^* = Theta(nlog(1/varepsilon)) with explicit constants, providing a principled approach to reduce inference costs while maintaining performance. Empirical validation on GPT-3 confirms predictions (1)-(3), with transformers reaching 99\% of theoretical entropy limits within 20 examples. Our framework provides practical methods for extracting calibrated uncertainty estimates from position-aware architectures and optimizing computational efficiency in deployment.

Identifying how much a model {p}_{theta}(Y|X) knows about the stochastic real-world process p(Y|X) it was trained on is important to ensure it avoids producing incorrect or "hallucinated" answers or taking unsafe actions. But this is difficult for generative models because probabilistic predictions do not distinguish between per-response noise (aleatoric uncertainty) and lack of knowledge about the process (epistemic uncertainty), and existing epistemic uncertainty quantification techniques tend to be overconfident when the model underfits. We propose a general strategy for teaching a model to both approximate p(Y|X) and also estimate the remaining gaps between {p}_{theta}(Y|X) and p(Y|X): train it to predict pairs of independent responses drawn from the true conditional distribution, allow it to "cheat" by observing one response while predicting the other, then measure how much it cheats. Remarkably, we prove that being good at cheating (i.e. cheating whenever it improves your prediction) is equivalent to being second-order calibrated, a principled extension of ordinary calibration that allows us to construct provably-correct frequentist confidence intervals for p(Y|X) and detect incorrect responses with high probability. We demonstrate empirically that our approach accurately estimates how much models don't know across ambiguous image classification, (synthetic) language modeling, and partially-observable navigation tasks, outperforming existing techniques.

Quantifying uncertainty in large language models (LLMs) is important for safety-critical applications because it helps spot incorrect answers, known as hallucinations. One major trend of uncertainty quantification methods is based on estimating the entropy of the distribution of the LLM's potential output sequences. This estimation is based on a set of output sequences and associated probabilities obtained by querying the LLM several times. In this paper, we advocate and experimentally show that the probability of unobserved sequences plays a crucial role, and we recommend future research to integrate it to enhance such LLM uncertainty quantification methods.

Fine-tuned large language models (LLMs) often exhibit overconfidence, particularly when trained on small datasets, resulting in poor calibration and inaccurate uncertainty estimates. Evidential Deep Learning (EDL), an uncertainty-aware approach, enables uncertainty estimation in a single forward pass, making it a promising method for calibrating fine-tuned LLMs. However, despite its computational efficiency, EDL is prone to overfitting, as its training objective can result in overly concentrated probability distributions. To mitigate this, we propose regularizing EDL by incorporating an information bottleneck (IB). Our approach IB-EDL suppresses spurious information in the evidence generated by the model and encourages truly predictive information to influence both the predictions and uncertainty estimates. Extensive experiments across various fine-tuned LLMs and tasks demonstrate that IB-EDL outperforms both existing EDL and non-EDL approaches. By improving the trustworthiness of LLMs, IB-EDL facilitates their broader adoption in domains requiring high levels of confidence calibration. Code is available at https://github.com/sandylaker/ib-edl.

Uncertainty estimation is a key factor that makes deep learning reliable in practical applications. Recently proposed evidential neural networks explicitly account for different uncertainties by treating the network's outputs as evidence to parameterize the Dirichlet distribution, and achieve impressive performance in uncertainty estimation. However, for high data uncertainty samples but annotated with the one-hot label, the evidence-learning process for those mislabeled classes is over-penalized and remains hindered. To address this problem, we propose a novel method, Fisher Information-based Evidential Deep Learning (I-EDL). In particular, we introduce Fisher Information Matrix (FIM) to measure the informativeness of evidence carried by each sample, according to which we can dynamically reweight the objective loss terms to make the network more focused on the representation learning of uncertain classes. The generalization ability of our network is further improved by optimizing the PAC-Bayesian bound. As demonstrated empirically, our proposed method consistently outperforms traditional EDL-related algorithms in multiple uncertainty estimation tasks, especially in the more challenging few-shot classification settings.

Large Language Models (LLMs) are increasingly deployed in high-stakes domains such as science, law, and healthcare, where accurate expressions of uncertainty are essential for reliability and trust. However, current LLMs are often observed to generate incorrect answers with high confidence, a phenomenon known as "overconfidence". Recent efforts have focused on calibrating LLMs' verbalized confidence: i.e., their expressions of confidence in text form, such as "I am 80% confident that...". Existing approaches either rely on prompt engineering or fine-tuning with heuristically generated uncertainty estimates, both of which have limited effectiveness and generalizability. Motivated by the notion of proper scoring rules for calibration in classical machine learning models, we introduce ConfTuner, a simple and efficient fine-tuning method that introduces minimal overhead and does not require ground-truth confidence scores or proxy confidence estimates. ConfTuner relies on a new loss function, tokenized Brier score, which we theoretically prove to be a proper scoring rule, intuitively meaning that it "correctly incentivizes the model to report its true probability of being correct". ConfTuner improves calibration across diverse reasoning tasks and generalizes to black-box models such as GPT-4o. Our results further show that better-calibrated confidence enables downstream gains in self-correction and model cascade, advancing the development of trustworthy LLM systems. The code is available at https://github.com/liushiliushi/ConfTuner.

Quantifying uncertainty in black-box LLMs is vital for reliable responses and scalable oversight. Existing methods, which gauge a model's uncertainty through evaluating self-consistency in responses to the target query, can be misleading: an LLM may confidently provide an incorrect answer to a target query, yet give a confident and accurate answer to that same target query when answering a knowledge-preserving perturbation of the query. We systematically analyze the model behaviors and demonstrate that this discrepancy stems from suboptimal retrieval of parametric knowledge, often due to contextual biases that prevent consistent access to stored knowledge. We then introduce DiverseAgentEntropy, a novel, theoretically-grounded method employing multi-agent interaction across diverse query variations for uncertainty estimation of black-box LLMs. This approach more accurately assesses an LLM's true uncertainty and improves hallucination detection, outperforming existing self-consistency based techniques.

We propose semantic entropy probes (SEPs), a cheap and reliable method for uncertainty quantification in Large Language Models (LLMs). Hallucinations, which are plausible-sounding but factually incorrect and arbitrary model generations, present a major challenge to the practical adoption of LLMs. Recent work by Farquhar et al. (2024) proposes semantic entropy (SE), which can detect hallucinations by estimating uncertainty in the space semantic meaning for a set of model generations. However, the 5-to-10-fold increase in computation cost associated with SE computation hinders practical adoption. To address this, we propose SEPs, which directly approximate SE from the hidden states of a single generation. SEPs are simple to train and do not require sampling multiple model generations at test time, reducing the overhead of semantic uncertainty quantification to almost zero. We show that SEPs retain high performance for hallucination detection and generalize better to out-of-distribution data than previous probing methods that directly predict model accuracy. Our results across models and tasks suggest that model hidden states capture SE, and our ablation studies give further insights into the token positions and model layers for which this is the case.

Recent language models have shown remarkable performance on natural language understanding (NLU) tasks. However, they are often sub-optimal when faced with ambiguous samples that can be interpreted in multiple ways, over-confidently predicting a single label without consideration for its correctness. To address this issue, we propose a novel self-knowledge distillation method that enables models to learn label distributions more accurately by leveraging knowledge distilled from their lower layers. This approach also includes a learning phase that re-calibrates the unnecessarily strengthened confidence for training samples judged as extremely ambiguous based on the distilled distribution knowledge. We validate our method on diverse NLU benchmark datasets and the experimental results demonstrate its effectiveness in producing better label distributions. Particularly, through the process of re-calibrating the confidence for highly ambiguous samples, the issue of over-confidence when predictions for unseen samples do not match with their ground-truth labels has been significantly alleviated. This has been shown to contribute to generating better distributions than the existing state-of-the-art method. Moreover, our method is more efficient in training the models compared to the existing method, as it does not involve additional training processes to refine label distributions.

Real-world machine learning deployments are characterized by mismatches between the source (training) and target (test) distributions that may cause performance drops. In this work, we investigate methods for predicting the target domain accuracy using only labeled source data and unlabeled target data. We propose Average Thresholded Confidence (ATC), a practical method that learns a threshold on the model's confidence, predicting accuracy as the fraction of unlabeled examples for which model confidence exceeds that threshold. ATC outperforms previous methods across several model architectures, types of distribution shifts (e.g., due to synthetic corruptions, dataset reproduction, or novel subpopulations), and datasets (Wilds, ImageNet, Breeds, CIFAR, and MNIST). In our experiments, ATC estimates target performance 2-4times more accurately than prior methods. We also explore the theoretical foundations of the problem, proving that, in general, identifying the accuracy is just as hard as identifying the optimal predictor and thus, the efficacy of any method rests upon (perhaps unstated) assumptions on the nature of the shift. Finally, analyzing our method on some toy distributions, we provide insights concerning when it works. Code is available at https://github.com/saurabhgarg1996/ATC_code/.

We argue that the estimation of mutual information between high dimensional continuous random variables can be achieved by gradient descent over neural networks. We present a Mutual Information Neural Estimator (MINE) that is linearly scalable in dimensionality as well as in sample size, trainable through back-prop, and strongly consistent. We present a handful of applications on which MINE can be used to minimize or maximize mutual information. We apply MINE to improve adversarially trained generative models. We also use MINE to implement Information Bottleneck, applying it to supervised classification; our results demonstrate substantial improvement in flexibility and performance in these settings.

Uncertainty Quantification (UQ) research has primarily focused on closed-book factual question answering (QA), while contextual QA remains unexplored, despite its importance in real-world applications. In this work, we focus on UQ for the contextual QA task and propose a theoretically grounded approach to quantify epistemic uncertainty. We begin by introducing a task-agnostic, token-level uncertainty measure defined as the cross-entropy between the predictive distribution of the given model and the unknown true distribution. By decomposing this measure, we isolate the epistemic component and approximate the true distribution by a perfectly prompted, idealized model. We then derive an upper bound for epistemic uncertainty and show that it can be interpreted as semantic feature gaps in the given model's hidden representations relative to the ideal model. We further apply this generic framework to the contextual QA task and hypothesize that three features approximate this gap: context-reliance (using the provided context rather than parametric knowledge), context comprehension (extracting relevant information from context), and honesty (avoiding intentional lies). Using a top-down interpretability approach, we extract these features by using only a small number of labeled samples and ensemble them to form a robust uncertainty score. Experiments on multiple QA benchmarks in both in-distribution and out-of-distribution settings show that our method substantially outperforms state-of-the-art unsupervised (sampling-free and sampling-based) and supervised UQ methods, achieving up to a 13-point PRR improvement while incurring a negligible inference overhead.

Despite their widespread applications, Large Language Models (LLMs) often struggle to express uncertainty, posing a challenge for reliable deployment in high stakes and safety critical domains like clinical diagnostics. Existing standard baseline methods such as model logits and elicited probabilities produce overconfident and poorly calibrated estimates. In this work, we propose Approximate Bayesian Computation (ABC), a likelihood-free Bayesian inference, based approach that treats LLMs as a stochastic simulator to infer posterior distributions over predictive probabilities. We evaluate our ABC approach on two clinically relevant benchmarks: a synthetic oral lesion diagnosis dataset and the publicly available GretelAI symptom-to-diagnosis dataset. Compared to standard baselines, our approach improves accuracy by up to 46.9\%, reduces Brier scores by 74.4\%, and enhances calibration as measured by Expected Calibration Error (ECE) and predictive entropy.

Recent reasoning Large Language Models (LLMs) demonstrate remarkable problem-solving abilities but often generate long thinking traces whose utility is unclear. Our work aims to improve their efficiency, enabling them to reach high performance without overthinking. First, we analyze the entropy of token probabilities in reasoning traces. Across three models, we observe a consistent U-shaped entropy pattern: high entropy on easy problems despite high accuracy, low entropy on problems with medium difficulty, and high entropy on hard problems reflecting uncertainty. Specifically, we notice 22--25\% entropy reduction from easy to medium difficulty regions, suggesting an {overthinking} phenomenon on easy instances. Building on these insights, we introduce DiffAdapt, a lightweight framework that selects Easy/Normal/Hard inference strategies per question based on their difficulty and reasoning trace entropy. Each inference strategy consists of a fixed prompt, temperature and maximum token length. In contrast to existing efficiency optimization methods, our approach does not fine-tune base LLM but a small probe that classifies LLM's final hidden state, allowing inexpensive adaptation. We comprehensively evaluate our method on five models and eight benchmarks. Our method achieves comparable or improved accuracy while reducing token usage by up to 22.4\%, establishing a practical path toward compute-efficient reasoning.

We present Entropy Adaptive Decoding (EAD), a novel approach for efficient language model inference that dynamically switches between different-sized models based on prediction uncertainty. By monitoring rolling entropy in model logit distributions, our method identifies text regions where a smaller model suffices and switches to a larger model only when prediction uncertainty exceeds a threshold. Unlike speculative decoding approaches that maintain perfect output fidelity through verification, EAD accepts controlled output divergence in exchange for computational efficiency. Our experiments on the MATH benchmark demonstrate remarkable efficiency gains across different model families. Using the LLaMA family, we maintain 96.7\% of the 11B model's performance (50.4\% vs 52.1\%) while using it for only 43\% of tokens, decreasing computational cost by 41.5\%. These gains become more pronounced with larger size differentials in the Qwen family, where we achieve 92.9\% of the 14B model's performance (74.3\% vs 80.0\%) while using it for just 25\% of tokens, decreasing computational cost by 67\%. The consistency of these results across model pairs suggests that language model computation can be significantly optimized by selectively deploying model capacity based on local generation complexity. Our findings indicate that current approaches to model inference may be unnecessarily conservative in their pursuit of perfect output fidelity, and that accepting minor performance trade-offs can enable dramatic reductions in computational costs.

Ensuring reliable confidence scores from deep networks is of pivotal importance in critical decision-making systems, notably in the medical domain. While recent literature on calibrating deep segmentation networks has led to significant progress, their uncertainty is usually modeled by leveraging the information of individual pixels, which disregards the local structure of the object of interest. In particular, only the recent Spatially Varying Label Smoothing (SVLS) approach addresses this issue by softening the pixel label assignments with a discrete spatial Gaussian kernel. In this work, we first present a constrained optimization perspective of SVLS and demonstrate that it enforces an implicit constraint on soft class proportions of surrounding pixels. Furthermore, our analysis shows that SVLS lacks a mechanism to balance the contribution of the constraint with the primary objective, potentially hindering the optimization process. Based on these observations, we propose a principled and simple solution based on equality constraints on the logit values, which enables to control explicitly both the enforced constraint and the weight of the penalty, offering more flexibility. Comprehensive experiments on a variety of well-known segmentation benchmarks demonstrate the superior performance of the proposed approach.

For large language models (LLMs) to be trusted by humans they need to be well-calibrated in the sense that they can accurately assess and communicate how likely it is that their predictions are correct. Recent work has focused on the quality of internal LLM confidence assessments, but the question remains of how well LLMs can communicate this internal model confidence to human users. This paper explores the disparity between external human confidence in an LLM's responses and the internal confidence of the model. Through experiments involving multiple-choice questions, we systematically examine human users' ability to discern the reliability of LLM outputs. Our study focuses on two key areas: (1) assessing users' perception of true LLM confidence and (2) investigating the impact of tailored explanations on this perception. The research highlights that default explanations from LLMs often lead to user overestimation of both the model's confidence and its' accuracy. By modifying the explanations to more accurately reflect the LLM's internal confidence, we observe a significant shift in user perception, aligning it more closely with the model's actual confidence levels. This adjustment in explanatory approach demonstrates potential for enhancing user trust and accuracy in assessing LLM outputs. The findings underscore the importance of transparent communication of confidence levels in LLMs, particularly in high-stakes applications where understanding the reliability of AI-generated information is essential.

The pervasiveness of proprietary language models has raised critical privacy concerns, necessitating advancements in private inference (PI), where computations are performed directly on encrypted data without revealing users' sensitive information. While PI offers a promising solution, its practical deployment is hindered by substantial communication and latency overheads, primarily stemming from nonlinear operations. To address this, we introduce an information-theoretic framework to characterize the role of nonlinearities in decoder-only language models, laying a principled foundation for optimizing transformer-architectures tailored to the demands of PI. By leveraging Shannon's entropy as a quantitative measure, we uncover the previously unexplored dual significance of nonlinearities: beyond ensuring training stability, they are crucial for maintaining attention head diversity. Specifically, we find that their removal triggers two critical failure modes: {\em entropy collapse} in deeper layers that destabilizes training, and {\em entropic overload} in earlier layers that leads to under-utilization of Multi-Head Attention's (MHA) representational capacity. We propose an entropy-guided attention mechanism paired with a novel entropy regularization technique to mitigate entropic overload. Additionally, we explore PI-friendly alternatives to layer normalization for preventing entropy collapse and stabilizing the training of LLMs with reduced-nonlinearities. Our study bridges the gap between information theory and architectural design, establishing entropy dynamics as a principled guide for developing efficient PI architectures. The code and implementation are available at https://github.com/Nandan91/entropy-guided-attention-llm{entropy-guided-llm}.

Recent advances in multimodal large reasoning models (MLRMs) have substantially improved their ability to solve complex textual and visual tasks. However, these models tend to overthink on simple problems, producing unnecessarily lengthy reasoning traces, while under-exploring on challenging ones, leading to missed solutions. To address this imbalance, we propose ARES, a unified open-source framework for adaptive reasoning that dynamically allocates exploration effort based on task difficulty. Our approach is motivated by two key empirical findings: (i) while single-token entropy is noisy, high window-entropy (HWE) tokens (token-level entropies averaged under a sliding window) can reliably capture reasoning-critical moments; and (ii) reducing HWE usage benefits easy problems, while increasing it is essential for solving hard ones. Building on these insights, ARES introduces a two-stage training pipeline. In the Adaptive Cold-Start stage, we curate multimodal and textual data paired with reasoning traces of length proportional to problem difficulty, equipping the model with initial difficulty awareness. In the second stage, we develop Adaptive Entropy Policy Optimization (AEPO), which uses HWE tokens as exploration triggers to decide when to explore, and a hierarchical entropy reward with dynamic KL control to decide how much to explore. Extensive experiments demonstrate that ARES achieves superior performance and reasoning efficiency across diverse mathematical, logical, and multimodal benchmarks, while closing the gap to leading commercial systems under significantly lower inference costs.

In continual learning, many classifiers use softmax function to learn confidence. However, numerous studies have pointed out its inability to accurately determine confidence distributions for outliers, often referred to as epistemic uncertainty. This inherent limitation also curtails the accurate decisions for selecting what to forget and keep in previously trained confidence distributions over continual learning process. To address the issue, we revisit the effects of masking softmax function. While this method is both simple and prevalent in literature, its implication for retaining confidence distribution during continual learning, also known as stability, has been under-investigated. In this paper, we revisit the impact of softmax masking, and introduce a methodology to utilize its confidence preservation effects. In class- and task-incremental learning benchmarks with and without memory replay, our approach significantly increases stability while maintaining sufficiently large plasticity. In the end, our methodology shows better overall performance than state-of-the-art methods, particularly in the use with zero or small memory. This lays a simple and effective foundation of strongly stable replay-based continual learning.

In recent years, multimodal large language models (MLLMs) have made significant progress but continue to face inherent challenges in multimodal reasoning, which requires multi-level (e.g., perception, reasoning) and multi-granular (e.g., multi-step reasoning chain) advanced inferencing. Prior work on estimating model confidence tends to focus on the overall response for training and calibration, but fails to assess confidence in each reasoning step, leading to undesirable hallucination snowballing. In this work, we present MMBoundary, a novel framework that advances the knowledge boundary awareness of MLLMs through reasoning step confidence calibration. To achieve this, we propose to incorporate complementary textual and cross-modal self-rewarding signals to estimate confidence at each step of the MLLM reasoning process. In addition to supervised fine-tuning MLLM on this set of self-rewarded confidence estimation signal for initial confidence expression warm-up, we introduce a reinforcement learning stage with multiple reward functions for further aligning model knowledge and calibrating confidence at each reasoning step, enhancing reasoning chain self-correction. Empirical results show that MMBoundary significantly outperforms existing methods across diverse domain datasets and metrics, achieving an average of 7.5% reduction in multimodal confidence calibration errors and up to 8.3% improvement in task performance.

Neural Radiance Fields (NeRF) exhibit remarkable performance for Novel View Synthesis (NVS) given a set of 2D images. However, NeRF training requires accurate camera pose for each input view, typically obtained by Structure-from-Motion (SfM) pipelines. Recent works have attempted to relax this constraint, but they still often rely on decent initial poses which they can refine. Here we aim at removing the requirement for pose initialization. We present Incremental CONfidence (ICON), an optimization procedure for training NeRFs from 2D video frames. ICON only assumes smooth camera motion to estimate initial guess for poses. Further, ICON introduces ``confidence": an adaptive measure of model quality used to dynamically reweight gradients. ICON relies on high-confidence poses to learn NeRF, and high-confidence 3D structure (as encoded by NeRF) to learn poses. We show that ICON, without prior pose initialization, achieves superior performance in both CO3D and HO3D versus methods which use SfM pose.

Multi-agent debates have been introduced to improve the accuracy of Large Language Models (LLMs) by having multiple agents discuss solutions to a problem over several rounds of debate. However, models often generate incorrect yet confident-sounding responses, which can mislead others. This issue arises partly because agents do not consider how confident their peers are. To address this, we propose DebUnc, a debate framework that uses uncertainty metrics to assess agent confidence. Confidence is then conveyed through a modified attention mechanism that adjusts token weights, or through textual prompts. Evaluations across benchmarks show that attention-based methods are particularly effective and that performance continues to improve as uncertainty estimation becomes more reliable. The code is available at https://github.com/lukeyoffe/debunc.

Large language models (LLMs) have demonstrated impressive performance on several tasks and are increasingly deployed in real-world applications. However, especially in high-stakes settings, it becomes vital to know when the output of an LLM may be unreliable. Depending on whether an answer is trustworthy, a system can then choose to route the question to another expert, or otherwise fall back on a safe default behavior. In this work, we study the extent to which LLMs can reliably indicate confidence in their answers, and how this notion of confidence can translate into downstream accuracy gains. We propose Self-REF, a lightweight training strategy to teach LLMs to express confidence in whether their answers are correct in a reliable manner. Self-REF introduces confidence tokens into the LLM, from which a confidence score can be extracted. Compared to conventional approaches such as verbalizing confidence and examining token probabilities, we demonstrate empirically that confidence tokens show significant improvements in downstream routing and rejection learning tasks.

Despite their widespread use, the mechanisms by which large language models (LLMs) represent and regulate uncertainty in next-token predictions remain largely unexplored. This study investigates two critical components believed to influence this uncertainty: the recently discovered entropy neurons and a new set of components that we term token frequency neurons. Entropy neurons are characterized by an unusually high weight norm and influence the final layer normalization (LayerNorm) scale to effectively scale down the logits. Our work shows that entropy neurons operate by writing onto an unembedding null space, allowing them to impact the residual stream norm with minimal direct effect on the logits themselves. We observe the presence of entropy neurons across a range of models, up to 7 billion parameters. On the other hand, token frequency neurons, which we discover and describe here for the first time, boost or suppress each token's logit proportionally to its log frequency, thereby shifting the output distribution towards or away from the unigram distribution. Finally, we present a detailed case study where entropy neurons actively manage confidence in the setting of induction, i.e. detecting and continuing repeated subsequences.

Large Language Models are known to capture real-world knowledge, allowing them to excel in many downstream tasks. Despite recent advances, these models are still prone to what are commonly known as hallucinations, causing them to emit unwanted and factually incorrect text. In this work, we propose a novel calibration method that can be used to combat hallucinations. We add a special [IDK] ("I don't know") token to the model's vocabulary and introduce an objective function that shifts probability mass to the [IDK] token for incorrect predictions. This approach allows the model to express uncertainty in its output explicitly. We evaluate our proposed method across multiple model architectures and factual downstream tasks. We find that models trained with our method are able to express uncertainty in places where they would previously make mistakes while suffering only a small loss of encoded knowledge. We further perform extensive ablation studies of multiple variations of our approach and provide a detailed analysis of the precision-recall tradeoff of our method.

In knowledge distillation literature, feature-based methods have dominated due to their ability to effectively tap into extensive teacher models. In contrast, logit-based approaches, which aim to distill `dark knowledge' from teachers, typically exhibit inferior performance compared to feature-based methods. To bridge this gap, we present LumiNet, a novel knowledge distillation algorithm designed to enhance logit-based distillation. We introduce the concept of 'perception', aiming to calibrate logits based on the model's representation capability. This concept addresses overconfidence issues in logit-based distillation method while also introducing a novel method to distill knowledge from the teacher. It reconstructs the logits of a sample/instances by considering relationships with other samples in the batch. LumiNet excels on benchmarks like CIFAR-100, ImageNet, and MSCOCO, outperforming leading feature-based methods, e.g., compared to KD with ResNet18 and MobileNetV2 on ImageNet, it shows improvements of 1.5% and 2.05%, respectively.

We show that the effectiveness of the well celebrated Mixup [Zhang et al., 2018] can be further improved if instead of using it as the sole learning objective, it is utilized as an additional regularizer to the standard cross-entropy loss. This simple change not only provides much improved accuracy but also significantly improves the quality of the predictive uncertainty estimation of Mixup in most cases under various forms of covariate shifts and out-of-distribution detection experiments. In fact, we observe that Mixup yields much degraded performance on detecting out-of-distribution samples possibly, as we show empirically, because of its tendency to learn models that exhibit high-entropy throughout; making it difficult to differentiate in-distribution samples from out-distribution ones. To show the efficacy of our approach (RegMixup), we provide thorough analyses and experiments on vision datasets (ImageNet & CIFAR-10/100) and compare it with a suite of recent approaches for reliable uncertainty estimation.

We propose ERA, a new paradigm that constrains the sampling entropy above given thresholds by applying specially designed activations to the outputs of models. Our approach demonstrates broad effectiveness across different domains: 1) for large language models(LLMs), boosting the AIME 2025 score for Qwen2.5-Math-7B by 37.4%; 2) for continuous control reinforcement learning agents, improving performance by more than 30% over strong baselines such as SAC on the challenging HumanoidBench; 3) for image classification, enhancing ImageNet top-1 accuracy by 0.69% for ResNet-50. These gains are achieved with a computational overhead of less than 7%. Our work validates output activation as a powerful tool for entropy control, opening a new direction for designing simpler and more robust algorithms.

We present a novel approach for attacking black-box large language models (LLMs) by exploiting their ability to express confidence in natural language. Existing black-box attacks require either access to continuous model outputs like logits or confidence scores (which are rarely available in practice), or rely on proxy signals from other models. Instead, we demonstrate how to prompt LLMs to express their internal confidence in a way that is sufficiently calibrated to enable effective adversarial optimization. We apply our general method to three attack scenarios: adversarial examples for vision-LLMs, jailbreaks and prompt injections. Our attacks successfully generate malicious inputs against systems that only expose textual outputs, thereby dramatically expanding the attack surface for deployed LLMs. We further find that better and larger models exhibit superior calibration when expressing confidence, creating a concerning security paradox where model capability improvements directly enhance vulnerability. Our code is available at this [link](https://github.com/zj-jayzhang/black_box_llm_optimization).

Reliable application of machine learning is of primary importance to the practical deployment of deep learning methods. A fundamental challenge is that models are often unreliable due to overconfidence. In this paper, we estimate a model's reliability by measuring the agreement between its latent space, and the latent space of a foundation model. However, it is challenging to measure the agreement between two different latent spaces due to their incoherence, \eg, arbitrary rotations and different dimensionality. To overcome this incoherence issue, we design a neighborhood agreement measure between latent spaces and find that this agreement is surprisingly well-correlated with the reliability of a model's predictions. Further, we show that fusing neighborhood agreement into a model's predictive confidence in a post-hoc way significantly improves its reliability. Theoretical analysis and extensive experiments on failure detection across various datasets verify the effectiveness of our method on both in-distribution and out-of-distribution settings.

Large language models (LLMs) have demonstrated remarkable performance across diverse tasks by encoding vast amounts of factual knowledge. However, they are still prone to hallucinations, generating incorrect or misleading information, often accompanied by high uncertainty. Existing methods for hallucination detection primarily focus on quantifying internal uncertainty, which arises from missing or conflicting knowledge within the model. However, hallucinations can also stem from external uncertainty, where ambiguous user queries lead to multiple possible interpretations. In this work, we introduce Semantic Volume, a novel mathematical measure for quantifying both external and internal uncertainty in LLMs. Our approach perturbs queries and responses, embeds them in a semantic space, and computes the determinant of the Gram matrix of the embedding vectors, capturing their dispersion as a measure of uncertainty. Our framework provides a generalizable and unsupervised uncertainty detection method without requiring white-box access to LLMs. We conduct extensive experiments on both external and internal uncertainty detection, demonstrating that our Semantic Volume method consistently outperforms existing baselines in both tasks. Additionally, we provide theoretical insights linking our measure to differential entropy, unifying and extending previous sampling-based uncertainty measures such as the semantic entropy. Semantic Volume is shown to be a robust and interpretable approach to improving the reliability of LLMs by systematically detecting uncertainty in both user queries and model responses.

As instruction-tuned large language models (LLMs) evolve, aligning pretrained foundation models presents increasing challenges. Existing alignment strategies, which typically leverage diverse and high-quality data sources, often overlook the intrinsic uncertainty of tasks, learning all data samples equally. This may lead to suboptimal data efficiency and model performance. In response, we propose uncertainty-aware learning (UAL) to improve the model alignment of different task scenarios, by introducing the sample uncertainty (elicited from more capable LLMs). We implement UAL in a simple fashion -- adaptively setting the label smoothing value of training according to the uncertainty of individual samples. Analysis shows that our UAL indeed facilitates better token clustering in the feature space, validating our hypothesis. Extensive experiments on widely used benchmarks demonstrate that our UAL significantly and consistently outperforms standard supervised fine-tuning. Notably, LLMs aligned in a mixed scenario have achieved an average improvement of 10.62\% on high-entropy tasks (i.e., AlpacaEval leaderboard), and 1.81\% on complex low-entropy tasks (i.e., MetaMath and GSM8K).

Current graph neural networks (GNNs) that tackle node classification on graphs tend to only focus on nodewise scores and are solely evaluated by nodewise metrics. This limits uncertainty estimation on graphs since nodewise marginals do not fully characterize the joint distribution given the graph structure. In this work, we propose novel edgewise metrics, namely the edgewise expected calibration error (ECE) and the agree/disagree ECEs, which provide criteria for uncertainty estimation on graphs beyond the nodewise setting. Our experiments demonstrate that the proposed edgewise metrics can complement the nodewise results and yield additional insights. Moreover, we show that GNN models which consider the structured prediction problem on graphs tend to have better uncertainty estimations, which illustrates the benefit of going beyond the nodewise setting.

FOLD-RM is an explainable machine learning classification algorithm that uses training data to create a set of classification rules. In this paper we introduce CON-FOLD which extends FOLD-RM in several ways. CON-FOLD assigns probability-based confidence scores to rules learned for a classification task. This allows users to know how confident they should be in a prediction made by the model. We present a confidence-based pruning algorithm that uses the unique structure of FOLD-RM rules to efficiently prune rules and prevent overfitting. Furthermore, CON-FOLD enables the user to provide pre-existing knowledge in the form of logic program rules that are either (fixed) background knowledge or (modifiable) initial rule candidates. The paper describes our method in detail and reports on practical experiments. We demonstrate the performance of the algorithm on benchmark datasets from the UCI Machine Learning Repository. For that, we introduce a new metric, Inverse Brier Score, to evaluate the accuracy of the produced confidence scores. Finally we apply this extension to a real world example that requires explainability: marking of student responses to a short answer question from the Australian Physics Olympiad.

Large Language Models (LLMs) have demonstrated great capabilities in solving a wide range of tasks in a resource-efficient manner through prompting, which does not require task-specific training, but suffers from performance fluctuation when there are multiple prompt candidates. Previous works have introduced gradient-free probability-based prompt selection methods that aim to choose the optimal prompt among the candidates for a given task but fail to provide a comprehensive and fair comparison between each other. In this paper, we propose a unified framework to interpret and evaluate the existing probability-based prompt selection methods by performing extensive experiments on 13 common NLP tasks. We find that all existing methods can be unified into some variant of the method that maximizes the mutual information between the input and the corresponding model output (denoted as MI). Using the finding, we develop several variants of MI and increases the effectiveness of the best prompt selection method from 87.79% to 94.98%, measured as the ratio of the performance of the selected prompt to that of the optimal oracle prompt. Furthermore, we propose a novel calibration method called Calibration by Marginalization (CBM) that is orthogonal to existing methods and helps increase the prompt selection effectiveness of the best method by 99.44%. The code and datasets used in our work will be released at https://github.com/soheeyang/unified-prompt-selection.

The mechanisms behind the success of multi-view self-supervised learning (MVSSL) are not yet fully understood. Contrastive MVSSL methods have been studied through the lens of InfoNCE, a lower bound of the Mutual Information (MI). However, the relation between other MVSSL methods and MI remains unclear. We consider a different lower bound on the MI consisting of an entropy and a reconstruction term (ER), and analyze the main MVSSL families through its lens. Through this ER bound, we show that clustering-based methods such as DeepCluster and SwAV maximize the MI. We also re-interpret the mechanisms of distillation-based approaches such as BYOL and DINO, showing that they explicitly maximize the reconstruction term and implicitly encourage a stable entropy, and we confirm this empirically. We show that replacing the objectives of common MVSSL methods with this ER bound achieves competitive performance, while making them stable when training with smaller batch sizes or smaller exponential moving average (EMA) coefficients. Github repo: https://github.com/apple/ml-entropy-reconstruction.

Current question-answering benchmarks predominantly focus on accuracy in realizable prediction tasks. Conditioned on a question and answer-key, does the most likely token match the ground truth? Such benchmarks necessarily fail to evaluate LLMs' ability to quantify ground-truth outcome uncertainty. In this work, we focus on the use of LLMs as risk scores for unrealizable prediction tasks. We introduce folktexts, a software package to systematically generate risk scores using LLMs, and evaluate them against US Census data products. A flexible API enables the use of different prompting schemes, local or web-hosted models, and diverse census columns that can be used to compose custom prediction tasks. We evaluate 17 recent LLMs across five proposed benchmark tasks. We find that zero-shot risk scores produced by multiple-choice question-answering have high predictive signal but are widely miscalibrated. Base models consistently overestimate outcome uncertainty, while instruction-tuned models underestimate uncertainty and produce over-confident risk scores. In fact, instruction-tuning polarizes answer distribution regardless of true underlying data uncertainty. This reveals a general inability of instruction-tuned LLMs to express data uncertainty using multiple-choice answers. A separate experiment using verbalized chat-style risk queries yields substantially improved calibration across instruction-tuned models. These differences in ability to quantify data uncertainty cannot be revealed in realizable settings, and highlight a blind-spot in the current evaluation ecosystem that folktexts covers.

As large language models continue to scale, their growing computational and storage demands pose significant challenges for real-world deployment. In this work, we investigate redundancy within Transformer-based models and propose an entropy-based pruning strategy to enhance efficiency while maintaining performance. Empirical analysis reveals that the entropy of hidden representations decreases in the early blocks but progressively increases across most subsequent blocks. This trend suggests that entropy serves as a more effective measure of information richness within computation blocks. Unlike cosine similarity, which primarily captures geometric relationships, entropy directly quantifies uncertainty and information content, making it a more reliable criterion for pruning. Extensive experiments demonstrate that our entropy-based pruning approach surpasses cosine similarity-based methods in reducing model size while preserving accuracy, offering a promising direction for efficient model deployment.

A set of novel approaches for estimating epistemic uncertainty in deep neural networks with a single forward pass has recently emerged as a valid alternative to Bayesian Neural Networks. On the premise of informative representations, these deterministic uncertainty methods (DUMs) achieve strong performance on detecting out-of-distribution (OOD) data while adding negligible computational costs at inference time. However, it remains unclear whether DUMs are well calibrated and can seamlessly scale to real-world applications - both prerequisites for their practical deployment. To this end, we first provide a taxonomy of DUMs, and evaluate their calibration under continuous distributional shifts. Then, we extend them to semantic segmentation. We find that, while DUMs scale to realistic vision tasks and perform well on OOD detection, the practicality of current methods is undermined by poor calibration under distributional shifts.

Allocating more computation during inference time (test-time scaling) improves language model performance, especially for reasoning tasks. However, popular methods like Best-of-N sampling often show diminishing returns as N increases. To address this inefficiency, we introduce a general test-time calibration framework that adaptively modifies the model toward high-reward reasoning paths, with theoretical guarantees of improving the lower bound of expected reward under finite sampling, all without large language model (LLM) retraining. Within this framework, we propose CarBoN (Calibrated Best-of-N), a two-phase method that first explores the solution space and then learns a calibration of the logits via an input-specific temperature T and additive shift vector delta, guiding generation toward more reliable reasoning. Experiments on MATH-500 and AIME-2024 show that CarBoN improves efficiency, with up to 4times fewer rollouts to reach the same accuracy, while often achieving higher accuracy under fixed budgets. We also analyze the complementary roles of T and delta in balancing output diversity and correctness, and demonstrate that the framework also generalizes to step-level sampling strategies such as beam search. For more information, please refer to our project page at huggingface.co/spaces/TrustSafeAI/Test-Time-Calibration.

Due to depth ambiguities and occlusions, lifting 2D poses to 3D is a highly ill-posed problem. Well-calibrated distributions of possible poses can make these ambiguities explicit and preserve the resulting uncertainty for downstream tasks. This study shows that previous attempts, which account for these ambiguities via multiple hypotheses generation, produce miscalibrated distributions. We identify that miscalibration can be attributed to the use of sample-based metrics such as minMPJPE. In a series of simulations, we show that minimizing minMPJPE, as commonly done, should converge to the correct mean prediction. However, it fails to correctly capture the uncertainty, thus resulting in a miscalibrated distribution. To mitigate this problem, we propose an accurate and well-calibrated model called Conditional Graph Normalizing Flow (cGNFs). Our model is structured such that a single cGNF can estimate both conditional and marginal densities within the same model - effectively solving a zero-shot density estimation problem. We evaluate cGNF on the Human~3.6M dataset and show that cGNF provides a well-calibrated distribution estimate while being close to state-of-the-art in terms of overall minMPJPE. Furthermore, cGNF outperforms previous methods on occluded joints while it remains well-calibrated.

Large language models (LLMs), despite their impressive performance across a wide range of tasks, often struggle to balance two competing objectives in open-ended text generation: fostering diversity and creativity while preserving logical coherence. Existing truncated sampling techniques, including temperature scaling, top-\p (nucleus) sampling, and min-\p sampling, aim to manage this trade-off. However, they exhibit limitations, particularly in the effective incorporation of the confidence of the model into the corresponding sampling strategy. For example, min-\p sampling relies on a single top token as a heuristic for confidence, eventually underutilizing the information of the probability distribution. Toward effective incorporation of the confidence of the model, in this paper, we present **top-H** decoding. We first establish the theoretical foundation of the interplay between creativity and coherence in truncated sampling by formulating an **entropy-constrained minimum divergence** problem. We then prove this minimization problem to be equivalent to an **entropy-constrained mass maximization** (ECMM) problem, which is NP-hard. Finally, we present top-H decoding, a computationally efficient greedy algorithm to solve the ECMM problem. Extensive empirical evaluations demonstrate that top-H outperforms the state-of-the-art (SoTA) alternative of min-\p sampling by up to **25.63%** on creative writing benchmarks, while maintaining robustness on question-answering datasets such as GPQA, GSM8K, and MT-Bench. Additionally, an *LLM-as-judge* evaluation confirms that top-H indeed produces coherent outputs even at higher temperatures, where creativity is especially critical. In summary, top-H advances SoTA in open-ended text generation and can be *easily integrated* into creative writing applications. The code is available at https://github.com/ErfanBaghaei/Top-H-Decoding.

This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape. Local extrema with low generalization error have a large proportion of almost-zero eigenvalues in the Hessian with very few positive or negative eigenvalues. We leverage upon this observation to construct a local-entropy-based objective function that favors well-generalizable solutions lying in large flat regions of the energy landscape, while avoiding poorly-generalizable solutions located in the sharp valleys. Conceptually, our algorithm resembles two nested loops of SGD where we use Langevin dynamics in the inner loop to compute the gradient of the local entropy before each update of the weights. We show that the new objective has a smoother energy landscape and show improved generalization over SGD using uniform stability, under certain assumptions. Our experiments on convolutional and recurrent networks demonstrate that Entropy-SGD compares favorably to state-of-the-art techniques in terms of generalization error and training time.

The mathematical problem-solving capabilities of large language models have become a focal point of research, with growing interests in leveraging self-generated reasoning paths as a promising way to refine and enhance these models. These paths capture step-by-step logical processes while requiring only the correct answer for supervision. The self-training method has been shown to be effective in reasoning tasks while eliminating the need for external models and manual annotations. However, optimizing the use of self-generated data for model training remains an open challenge. In this work, we propose Entropy-Based Adaptive Weighting for Self-Training (EAST), an adaptive weighting strategy designed to prioritize uncertain data during self-training. Specifically, EAST employs a mapping function with a tunable parameter that controls the sharpness of the weighting, assigning higher weights to data where the model exhibits greater uncertainty. This approach guides the model to focus on more informative and challenging examples, thereby enhancing its reasoning ability. We evaluate our approach on GSM8K and MATH benchmarks. Empirical results show that, while the vanilla method yields virtually no improvement (0%) on MATH, EAST achieves around a 1% gain over backbone model. On GSM8K, EAST attains a further 1-2% performance boost compared to the vanilla method.

We study whether language models can evaluate the validity of their own claims and predict which questions they will be able to answer correctly. We first show that larger models are well-calibrated on diverse multiple choice and true/false questions when they are provided in the right format. Thus we can approach self-evaluation on open-ended sampling tasks by asking models to first propose answers, and then to evaluate the probability "P(True)" that their answers are correct. We find encouraging performance, calibration, and scaling for P(True) on a diverse array of tasks. Performance at self-evaluation further improves when we allow models to consider many of their own samples before predicting the validity of one specific possibility. Next, we investigate whether models can be trained to predict "P(IK)", the probability that "I know" the answer to a question, without reference to any particular proposed answer. Models perform well at predicting P(IK) and partially generalize across tasks, though they struggle with calibration of P(IK) on new tasks. The predicted P(IK) probabilities also increase appropriately in the presence of relevant source materials in the context, and in the presence of hints towards the solution of mathematical word problems. We hope these observations lay the groundwork for training more honest models, and for investigating how honesty generalizes to cases where models are trained on objectives other than the imitation of human writing.

Language models are increasingly used in Brazil, but most evaluation remains English-centric. This paper presents Alvorada-Bench, a 4,515-question, text-only benchmark drawn from five Brazilian university entrance examinations. Evaluating twenty models under zero-shot, role-playing, and chain-of-thought prompting, producing 270,900 responses with structured self-reports of confidence, perceived difficulty, and Bloom level. The top models exceed 94% accuracy overall, but accuracy declines on Mathematics and on the engineering oriented IME and ITA exams, indicating persistent weaknesses in multi-step reasoning. Confidence is well calibrated and correlates with perceived difficulty, revealing that models can accurately assess their own certainty capabilities. A cost accuracy analysis shows that high accuracy is achievable at under $2 per 1K tokens. On ENEM 2024 the top model (O3) achieved perfect scores in Languages subject questions while even the weakest system (GPT-4.1 Nano) only underperforms humans in Mathematics. Through exams that distill decades of Brazilian educational priorities and assess millions of students yearly, Alvorada-Bench establishes whether language models can navigate the intersection of language, culture, and reasoning that defines academic readiness in Brazil.

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or whether a patient has died or not), because the ground-truth probabilities of the events of interest are typically unknown. The problem is therefore analogous to binary classification, with the difference that the objective is to estimate probabilities rather than predicting the specific outcome. This work investigates probability estimation from high-dimensional data using deep neural networks. There exist several methods to improve the probabilities generated by these models but they mostly focus on model (epistemic) uncertainty. For problems with inherent uncertainty, it is challenging to evaluate performance without access to ground-truth probabilities. To address this, we build a synthetic dataset to study and compare different computable metrics. We evaluate existing methods on the synthetic data as well as on three real-world probability estimation tasks, all of which involve inherent uncertainty: precipitation forecasting from radar images, predicting cancer patient survival from histopathology images, and predicting car crashes from dashcam videos. We also give a theoretical analysis of a model for high-dimensional probability estimation which reproduces several of the phenomena evinced in our experiments. Finally, we propose a new method for probability estimation using neural networks, which modifies the training process to promote output probabilities that are consistent with empirical probabilities computed from the data. The method outperforms existing approaches on most metrics on the simulated as well as real-world data.

The hallucination of non-existent facts by LLMs is an important problem given its widespread adoption across various applications. Previous research addresses this problem by analyzing the internal parameterized knowledge boundaries to estimate confidence. However, these studies focus on the single-problem setting and have not explored the more challenging multi-problem setting, which requires accurately answering multiple questions simultaneously. We introduce a novel method for the multi-problem setting, Multiple Answers and Confidence Stepwise Tuning (MAC-Tuning), that separates the learning of answer prediction and confidence estimation during fine-tuning on instruction data. Extensive experiments demonstrate that our method outperforms baselines by up to 25\% in average precision.

Large Language Models (LLMs) hallucinate, generating factually incorrect yet confident assertions. We argue this stems from the Transformer's Softmax function, which creates "Artificial Certainty" by collapsing ambiguous attention scores into a single probability distribution, discarding uncertainty information at each layer. To fix this, we introduce the Credal Transformer, which replaces standard attention with a Credal Attention Mechanism (CAM) based on evidential theory. CAM produces a "credal set" (a set of distributions) instead of a single attention vector, with the set's size directly measuring model uncertainty. We implement this by re-conceptualizing attention scores as evidence masses for a Dirichlet distribution: sufficient evidence recovers standard attention, while insufficient evidence yields a diffuse distribution, representing ambiguity. Empirically, the Credal Transformer identifies out-of-distribution inputs, quantifies ambiguity, and significantly reduces confident errors on unanswerable questions by abstaining. Our contribution is a new architecture to mitigate hallucinations and a design paradigm that integrates uncertainty quantification directly into the model, providing a foundation for more reliable AI.

As Large Language Models (LLMs) become increasingly computationally complex, developing efficient deployment strategies, such as quantization, becomes crucial. State-of-the-art Post-training Quantization (PTQ) techniques often rely on calibration processes to maintain the accuracy of these models. However, while these calibration techniques can enhance performance in certain domains, they may not be as effective in others. This paper aims to draw attention to robust statistical approaches that can mitigate such issues. We propose a weight-adaptive PTQ method that can be considered a precursor to calibration-based PTQ methods, guiding the quantization process to preserve the distribution of weights by minimizing the Kullback-Leibler divergence between the quantized weights and the originally trained weights. This minimization ensures that the quantized model retains the Shannon information content of the original model to a great extent, guaranteeing robust and efficient deployment across many tasks. As such, our proposed approach can perform on par with most common calibration-based PTQ methods, establishing a new pre-calibration step for further adjusting the quantized weights with calibration. We show that our pre-calibration results achieve the same accuracy as some existing calibration-based PTQ methods on various LLMs.

Conformal Prediction (CP) controls the prediction uncertainty of classification systems by producing a small prediction set, ensuring a predetermined probability that the true class lies within this set. This is commonly done by defining a score, based on the model predictions, and setting a threshold on this score using a validation set. In this study, we address the problem of CP calibration when we only have access to a calibration set with noisy labels. We show how we can estimate the noise-free conformal threshold based on the noisy labeled data. We derive a finite sample coverage guarantee for uniform noise that remains effective even in tasks with a large number of classes. We dub our approach Noise-Aware Conformal Prediction (NACP). We illustrate the performance of the proposed results on several standard image classification datasets with a large number of classes.

Recent work has sought to quantify large language model uncertainty to facilitate model control and modulate user trust. Previous works focus on measures of uncertainty that are theoretically grounded or reflect the average overt behavior of the model. In this work, we investigate a variety of uncertainty measures, in order to identify measures that correlate with human group-level uncertainty. We find that Bayesian measures and a variation on entropy measures, top-k entropy, tend to agree with human behavior as a function of model size. We find that some strong measures decrease in human-similarity with model size, but, by multiple linear regression, we find that combining multiple uncertainty measures provide comparable human-alignment with reduced size-dependency.

Balancing exploration and exploitation is a central goal in reinforcement learning (RL). Despite recent advances in enhancing language model (LM) reasoning, most methods lean toward exploitation, and increasingly encounter performance plateaus. In this work, we revisit entropy -- a signal of exploration in RL -- and examine its relationship to exploratory reasoning in LMs. Through empirical analysis, we uncover strong positive correlations between high-entropy regions and three types of exploratory reasoning actions: (1) pivotal tokens that determine or connect logical steps, (2) reflective actions such as self-verification and correction, and (3) rare behaviors under-explored by the base LMs. Motivated by this, we introduce a minimal modification to standard RL with only one line of code: augmenting the advantage function with an entropy-based term. Unlike traditional maximum-entropy methods which encourage exploration by promoting uncertainty, we encourage exploration by promoting longer and deeper reasoning chains. Notably, our method achieves significant gains on the Pass@K metric -- an upper-bound estimator of LM reasoning capabilities -- even when evaluated with extremely large K values, pushing the boundaries of LM reasoning.

Datasets scraped from the internet have been critical to the successes of large-scale machine learning. Yet, this very success puts the utility of future internet-derived datasets at potential risk, as model outputs begin to replace human annotations as a source of supervision. In this work, we first formalize a system where interactions with one model are recorded as history and scraped as training data in the future. We then analyze its stability over time by tracking changes to a test-time bias statistic (e.g. gender bias of model predictions). We find that the degree of bias amplification is closely linked to whether the model's outputs behave like samples from the training distribution, a behavior which we characterize and define as consistent calibration. Experiments in three conditional prediction scenarios - image classification, visual role-labeling, and language generation - demonstrate that models that exhibit a sampling-like behavior are more calibrated and thus more stable. Based on this insight, we propose an intervention to help calibrate and stabilize unstable feedback systems. Code is available at https://github.com/rtaori/data_feedback.

We consider the issue of calibration in large language models (LLM). Recent studies have found that common interventions such as instruction tuning often result in poorly calibrated LLMs. Although calibration is well-explored in traditional applications, calibrating LLMs is uniquely challenging. These challenges stem as much from the severe computational requirements of LLMs as from their versatility, which allows them to be applied to diverse tasks. Addressing these challenges, we propose THERMOMETER, a calibration approach tailored to LLMs. THERMOMETER learns an auxiliary model, given data from multiple tasks, for calibrating a LLM. It is computationally efficient, preserves the accuracy of the LLM, and produces better-calibrated responses for new tasks. Extensive empirical evaluations across various benchmarks demonstrate the effectiveness of the proposed method.

Popular approaches for quantifying predictive uncertainty in deep neural networks often involve distributions over weights or multiple models, for instance via Markov Chain sampling, ensembling, or Monte Carlo dropout. These techniques usually incur overhead by having to train multiple model instances or do not produce very diverse predictions. This comprehensive and extensive survey aims to familiarize the reader with an alternative class of models based on the concept of Evidential Deep Learning: For unfamiliar data, they aim to admit "what they don't know", and fall back onto a prior belief. Furthermore, they allow uncertainty estimation in a single model and forward pass by parameterizing distributions over distributions. This survey recapitulates existing works, focusing on the implementation in a classification setting, before surveying the application of the same paradigm to regression. We also reflect on the strengths and weaknesses compared to other existing methods and provide the most fundamental derivations using a unified notation to aid future research.

Extracting low-dimensional summary statistics from large datasets is essential for efficient (likelihood-free) inference. We characterize different classes of summaries and demonstrate their importance for correctly analysing dimensionality reduction algorithms. We demonstrate that minimizing the expected posterior entropy (EPE) under the prior predictive distribution of the model subsumes many existing methods. They are equivalent to or are special or limiting cases of minimizing the EPE. We offer a unifying framework for obtaining informative summaries, provide concrete recommendations for practitioners, and propose a practical method to obtain high-fidelity summaries whose utility we demonstrate for both benchmark and practical examples.

We present a comprehensive evaluation of proprietary and open-weights large language models using the first astronomy-specific benchmarking dataset. This dataset comprises 4,425 multiple-choice questions curated from the Annual Review of Astronomy and Astrophysics, covering a broad range of astrophysical topics. Our analysis examines model performance across various astronomical subfields and assesses response calibration, crucial for potential deployment in research environments. Claude-3.5-Sonnet outperforms competitors by up to 4.6 percentage points, achieving 85.0% accuracy. For proprietary models, we observed a universal reduction in cost every 3-to-12 months to achieve similar score in this particular astronomy benchmark. Open-source models have rapidly improved, with LLaMA-3-70b (80.6%) and Qwen-2-72b (77.7%) now competing with some of the best proprietary models. We identify performance variations across topics, with non-English-focused models generally struggling more in exoplanet-related fields, stellar astrophysics, and instrumentation related questions. These challenges likely stem from less abundant training data, limited historical context, and rapid recent developments in these areas. This pattern is observed across both open-weights and proprietary models, with regional dependencies evident, highlighting the impact of training data diversity on model performance in specialized scientific domains. Top-performing models demonstrate well-calibrated confidence, with correlations above 0.9 between confidence and correctness, though they tend to be slightly underconfident. The development for fast, low-cost inference of open-weights models presents new opportunities for affordable deployment in astronomy. The rapid progress observed suggests that LLM-driven research in astronomy may become feasible in the near future.

Large Language Models (LLMs) suffer significant performance degradation in multi-turn conversations when information is presented incrementally. Given that multi-turn conversations characterize everyday interactions with LLMs, this degradation poses a severe challenge to real world usability. We hypothesize that abrupt increases in model uncertainty signal misalignment in multi-turn LLM interactions, and we exploit this insight to dynamically realign conversational context. We introduce ERGO (Entropy-guided Resetting for Generation Optimization), which continuously quantifies internal uncertainty via Shannon entropy over next token distributions and triggers adaptive prompt consolidation when a sharp spike in entropy is detected. By treating uncertainty as a first class signal rather than a nuisance to eliminate, ERGO embraces variability in language and modeling, representing and responding to uncertainty. In multi-turn tasks with incrementally revealed instructions, ERGO yields a 56.6% average performance gain over standard baselines, increases aptitude (peak performance capability) by 24.7%, and decreases unreliability (variability in performance) by 35.3%, demonstrating that uncertainty aware interventions can improve both accuracy and reliability in conversational AI.

Adversarial robustness often comes at the cost of degraded accuracy, impeding the real-life application of robust classification models. Training-based solutions for better trade-offs are limited by incompatibilities with already-trained high-performance large models, necessitating the exploration of training-free ensemble approaches. Observing that robust models are more confident in correct predictions than in incorrect ones on clean and adversarial data alike, we speculate amplifying this "benign confidence property" can reconcile accuracy and robustness in an ensemble setting. To achieve so, we propose "MixedNUTS", a training-free method where the output logits of a robust classifier and a standard non-robust classifier are processed by nonlinear transformations with only three parameters, which are optimized through an efficient algorithm. MixedNUTS then converts the transformed logits into probabilities and mixes them as the overall output. On CIFAR-10, CIFAR-100, and ImageNet datasets, experimental results with custom strong adaptive attacks demonstrate MixedNUTS's vastly improved accuracy and near-SOTA robustness -- it boosts CIFAR-100 clean accuracy by 7.86 points, sacrificing merely 0.87 points in robust accuracy.

Reinforcement learning with verifiable rewards (RLVR) has shown great promise in enhancing the reasoning abilities of large reasoning models (LRMs). However, it suffers from a critical issue: entropy collapse and premature convergence. Naive entropy regularization, a common approach for encouraging exploration in the traditional RL literature, fails to address this problem in the context of LRM. Our analysis reveals that this failure stems from the vast action space and long trajectories in LRMs, which easily trigger a global entropy explosion as the model indiscriminately explores all possible actions and states. To address this, we propose SIREN (SelectIve entRopy rEgularizatioN), a method that confines exploration to a meaningful subset of actions and states. SIREN achieves this through a two-step entropy masking mechanism, consisting of a top-p mask and a peak-entropy mask. In addition, regularization is transformed into a self-anchored form to stabilize training. Across five mathematical benchmarks, SIREN attains superior average performance over previous entropy-related RLVR approaches, exemplified by a +6.6 maj@k improvement on AIME24/25 with Qwen2.5-Math-7B. Further analysis confirms that SIREN promotes greater response diversity and maintains entropy at an appropriate level, which helps to preserve the validation pass@k throughout training. This effectively mitigates the premature convergence problem common in RLVR for LRM.

Large language models (LLMs) offer powerful capabilities but incur substantial computational costs, driving the need for efficient compression techniques. This study evaluates the impact of popular compression methods - Magnitude Pruning, SparseGPT, and Wanda - on the LLaMA-2-7B model, focusing on the trade-offs between model size reduction, downstream task performance, and the role of calibration data. Our findings reveal that while SparseGPT and Wanda preserve perplexity even at 50% sparsity, they suffer significant degradation on downstream tasks, highlighting the inadequacy of perplexity as the sole evaluation metric. To address this, we introduce Jensen-Shannon (JS) Divergence as a more comprehensive metric that captures nuanced changes in model behavior post-compression. We further demonstrate that task-specific calibration data significantly enhances the downstream performance of compressed models compared to general calibration data. This research underscores the necessity for diverse evaluation metrics and careful calibration data selection to fully understand the complexities of LLM compression and its implications for practical applications.

Tagging systems play an essential role in various information retrieval applications such as search engines and recommender systems. Recently, Large Language Models (LLMs) have been applied in tagging systems due to their extensive world knowledge, semantic understanding, and reasoning capabilities. Despite achieving remarkable performance, existing methods still have limitations, including difficulties in retrieving relevant candidate tags comprehensively, challenges in adapting to emerging domain-specific knowledge, and the lack of reliable tag confidence quantification. To address these three limitations above, we propose an automatic tagging system LLM4Tag. First, a graph-based tag recall module is designed to effectively and comprehensively construct a small-scale highly relevant candidate tag set. Subsequently, a knowledge-enhanced tag generation module is employed to generate accurate tags with long-term and short-term knowledge injection. Finally, a tag confidence calibration module is introduced to generate reliable tag confidence scores. Extensive experiments over three large-scale industrial datasets show that LLM4Tag significantly outperforms the state-of-the-art baselines and LLM4Tag has been deployed online for content tagging to serve hundreds of millions of users.

Recent studies introduced effective compression techniques for Large Language Models (LLMs) via post-training quantization or low-bit weight representation. Although quantized weights offer storage efficiency and allow for faster inference, existing works have indicated that quantization might compromise performance and exacerbate biases in LLMs. This study investigates the confidence and calibration of quantized models, considering factors such as language model type and scale as contributors to quantization loss. Firstly, we reveal that quantization with GPTQ to 4-bit results in a decrease in confidence regarding true labels, with varying impacts observed among different language models. Secondly, we observe fluctuations in the impact on confidence across different scales. Finally, we propose an explanation for quantization loss based on confidence levels, indicating that quantization disproportionately affects samples where the full model exhibited low confidence levels in the first place.

With the widespread application of Large Language Models (LLMs) to various domains, concerns regarding the trustworthiness of LLMs in safety-critical scenarios have been raised, due to their unpredictable tendency to hallucinate and generate misinformation. Existing LLMs do not have an inherent functionality to provide the users with an uncertainty/confidence metric for each response it generates, making it difficult to evaluate trustworthiness. Although several studies aim to develop uncertainty quantification methods for LLMs, they have fundamental limitations, such as being restricted to classification tasks, requiring additional training and data, considering only lexical instead of semantic information, and being prompt-wise but not response-wise. A new framework is proposed in this paper to address these issues. Semantic density extracts uncertainty/confidence information for each response from a probability distribution perspective in semantic space. It has no restriction on task types and is "off-the-shelf" for new models and tasks. Experiments on seven state-of-the-art LLMs, including the latest Llama 3 and Mixtral-8x22B models, on four free-form question-answering benchmarks demonstrate the superior performance and robustness of semantic density compared to prior approaches.

Recent advances in large language models (LLMs) have fueled the vision of automated scientific discovery, often called AI Co-Scientists. To date, prior work casts these systems as generative co-authors responsible for crafting hypotheses, synthesizing code, or drafting manuscripts. In this work, we explore a complementary application: using LLMs as verifiers to automate the academic verification of scientific manuscripts. To that end, we introduce SPOT, a dataset of 83 published papers paired with 91 errors significant enough to prompt errata or retraction, cross-validated with actual authors and human annotators. Evaluating state-of-the-art LLMs on SPOT, we find that none surpasses 21.1\% recall or 6.1\% precision (o3 achieves the best scores, with all others near zero). Furthermore, confidence estimates are uniformly low, and across eight independent runs, models rarely rediscover the same errors, undermining their reliability. Finally, qualitative analysis with domain experts reveals that even the strongest models make mistakes resembling student-level misconceptions derived from misunderstandings. These findings highlight the substantial gap between current LLM capabilities and the requirements for dependable AI-assisted academic verification.

In legal decisions, split votes (SV) occur when judges cannot reach a unanimous decision, posing a difficulty for lawyers who must navigate diverse legal arguments and opinions. In high-stakes domains, understanding the alignment of perceived difficulty between humans and AI systems is crucial to build trust. However, existing NLP calibration methods focus on a classifier's awareness of predictive performance, measured against the human majority class, overlooking inherent human label variation (HLV). This paper explores split votes as naturally observable human disagreement and value pluralism. We collect judges' vote distributions from the European Court of Human Rights (ECHR), and present SV-ECHR, a case outcome classification (COC) dataset with SV information. We build a taxonomy of disagreement with SV-specific subcategories. We further assess the alignment of perceived difficulty between models and humans, as well as confidence- and human-calibration of COC models. We observe limited alignment with the judge vote distribution. To our knowledge, this is the first systematic exploration of calibration to human judgements in legal NLP. Our study underscores the necessity for further research on measuring and enhancing model calibration considering HLV in legal decision tasks.

A crucial requirement for reliable deployment of deep learning models for safety-critical applications is the ability to identify out-of-distribution (OOD) data points, samples which differ from the training data and on which a model might underperform. Previous work has attempted to tackle this problem using uncertainty estimation techniques. However, there is empirical evidence that a large family of these techniques do not detect OOD reliably in classification tasks. This paper gives a theoretical explanation for said experimental findings and illustrates it on synthetic data. We prove that such techniques are not able to reliably identify OOD samples in a classification setting, since their level of confidence is generalized to unseen areas of the feature space. This result stems from the interplay between the representation of ReLU networks as piece-wise affine transformations, the saturating nature of activation functions like softmax, and the most widely-used uncertainty metrics.

Transformers, currently the state-of-the-art in natural language understanding (NLU) tasks, are prone to generate uncalibrated predictions or extreme probabilities, making the process of taking different decisions based on their output relatively difficult. In this paper we propose to build several inductive Venn--ABERS predictors (IVAP), which are guaranteed to be well calibrated under minimal assumptions, based on a selection of pre-trained transformers. We test their performance over a set of diverse NLU tasks and show that they are capable of producing well-calibrated probabilistic predictions that are uniformly spread over the [0,1] interval -- all while retaining the original model's predictive accuracy.