Daily Papers

We propose a lightweight explainable guardrail (LEG) method for the classification of unsafe prompts. LEG uses a multi-task learning architecture to jointly learn a prompt classifier and an explanation classifier, where the latter labels prompt words that explain the safe/unsafe overall decision. LEG is trained using synthetic data for explainability, which is generated using a novel strategy that counteracts the confirmation biases of LLMs. Lastly, LEG's training process uses a novel loss that captures global explanation signals and combines cross-entropy and focal losses with uncertainty-based weighting. LEG obtains equivalent or better performance than the state-of-the-art for both prompt classification and explainability, both in-domain and out-of-domain on three datasets, despite the fact that its model size is considerably smaller than current approaches. If accepted, we will release all models and the annotated dataset publicly.

We investigate the convergence rates and data sample sizes required for training a machine learning model using a stochastic gradient descent (SGD) algorithm, where data points are sampled based on either their loss value or uncertainty value. These training methods are particularly relevant for active learning and data subset selection problems. For SGD with a constant step size update, we present convergence results for linear classifiers and linearly separable datasets using squared hinge loss and similar training loss functions. Additionally, we extend our analysis to more general classifiers and datasets, considering a wide range of loss-based sampling strategies and smooth convex training loss functions. We propose a novel algorithm called Adaptive-Weight Sampling (AWS) that utilizes SGD with an adaptive step size that achieves stochastic Polyak's step size in expectation. We establish convergence rate results for AWS for smooth convex training loss functions. Our numerical experiments demonstrate the efficiency of AWS on various datasets by using either exact or estimated loss values.

We introduce Entropy-Guided Sequence Weighting (EGSW), a novel approach that enhances the exploration-exploitation tradeoff by dynamically assigning weights to generated outputs based on their advantage and entropy for Reinforcement Learning-based Large Language Model fine-tuning. EGSW integrates entropy regularization with advantage-based weighting to balance policy updates, enabling efficient exploration in high-dimensional state spaces. By employing temperature-scaled softmax weighting over sequences, EGSW prioritizing high-reward, high-uncertainty steps while maintaining training stability. Although originally developed to improve Group Relative Policy Optimization (GRPO) during large language model (LLM) fine-tuning, EGSW is generalizable to other reinforcement learning (RL) algorithms and can be implemented in both step-wise and trajectory-wise settings. Empirical evaluations demonstrate that EGSW enhances GRPO reasoning ability, yielding improvements in sample efficiency. Future work will explore the application of EGSW to advanced RL methodologies.

Diffusion-based image super-resolution methods have demonstrated significant advantages over GAN-based approaches, particularly in terms of perceptual quality. Building upon a lengthy Markov chain, diffusion-based methods possess remarkable modeling capacity, enabling them to achieve outstanding performance in real-world scenarios. Unlike previous methods that focus on modifying the noise schedule or sampling process to enhance performance, our approach emphasizes the improved utilization of LR information. We find that different regions of the LR image can be viewed as corresponding to different timesteps in a diffusion process, where flat areas are closer to the target HR distribution but edge and texture regions are farther away. In these flat areas, applying a slight noise is more advantageous for the reconstruction. We associate this characteristic with uncertainty and propose to apply uncertainty estimate to guide region-specific noise level control, a technique we refer to as Uncertainty-guided Noise Weighting. Pixels with lower uncertainty (i.e., flat regions) receive reduced noise to preserve more LR information, therefore improving performance. Furthermore, we modify the network architecture of previous methods to develop our Uncertainty-guided Perturbation Super-Resolution (UPSR) model. Extensive experimental results demonstrate that, despite reduced model size and training overhead, the proposed UWSR method outperforms current state-of-the-art methods across various datasets, both quantitatively and qualitatively.

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 propose the MAC-VO, a novel learning-based stereo VO that leverages the learned metrics-aware matching uncertainty for dual purposes: selecting keypoint and weighing the residual in pose graph optimization. Compared to traditional geometric methods prioritizing texture-affluent features like edges, our keypoint selector employs the learned uncertainty to filter out the low-quality features based on global inconsistency. In contrast to the learning-based algorithms that model the scale-agnostic diagonal weight matrix for covariance, we design a metrics-aware covariance model to capture the spatial error during keypoint registration and the correlations between different axes. Integrating this covariance model into pose graph optimization enhances the robustness and reliability of pose estimation, particularly in challenging environments with varying illumination, feature density, and motion patterns. On public benchmark datasets, MAC-VO outperforms existing VO algorithms and even some SLAM algorithms in challenging environments. The covariance map also provides valuable information about the reliability of the estimated poses, which can benefit decision-making for autonomous systems.

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.

Text embeddings are essential components in modern NLP pipelines. While numerous embedding models have been proposed, their performance varies across domains. This variability motivates the use of ensemble techniques to combine complementary strengths. However, most existing ensemble methods operate on deterministic embeddings and fail to account for model-specific uncertainty, limiting their robustness and reliability in downstream applications. To address these limitations, we propose Uncertainty-driven Embedding Convolution (UEC). UEC first transforms deterministic embeddings into probabilistic ones in a post-hoc manner. It then computes adaptive ensemble weights based on embedding uncertainty, grounded in a Bayes-optimal solution under a surrogate loss. Additionally, UEC employs an uncertainty-aware similarity function that directly incorporates uncertainty into the similarity scoring, providing a theoretically grounded and efficient surrogate to distributional distances. Extensive experiments on diverse benchmarks demonstrate that UEC consistently improves both performance and robustness by leveraging principled uncertainty modeling.

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.

This paper introduces Bayesian uncertainty modeling using Stochastic Weight Averaging-Gaussian (SWAG) in Natural Language Understanding (NLU) tasks. We apply the approach to standard tasks in natural language inference (NLI) and demonstrate the effectiveness of the method in terms of prediction accuracy and correlation with human annotation disagreements. We argue that the uncertainty representations in SWAG better reflect subjective interpretation and the natural variation that is also present in human language understanding. The results reveal the importance of uncertainty modeling, an often neglected aspect of neural language modeling, in NLU tasks.

Uncertainty Quantification (UQ) is essential for creating trustworthy machine learning models. Recent years have seen a steep rise in UQ methods that can flag suspicious examples, however, it is often unclear what exactly these methods identify. In this work, we propose a framework for categorizing uncertain examples flagged by UQ methods in classification tasks. We introduce the confusion density matrix -- a kernel-based approximation of the misclassification density -- and use this to categorize suspicious examples identified by a given uncertainty method into three classes: out-of-distribution (OOD) examples, boundary (Bnd) examples, and examples in regions of high in-distribution misclassification (IDM). Through extensive experiments, we show that our framework provides a new and distinct perspective for assessing differences between uncertainty quantification methods, thereby forming a valuable assessment benchmark.

In an educational setting, an estimate of the difficulty of multiple-choice questions (MCQs), a commonly used strategy to assess learning progress, constitutes very useful information for both teachers and students. Since human assessment is costly from multiple points of view, automatic approaches to MCQ item difficulty estimation are investigated, yielding however mixed success until now. Our approach to this problem takes a different angle from previous work: asking various Large Language Models to tackle the questions included in two different MCQ datasets, we leverage model uncertainty to estimate item difficulty. By using both model uncertainty features as well as textual features in a Random Forest regressor, we show that uncertainty features contribute substantially to difficulty prediction, where difficulty is inversely proportional to the number of students who can correctly answer a question. In addition to showing the value of our approach, we also observe that our model achieves state-of-the-art results on the BEA publicly available dataset.

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.

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.

Automated evaluation of free-form outputs from large language models (LLMs) is challenging because many distinct answers can be equally valid. A common practice is to use LLMs themselves as judges, but the theoretical properties of this approach are not yet well understood. We show that a geometric framework that represents both judges and candidates as points on a probability simplex can provide helpful insight on what is or is not identifiable using LLM judges. Our theoretical analysis uncovers a "phase transition" in ranking identifiability: for binary scoring systems, true rankings are identifiable even with weak judges under mild assumptions, while rankings become non-identifiable for three or more scoring levels even with infinite data, absent additional prior knowledge. This non-identifiability highlights how uncertainty in rankings stems from not only aleatoric uncertainty (i.e., inherent stochasticity in the data) but also epistemic uncertainty regarding which assumptions hold, an aspect that has received limited attention until now. To integrate both types of uncertainty, we use Bayesian inference to encode assumptions as priors and conduct sensitivity analysis of ranking estimates and credible intervals. Empirical evaluations across multiple benchmarks demonstrate that Bayesian inference yields more accurate rankings and substantially improves coverage rates. These results underscore the importance of taking a more holistic approach to uncertainty quantification when using LLMs as judges.

In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order probability distributions, i.e., predictions in the form of distributions on probability distributions. A completely conclusive solution has not yet been found, however, as shown by recent criticisms of commonly used uncertainty measures associated with second-order distributions, identifying undesirable theoretical properties of these measures. In light of these criticisms, we propose a set of formal criteria that meaningful uncertainty measures for predictive uncertainty based on second-order distributions should obey. Moreover, we provide a general framework for developing uncertainty measures to account for these criteria, and offer an instantiation based on the Wasserstein distance, for which we prove that all criteria are satisfied.

Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, there is no universal agreement on how to best quantify predictive uncertainty. In this work, we revisit core concepts to propose a framework for information-theoretic measures of predictive uncertainty. Our proposed framework categorizes predictive uncertainty measures according to two factors: (I) The predicting model (II) The approximation of the true predictive distribution. Examining all possible combinations of these two factors, we derive a set of predictive uncertainty measures that includes both known and newly introduced ones. We extensively evaluate these measures across a broad set of tasks, identifying conditions under which certain measures excel. Our findings show the importance of aligning the choice of uncertainty measure with the predicting model on in-distribution (ID) data, the limitations of epistemic uncertainty measures for out-of-distribution (OOD) data, and that the disentanglement between measures varies substantially between ID and OOD data. Together, these insights provide a more comprehensive understanding of predictive uncertainty measures, revealing their implicit assumptions and relationships.

Uncertainty quantification (UQ) is a critical aspect of artificial intelligence (AI) systems, particularly in high-risk domains such as healthcare, autonomous systems, and financial technology, where decision-making processes must account for uncertainty. This review explores the evolution of uncertainty quantification techniques in AI, distinguishing between aleatoric and epistemic uncertainties, and discusses the mathematical foundations and methods used to quantify these uncertainties. We provide an overview of advanced techniques, including probabilistic methods, ensemble learning, sampling-based approaches, and generative models, while also highlighting hybrid approaches that integrate domain-specific knowledge. Furthermore, we examine the diverse applications of UQ across various fields, emphasizing its impact on decision-making, predictive accuracy, and system robustness. The review also addresses key challenges such as scalability, efficiency, and integration with explainable AI, and outlines future directions for research in this rapidly developing area. Through this comprehensive survey, we aim to provide a deeper understanding of UQ's role in enhancing the reliability, safety, and trustworthiness of AI systems.

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.

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.

We investigate composed image retrieval with text feedback. Users gradually look for the target of interest by moving from coarse to fine-grained feedback. However, existing methods merely focus on the latter, i.e., fine-grained search, by harnessing positive and negative pairs during training. This pair-based paradigm only considers the one-to-one distance between a pair of specific points, which is not aligned with the one-to-many coarse-grained retrieval process and compromises the recall rate. In an attempt to fill this gap, we introduce a unified learning approach to simultaneously modeling the coarse- and fine-grained retrieval by considering the multi-grained uncertainty. The key idea underpinning the proposed method is to integrate fine- and coarse-grained retrieval as matching data points with small and large fluctuations, respectively. Specifically, our method contains two modules: uncertainty modeling and uncertainty regularization. (1) The uncertainty modeling simulates the multi-grained queries by introducing identically distributed fluctuations in the feature space. (2) Based on the uncertainty modeling, we further introduce uncertainty regularization to adapt the matching objective according to the fluctuation range. Compared with existing methods, the proposed strategy explicitly prevents the model from pushing away potential candidates in the early stage, and thus improves the recall rate. On the three public datasets, i.e., FashionIQ, Fashion200k, and Shoes, the proposed method has achieved +4.03%, +3.38%, and +2.40% Recall@50 accuracy over a strong baseline, respectively.

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.

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.

Trainable evaluation metrics for machine translation (MT) exhibit strong correlation with human judgements, but they are often hard to interpret and might produce unreliable scores under noisy or out-of-domain data. Recent work has attempted to mitigate this with simple uncertainty quantification techniques (Monte Carlo dropout and deep ensembles), however these techniques (as we show) are limited in several ways -- for example, they are unable to distinguish between different kinds of uncertainty, and they are time and memory consuming. In this paper, we propose more powerful and efficient uncertainty predictors for MT evaluation, and we assess their ability to target different sources of aleatoric and epistemic uncertainty. To this end, we develop and compare training objectives for the COMET metric to enhance it with an uncertainty prediction output, including heteroscedastic regression, divergence minimization, and direct uncertainty prediction. Our experiments show improved results on uncertainty prediction for the WMT metrics task datasets, with a substantial reduction in computational costs. Moreover, they demonstrate the ability of these predictors to address specific uncertainty causes in MT evaluation, such as low quality references and out-of-domain data.

Estimating the uncertainty of responses of Large Language Models~(LLMs) remains a critical challenge. While recent Bayesian methods have demonstrated effectiveness in quantifying uncertainty through low-rank weight updates, they typically require complex fine-tuning or post-training procedures. In this paper, we propose Training-Free Bayesianization~(TFB), a novel framework that transforms existing off-the-shelf trained LoRA adapters into Bayesian ones without additional training. TFB systematically searches for the maximally acceptable level of variance in the weight posterior, constrained within a family of low-rank isotropic Gaussian distributions. We theoretically demonstrate that under mild conditions, this search process is equivalent to variational inference for the weights. Through comprehensive experiments, we show that TFB achieves superior uncertainty estimation and generalization compared to existing methods while eliminating the need for complex training procedures. Code will be available at https://github.com/Wang-ML-Lab/bayesian-peft.

While Large Language Models (LLMs) have demonstrated remarkable potential in natural language generation and instruction following, a persistent challenge lies in their susceptibility to "hallucinations", which erodes trust in their outputs. Although Uncertainty Quantification (UQ) presents a promising solution, its accurate implementation within the context of LLMs remains a significant hurdle. To address this critical roadblock, our research originates from a fundamental heuristic insight: tokens within auto-regressive LLM-generated text do not equally reflect the underlying meaning. Some tokens carry greater relevance and representativeness than others, owing to the phenomenon of "linguistic redundancy", wherein a select few keywords suffice to convey the essence of lengthy sentences. Regrettably, existing methodologies treat all tokens with equal importance when estimating uncertainty, disregarding these inherent generative inequalities. Our analysis reveals a significant issue with state-of-the-art: numerous tokens (and sentences) of limited semantic significance receive equal or even excessive weighting during uncertainty estimation. To rectify this bias, we propose to jointly Shifting Attention to more Relevant (SAR) components, at both the token- and the sentence-levels for accurate uncertainty estimation. We conduct extensive experiments involving a range of popular "off-the-shelf" LLMs, including instruction-tuned LLMs such as Vicuna, WizardLM, and LLaMA-2-chat, as well as pretrained LLMs like OPT and LLaMA, with model sizes extending up to 33B parameters. We carry out evaluation across various free-form question-answering tasks, encompassing domains such as reading comprehension, science Q&A, and medical Q&A. Our experimental results demonstrate the superior performance of SAR in addressing the challenges of uncertainty estimation within the realm of LLMs.

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.

Estimating uncertainty in Large Language Models (LLMs) is important for properly evaluating LLMs, and ensuring safety for users. However, prior approaches to uncertainty estimation focus on the final answer in generated text, ignoring intermediate steps that might dramatically impact the outcome. We hypothesize that there exist key forking tokens, such that re-sampling the system at those specific tokens, but not others, leads to very different outcomes. To test this empirically, we develop a novel approach to representing uncertainty dynamics across individual tokens of text generation, and applying statistical models to test our hypothesis. Our approach is highly flexible: it can be applied to any dataset and any LLM, without fine tuning or accessing model weights. We use our method to analyze LLM responses on 7 different tasks across 4 domains, spanning a wide range of typical use cases. We find many examples of forking tokens, including surprising ones such as punctuation marks, suggesting that LLMs are often just a single token away from saying something very different.

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.

Active learning (AL) in open set scenarios presents a novel challenge of identifying the most valuable examples in an unlabeled data pool that comprises data from both known and unknown classes. Traditional methods prioritize selecting informative examples with low confidence, with the risk of mistakenly selecting unknown-class examples with similarly low confidence. Recent methods favor the most probable known-class examples, with the risk of picking simple already mastered examples. In this paper, we attempt to query examples that are both likely from known classes and highly informative, and propose a Bidirectional Uncertainty-based Active Learning (BUAL) framework. Specifically, we achieve this by first pushing the unknown class examples toward regions with high-confidence predictions, i.e., the proposed Random Label Negative Learning method. Then, we propose a Bidirectional Uncertainty sampling strategy by jointly estimating uncertainty posed by both positive and negative learning to perform consistent and stable sampling. BUAL successfully extends existing uncertainty-based AL methods to complex open-set scenarios. Extensive experiments on multiple datasets with varying openness demonstrate that BUAL achieves state-of-the-art performance. The code is available at https://github.com/chenchenzong/BUAL.

Uncertainty sampling in active learning is heavily used in practice to reduce the annotation cost. However, there has been no wide consensus on the function to be used for uncertainty estimation in binary classification tasks and convergence guarantees of the corresponding active learning algorithms are not well understood. The situation is even more challenging for multi-category classification. In this work, we propose an efficient uncertainty estimator for binary classification which we also extend to multiple classes, and provide a non-asymptotic rate of convergence for our uncertainty sampling-based active learning algorithm in both cases under no-noise conditions (i.e., linearly separable data). We also extend our analysis to the noisy case and provide theoretical guarantees for our algorithm under the influence of noise in the task of binary and multi-class classification.

The recent performance leap of Large Language Models (LLMs) opens up new opportunities across numerous industrial applications and domains. However, erroneous generations, such as false predictions, misinformation, and hallucination made by LLMs, have also raised severe concerns for the trustworthiness of LLMs', especially in safety-, security- and reliability-sensitive scenarios, potentially hindering real-world adoptions. While uncertainty estimation has shown its potential for interpreting the prediction risks made by general machine learning (ML) models, little is known about whether and to what extent it can help explore an LLM's capabilities and counteract its undesired behavior. To bridge the gap, in this paper, we initiate an exploratory study on the risk assessment of LLMs from the lens of uncertainty. In particular, we experiment with twelve uncertainty estimation methods and four LLMs on four prominent natural language processing (NLP) tasks to investigate to what extent uncertainty estimation techniques could help characterize the prediction risks of LLMs. Our findings validate the effectiveness of uncertainty estimation for revealing LLMs' uncertain/non-factual predictions. In addition to general NLP tasks, we extensively conduct experiments with four LLMs for code generation on two datasets. We find that uncertainty estimation can potentially uncover buggy programs generated by LLMs. Insights from our study shed light on future design and development for reliable LLMs, facilitating further research toward enhancing the trustworthiness of LLMs.

Uncertainty quantification has received increasing attention in machine learning in the recent past. In particular, a distinction between aleatoric and epistemic uncertainty has been found useful in this regard. The latter refers to the learner's (lack of) knowledge and appears to be especially difficult to measure and quantify. In this paper, we analyse a recent proposal based on the idea of a second-order learner, which yields predictions in the form of distributions over probability distributions. While standard (first-order) learners can be trained to predict accurate probabilities, namely by minimising suitable loss functions on sample data, we show that loss minimisation does not work for second-order predictors: The loss functions proposed for inducing such predictors do not incentivise the learner to represent its epistemic uncertainty in a faithful way.

In this paper, we focus on the task of conditional image generation, where an image is synthesized according to user instructions. The critical challenge underpinning this task is ensuring both the fidelity of the generated images and their semantic alignment with the provided conditions. To tackle this issue, previous studies have employed supervised perceptual losses derived from pre-trained models, i.e., reward models, to enforce alignment between the condition and the generated result. However, we observe one inherent shortcoming: considering the diversity of synthesized images, the reward model usually provides inaccurate feedback when encountering newly generated data, which can undermine the training process. To address this limitation, we propose an uncertainty-aware reward modeling, called Ctrl-U, including uncertainty estimation and uncertainty-aware regularization, designed to reduce the adverse effects of imprecise feedback from the reward model. Given the inherent cognitive uncertainty within reward models, even images generated under identical conditions often result in a relatively large discrepancy in reward loss. Inspired by the observation, we explicitly leverage such prediction variance as an uncertainty indicator. Based on the uncertainty estimation, we regularize the model training by adaptively rectifying the reward. In particular, rewards with lower uncertainty receive higher loss weights, while those with higher uncertainty are given reduced weights to allow for larger variability. The proposed uncertainty regularization facilitates reward fine-tuning through consistency construction. Extensive experiments validate the effectiveness of our methodology in improving the controllability and generation quality, as well as its scalability across diverse conditional scenarios. Code will soon be available at https://grenoble-zhang.github.io/Ctrl-U-Page/.

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.

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.

Epistemic Uncertainty is a measure of the lack of knowledge of a learner which diminishes with more evidence. While existing work focuses on using the variance of the Bayesian posterior due to parameter uncertainty as a measure of epistemic uncertainty, we argue that this does not capture the part of lack of knowledge induced by model misspecification. We discuss how the excess risk, which is the gap between the generalization error of a predictor and the Bayes predictor, is a sound measure of epistemic uncertainty which captures the effect of model misspecification. We thus propose a principled framework for directly estimating the excess risk by learning a secondary predictor for the generalization error and subtracting an estimate of aleatoric uncertainty, i.e., intrinsic unpredictability. We discuss the merits of this novel measure of epistemic uncertainty, and highlight how it differs from variance-based measures of epistemic uncertainty and addresses its major pitfall. Our framework, Direct Epistemic Uncertainty Prediction (DEUP) is particularly interesting in interactive learning environments, where the learner is allowed to acquire novel examples in each round. Through a wide set of experiments, we illustrate how existing methods in sequential model optimization can be improved with epistemic uncertainty estimates from DEUP, and how DEUP can be used to drive exploration in reinforcement learning. We also evaluate the quality of uncertainty estimates from DEUP for probabilistic image classification and predicting synergies of drug combinations.

Representation learning has significantly driven the field to develop pretrained models that can act as a valuable starting point when transferring to new datasets. With the rising demand for reliable machine learning and uncertainty quantification, there is a need for pretrained models that not only provide embeddings but also transferable uncertainty estimates. To guide the development of such models, we propose the Uncertainty-aware Representation Learning (URL) benchmark. Besides the transferability of the representations, it also measures the zero-shot transferability of the uncertainty estimate using a novel metric. We apply URL to evaluate eleven uncertainty quantifiers that are pretrained on ImageNet and transferred to eight downstream datasets. We find that approaches that focus on the uncertainty of the representation itself or estimate the prediction risk directly outperform those that are based on the probabilities of upstream classes. Yet, achieving transferable uncertainty quantification remains an open challenge. Our findings indicate that it is not necessarily in conflict with traditional representation learning goals. Code is provided under https://github.com/mkirchhof/url .

High-quality arguments are an essential part of decision-making. Automatically predicting the quality of an argument is a complex task that recently got much attention in argument mining. However, the annotation effort for this task is exceptionally high. Therefore, we test uncertainty-based active learning (AL) methods on two popular argument-strength data sets to estimate whether sample-efficient learning can be enabled. Our extensive empirical evaluation shows that uncertainty-based acquisition functions can not surpass the accuracy reached with the random acquisition on these data sets.

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 LLM-based judges become integral to industry applications, obtaining well-calibrated uncertainty estimates efficiently has become critical for production deployment. However, existing techniques, such as verbalized confidence and multi-generation methods, are often either poorly calibrated or computationally expensive. We introduce linear probes trained with a Brier score-based loss to provide calibrated uncertainty estimates from reasoning judges' hidden states, requiring no additional model training. We evaluate our approach on both objective tasks (reasoning, mathematics, factuality, coding) and subjective human preference judgments. Our results demonstrate that probes achieve superior calibration compared to existing methods with approx10x computational savings, generalize robustly to unseen evaluation domains, and deliver higher accuracy on high-confidence predictions. However, probes produce conservative estimates that underperform on easier datasets but may benefit safety-critical deployments prioritizing low false-positive rates. Overall, our work demonstrates that interpretability-based uncertainty estimation provides a practical and scalable plug-and-play solution for LLM judges in production.

Rigorous statistical evaluations of large language models (LLMs), including valid error bars and significance testing, are essential for meaningful and reliable performance assessment. Currently, when such statistical measures are reported, they typically rely on the Central Limit Theorem (CLT). In this position paper, we argue that while CLT-based methods for uncertainty quantification are appropriate when benchmarks consist of thousands of examples, they fail to provide adequate uncertainty estimates for LLM evaluations that rely on smaller, highly specialized benchmarks. In these small-data settings, we demonstrate that CLT-based methods perform very poorly, usually dramatically underestimating uncertainty (i.e. producing error bars that are too small). We give recommendations for alternative frequentist and Bayesian methods that are both easy to implement and more appropriate in these increasingly common scenarios. We provide a simple Python library for these Bayesian methods at https://github.com/sambowyer/bayes_evals .

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 the real world, the frequency of occurrence of objects is naturally skewed forming long-tail class distributions, which results in poor performance on the statistically rare classes. A promising solution is to mine tail-class examples to balance the training dataset. However, mining tail-class examples is a very challenging task. For instance, most of the otherwise successful uncertainty-based mining approaches struggle due to distortion of class probabilities resulting from skewness in data. In this work, we propose an effective, yet simple, approach to overcome these challenges. Our framework enhances the subdued tail-class activations and, thereafter, uses a one-class data-centric approach to effectively identify tail-class examples. We carry out an exhaustive evaluation of our framework on three datasets spanning over two computer vision tasks. Substantial improvements in the minority-class mining and fine-tuned model's performance strongly corroborate the value of our proposed solution.

Predictions made by deep learning models are prone to data perturbations, adversarial attacks, and out-of-distribution inputs. To build a trusted AI system, it is therefore critical to accurately quantify the prediction uncertainties. While current efforts focus on improving uncertainty quantification accuracy and efficiency, there is a need to identify uncertainty sources and take actions to mitigate their effects on predictions. Therefore, we propose to develop explainable and actionable Bayesian deep learning methods to not only perform accurate uncertainty quantification but also explain the uncertainties, identify their sources, and propose strategies to mitigate the uncertainty impacts. Specifically, we introduce a gradient-based uncertainty attribution method to identify the most problematic regions of the input that contribute to the prediction uncertainty. Compared to existing methods, the proposed UA-Backprop has competitive accuracy, relaxed assumptions, and high efficiency. Moreover, we propose an uncertainty mitigation strategy that leverages the attribution results as attention to further improve the model performance. Both qualitative and quantitative evaluations are conducted to demonstrate the effectiveness of our proposed methods.

We study the problem of uncertainty quantification via prediction sets, in an online setting where the data distribution may vary arbitrarily over time. Recent work develops online conformal prediction techniques that leverage regret minimization algorithms from the online learning literature to learn prediction sets with approximately valid coverage and small regret. However, standard regret minimization could be insufficient for handling changing environments, where performance guarantees may be desired not only over the full time horizon but also in all (sub-)intervals of time. We develop new online conformal prediction methods that minimize the strongly adaptive regret, which measures the worst-case regret over all intervals of a fixed length. We prove that our methods achieve near-optimal strongly adaptive regret for all interval lengths simultaneously, and approximately valid coverage. Experiments show that our methods consistently obtain better coverage and smaller prediction sets than existing methods on real-world tasks, such as time series forecasting and image classification under distribution shift.

Large Language Models (LLMs) are increasingly employed in real-world applications, driving the need to evaluate the trustworthiness of their generated text. To this end, reliable uncertainty estimation is essential. Since current LLMs generate text autoregressively through a stochastic process, the same prompt can lead to varying outputs. Consequently, leading uncertainty estimation methods generate and analyze multiple output sequences to determine the LLM's uncertainty. However, generating output sequences is computationally expensive, making these methods impractical at scale. In this work, we inspect the theoretical foundations of the leading methods and explore new directions to enhance their computational efficiency. Building on the framework of proper scoring rules, we find that the negative log-likelihood of the most likely output sequence constitutes a theoretically grounded uncertainty measure. To approximate this alternative measure, we propose G-NLL, which has the advantage of being obtained using only a single output sequence generated by greedy decoding. This makes uncertainty estimation more efficient and straightforward, while preserving theoretical rigor. Empirical results demonstrate that G-NLL achieves state-of-the-art performance across various LLMs and tasks. Our work lays the foundation for efficient and reliable uncertainty estimation in natural language generation, challenging the necessity of more computationally involved methods currently leading the field.

Several neural-based metrics have been recently proposed to evaluate machine translation quality. However, all of them resort to point estimates, which provide limited information at segment level. This is made worse as they are trained on noisy, biased and scarce human judgements, often resulting in unreliable quality predictions. In this paper, we introduce uncertainty-aware MT evaluation and analyze the trustworthiness of the predicted quality. We combine the COMET framework with two uncertainty estimation methods, Monte Carlo dropout and deep ensembles, to obtain quality scores along with confidence intervals. We compare the performance of our uncertainty-aware MT evaluation methods across multiple language pairs from the QT21 dataset and the WMT20 metrics task, augmented with MQM annotations. We experiment with varying numbers of references and further discuss the usefulness of uncertainty-aware quality estimation (without references) to flag possibly critical translation mistakes.

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.

Uncertainty estimation is critical for cost-sensitive deep-learning applications (i.e. disease diagnosis). It is very challenging partly due to the inaccessibility of uncertainty groundtruth in most datasets. Previous works proposed to estimate the uncertainty from softmax calibration, Monte Carlo sampling, subjective logic and so on. However, these existing methods tend to be over-confident about their predictions with unreasonably low overall uncertainty, which originates from the imbalance between positive (correct classifications) and negative (incorrect classifications) samples. For this issue, we firstly propose the distributional imbalance to model the imbalance in uncertainty estimation as two kinds of distribution biases, and secondly propose Balanced True Class Probability (BTCP) framework, which learns an uncertainty estimator with a novel Distributional Focal Loss (DFL) objective. Finally, we evaluate the BTCP in terms of failure prediction and out-of-distribution (OOD) detection on multiple datasets. The experimental results show that BTCP outperforms other uncertainty estimation methods especially in identifying incorrect classifications.

We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence." We explore how to interpret uncertain evidence, and by extension the importance of proper interpretation as it pertains to inference about latent variables. We consider a recently-proposed method "distributional evidence" as well as revisit two older methods: Jeffrey's rule and virtual evidence. We devise guidelines on how to account for uncertain evidence and we provide new insights, particularly regarding consistency. To showcase the impact of different interpretations of the same uncertain evidence, we carry out experiments in which one interpretation is defined as "correct." We then compare inference results from each different interpretation illustrating the importance of careful consideration of uncertain evidence.

Accurate uncertainty quantification (UQ) in Large Language Models (LLMs) is critical for trustworthy deployment. While real-world language is inherently ambiguous, reflecting aleatoric uncertainty, existing UQ methods are typically benchmarked against tasks with no ambiguity. In this work, we demonstrate that while current uncertainty estimators perform well under the restrictive assumption of no ambiguity, they degrade to close-to-random performance on ambiguous data. To this end, we introduce MAQA* and AmbigQA*, the first ambiguous question-answering (QA) datasets equipped with ground-truth answer distributions estimated from factual co-occurrence. We find this performance deterioration to be consistent across different estimation paradigms: using the predictive distribution itself, internal representations throughout the model, and an ensemble of models. We show that this phenomenon can be theoretically explained, revealing that predictive-distribution and ensemble-based estimators are fundamentally limited under ambiguity. Overall, our study reveals a key shortcoming of current UQ methods for LLMs and motivates a rethinking of current modeling paradigms.

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.

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.

Models trained on different datasets can be merged by a weighted-averaging of their parameters, but why does it work and when can it fail? Here, we connect the inaccuracy of weighted-averaging to mismatches in the gradients and propose a new uncertainty-based scheme to improve the performance by reducing the mismatch. The connection also reveals implicit assumptions in other schemes such as averaging, task arithmetic, and Fisher-weighted averaging. Our new method gives consistent improvements for large language models and vision transformers, both in terms of performance and robustness to hyperparameters.

Retrieval Augmented Generation (RAG) improves correctness of Question Answering (QA) and addresses hallucinations in Large Language Models (LLMs), yet greatly increase computational costs. Besides, RAG is not always needed as may introduce irrelevant information. Recent adaptive retrieval methods integrate LLMs' intrinsic knowledge with external information appealing to LLM self-knowledge, but they often neglect efficiency evaluations and comparisons with uncertainty estimation techniques. We bridge this gap by conducting a comprehensive analysis of 35 adaptive retrieval methods, including 8 recent approaches and 27 uncertainty estimation techniques, across 6 datasets using 10 metrics for QA performance, self-knowledge, and efficiency. Our findings show that uncertainty estimation techniques often outperform complex pipelines in terms of efficiency and self-knowledge, while maintaining comparable QA performance.

Contrastively trained encoders have recently been proven to invert the data-generating process: they encode each input, e.g., an image, into the true latent vector that generated the image (Zimmermann et al., 2021). However, real-world observations often have inherent ambiguities. For instance, images may be blurred or only show a 2D view of a 3D object, so multiple latents could have generated them. This makes the true posterior for the latent vector probabilistic with heteroscedastic uncertainty. In this setup, we extend the common InfoNCE objective and encoders to predict latent distributions instead of points. We prove that these distributions recover the correct posteriors of the data-generating process, including its level of aleatoric uncertainty, up to a rotation of the latent space. In addition to providing calibrated uncertainty estimates, these posteriors allow the computation of credible intervals in image retrieval. They comprise images with the same latent as a given query, subject to its uncertainty. Code is available at https://github.com/mkirchhof/Probabilistic_Contrastive_Learning

We propose a novel method to capture data points near decision boundary in neural network that are often referred to a specific type of uncertainty. In our approach, we sought to perform uncertainty estimation based on the idea of adversarial attack method. In this paper, uncertainty estimates are derived from the input perturbations, unlike previous studies that provide perturbations on the model's parameters as in Bayesian approach. We are able to produce uncertainty with couple of perturbations on the inputs. Interestingly, we apply the proposed method to datasets derived from blockchain. We compare the performance of model uncertainty with the most recent uncertainty methods. We show that the proposed method has revealed a significant outperformance over other methods and provided less risk to capture model uncertainty in machine learning.

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.

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.

Retrieval-Augmented Generation (RAG) has emerged as a widely adopted approach for enhancing LLMs in scenarios that demand extensive factual knowledge. However, current RAG evaluations concentrate primarily on correctness, which may not fully capture the impact of retrieval on LLM uncertainty and reliability. To bridge this gap, we introduce URAG, a comprehensive benchmark designed to assess the uncertainty of RAG systems across various fields like healthcare, programming, science, math, and general text. By reformulating open-ended generation tasks into multiple-choice question answering, URAG allows for principled uncertainty quantification via conformal prediction. We apply the evaluation pipeline to 8 standard RAG methods, measuring their performance through both accuracy and prediction-set sizes based on LAC and APS metrics. Our analysis shows that (1) accuracy gains often coincide with reduced uncertainty, but this relationship breaks under retrieval noise; (2) simple modular RAG methods tend to offer better accuracy-uncertainty trade-offs than more complex reasoning pipelines; and (3) no single RAG approach is universally reliable across domains. We further show that (4) retrieval depth, parametric knowledge dependence, and exposure to confidence cues can amplify confident errors and hallucinations. Ultimately, URAG establishes a systematic benchmark for analyzing and enhancing the trustworthiness of retrieval-augmented systems. Our code is available on GitHub.

Deep Neural Networks (DNNs) have demonstrated remarkable performance across various domains, including computer vision and natural language processing. However, they often struggle to accurately quantify the uncertainty of their predictions, limiting their broader adoption in critical real-world applications. Uncertainty Quantification (UQ) for Deep Learning seeks to address this challenge by providing methods to improve the reliability of uncertainty estimates. Although numerous techniques have been proposed, a unified tool offering a seamless workflow to evaluate and integrate these methods remains lacking. To bridge this gap, we introduce Torch-Uncertainty, a PyTorch and Lightning-based framework designed to streamline DNN training and evaluation with UQ techniques and metrics. In this paper, we outline the foundational principles of our library and present comprehensive experimental results that benchmark a diverse set of UQ methods across classification, segmentation, and regression tasks. Our library is available at https://github.com/ENSTA-U2IS-AI/Torch-Uncertainty

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.

For safety, medical AI systems undergo thorough evaluations before deployment, validating their predictions against a ground truth which is assumed to be fixed and certain. However, this ground truth is often curated in the form of differential diagnoses. While a single differential diagnosis reflects the uncertainty in one expert assessment, multiple experts introduce another layer of uncertainty through disagreement. Both forms of uncertainty are ignored in standard evaluation which aggregates these differential diagnoses to a single label. In this paper, we show that ignoring uncertainty leads to overly optimistic estimates of model performance, therefore underestimating risk associated with particular diagnostic decisions. To this end, we propose a statistical aggregation approach, where we infer a distribution on probabilities of underlying medical condition candidates themselves, based on observed annotations. This formulation naturally accounts for the potential disagreements between different experts, as well as uncertainty stemming from individual differential diagnoses, capturing the entire ground truth uncertainty. Our approach boils down to generating multiple samples of medical condition probabilities, then evaluating and averaging performance metrics based on these sampled probabilities. In skin condition classification, we find that a large portion of the dataset exhibits significant ground truth uncertainty and standard evaluation severely over-estimates performance without providing uncertainty estimates. In contrast, our framework provides uncertainty estimates on common metrics of interest such as top-k accuracy and average overlap, showing that performance can change multiple percentage points. We conclude that, while assuming a crisp ground truth can be acceptable for many AI applications, a more nuanced evaluation protocol should be utilized in medical diagnosis.

Reward models (RM) play a critical role in aligning generations of large language models (LLM) to human expectations. However, prevailing RMs fail to capture the stochasticity within human preferences and cannot effectively evaluate the reliability of reward predictions. To address these issues, we propose Uncertain-aware RM (URM) and Uncertain-aware RM Ensemble (URME) to incorporate and manage uncertainty in reward modeling. URM can model the distribution of disentangled attributes within human preferences, while URME quantifies uncertainty through discrepancies in the ensemble, thereby identifying potential lack of knowledge during reward evaluation. Experiment results indicate that the proposed URM achieves state-of-the-art performance compared to models with the same size, demonstrating the effectiveness of modeling uncertainty within human preferences. Furthermore, empirical results show that through uncertainty quantification, URM and URME can identify unreliable predictions to improve the quality of reward evaluations.

While Large Language Models (LLMs) demonstrate impressive capabilities, they still struggle with generating factually incorrect content (i.e., hallucinations). A promising approach to mitigate this issue is enabling models to express uncertainty when unsure. Previous research on uncertainty modeling has primarily focused on short-form QA, but realworld applications often require much longer responses. In this work, we introduce the task of Long-form Generation with Uncertainty(LoGU). We identify two key challenges: Uncertainty Suppression, where models hesitate to express uncertainty, and Uncertainty Misalignment, where models convey uncertainty inaccurately. To tackle these challenges, we propose a refinement-based data collection framework and a two-stage training pipeline. Our framework adopts a divide-and-conquer strategy, refining uncertainty based on atomic claims. The collected data are then used in training through supervised fine-tuning (SFT) and direct preference optimization (DPO) to enhance uncertainty expression. Extensive experiments on three long-form instruction following datasets show that our method significantly improves accuracy, reduces hallucinations, and maintains the comprehensiveness of responses.

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.

We present a state-of-the-art model for fine-grained probability estimation of propositions conditioned on context. Recent advances in large language models (LLMs) have significantly enhanced their reasoning capabilities, particularly on well-defined tasks with complete information. However, LLMs continue to struggle with making accurate and well-calibrated probabilistic predictions under uncertainty or partial information. While incorporating uncertainty into model predictions often boosts performance, obtaining reliable estimates of that uncertainty remains understudied. In particular, LLM probability estimates tend to be coarse and biased towards more frequent numbers. Through a combination of human and synthetic data creation and assessment, scaling to larger models, and better supervision, we propose a set of strong and precise probability estimation models. We conduct systematic evaluations across tasks that rely on conditional probability estimation and show that our approach consistently outperforms existing fine-tuned and prompting-based methods by a large margin.

Large language models (LLMs) specializing in natural language generation (NLG) have recently started exhibiting promising capabilities across a variety of domains. However, gauging the trustworthiness of responses generated by LLMs remains an open challenge, with limited research on uncertainty quantification (UQ) for NLG. Furthermore, existing literature typically assumes white-box access to language models, which is becoming unrealistic either due to the closed-source nature of the latest LLMs or computational constraints. In this work, we investigate UQ in NLG for black-box LLMs. We first differentiate uncertainty vs confidence: the former refers to the "dispersion" of the potential predictions for a fixed input, and the latter refers to the confidence on a particular prediction/generation. We then propose and compare several confidence/uncertainty metrics, applying them to selective NLG where unreliable results could either be ignored or yielded for further assessment. Experiments were carried out with several popular LLMs on question-answering datasets (for evaluation purposes). Results reveal that a simple metric for the semantic dispersion can be a reliable predictor of the quality of LLM responses, providing valuable insights for practitioners on uncertainty management when adopting LLMs. The code to replicate our experiments is available at https://github.com/zlin7/UQ-NLG.

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.

Retrieval-Augmented Generation equips large language models with the capability to retrieve external knowledge, thereby mitigating hallucinations by incorporating information beyond the model's intrinsic abilities. However, most prior works have focused on invoking retrieval deterministically, which makes it unsuitable for tasks such as long-form question answering. Instead, dynamically performing retrieval by invoking it only when the underlying LLM lacks the required knowledge can be more efficient. In this context, we delve deeper into the question, "To Retrieve or Not to Retrieve?" by exploring multiple uncertainty detection methods. We evaluate these methods for the task of long-form question answering, employing dynamic retrieval, and present our comparisons. Our findings suggest that uncertainty detection metrics, such as Degree Matrix Jaccard and Eccentricity, can reduce the number of retrieval calls by almost half, with only a slight reduction in question-answering accuracy.

Binary classification involves predicting the label of an instance based on whether the model score for the positive class exceeds a threshold chosen based on the application requirements (e.g., maximizing recall for a precision bound). However, model scores are often not aligned with the true positivity rate. This is especially true when the training involves a differential sampling across classes or there is distributional drift between train and test settings. In this paper, we provide theoretical analysis and empirical evidence of the dependence of model score estimation bias on both uncertainty and score itself. Further, we formulate the decision boundary selection in terms of both model score and uncertainty, prove that it is NP-hard, and present algorithms based on dynamic programming and isotonic regression. Evaluation of the proposed algorithms on three real-world datasets yield 25%-40% gain in recall at high precision bounds over the traditional approach of using model score alone, highlighting the benefits of leveraging uncertainty.

Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the uncertainty of model outputs has received relatively little attention. We adapt the popular Shapley value framework to explain various types of predictive uncertainty, quantifying each feature's contribution to the conditional entropy of individual model outputs. We consider games with modified characteristic functions and find deep connections between the resulting Shapley values and fundamental quantities from information theory and conditional independence testing. We outline inference procedures for finite sample error rate control with provable guarantees, and implement efficient algorithms that perform well in a range of experiments on real and simulated data. Our method has applications to covariate shift detection, active learning, feature selection, and active feature-value acquisition.

Prediction sets capture uncertainty by predicting sets of labels rather than individual labels, enabling downstream decisions to conservatively account for all plausible outcomes. Conformal inference algorithms construct prediction sets guaranteed to contain the true label with high probability. These guarantees fail to hold in the face of distribution shift, which is precisely when reliable uncertainty quantification can be most useful. We propose a novel algorithm for constructing prediction sets with PAC guarantees in the label shift setting. This method estimates the predicted probabilities of the classes in a target domain, as well as the confusion matrix, then propagates uncertainty in these estimates through a Gaussian elimination algorithm to compute confidence intervals for importance weights. Finally, it uses these intervals to construct prediction sets. We evaluate our approach on five datasets: the CIFAR-10, ChestX-Ray and Entity-13 image datasets, the tabular CDC Heart dataset, and the AGNews text dataset. Our algorithm satisfies the PAC guarantee while producing smaller, more informative, prediction sets compared to several baselines.

Subset selection-based methods are widely used to explain deep vision models: they attribute predictions by highlighting the most influential image regions and support object-level explanations. While these methods perform well in in-distribution (ID) settings, their behavior under out-of-distribution (OOD) conditions remains poorly understood. Through extensive experiments across multiple ID-OOD sets, we find that reliability of the existing subset based methods degrades markedly, yielding redundant, unstable, and uncertainty-sensitive explanations. To address these shortcomings, we introduce a framework that combines submodular subset selection with layer-wise, gradient-based uncertainty estimation to improve robustness and fidelity without requiring additional training or auxiliary models. Our approach estimates uncertainty via adaptive weight perturbations and uses these estimates to guide submodular optimization, ensuring diverse and informative subset selection. Empirical evaluations show that, beyond mitigating the weaknesses of existing methods under OOD scenarios, our framework also yields improvements in ID settings. These findings highlight limitations of current subset-based approaches and demonstrate how uncertainty-driven optimization can enhance attribution and object-level interpretability, paving the way for more transparent and trustworthy AI in real-world vision applications.

Bayesian neural learning feature a rigorous approach to estimation and uncertainty quantification via the posterior distribution of weights that represent knowledge of the neural network. This not only provides point estimates of optimal set of weights but also the ability to quantify uncertainty in decision making using the posterior distribution. Markov chain Monte Carlo (MCMC) techniques are typically used to obtain sample-based estimates of the posterior distribution. However, these techniques face challenges in convergence and scalability, particularly in settings with large datasets and network architectures. This paper address these challenges in two ways. First, parallel tempering is used used to explore multiple modes of the posterior distribution and implemented in multi-core computing architecture. Second, we make within-chain sampling schemes more efficient by using Langevin gradient information in forming Metropolis-Hastings proposal distributions. We demonstrate the techniques using time series prediction and pattern classification applications. The results show that the method not only improves the computational time, but provides better prediction or decision making capabilities when compared to related methods.

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.

Uncertainty estimation is an essential and heavily-studied component for the reliable application of semantic segmentation methods. While various studies exist claiming methodological advances on the one hand, and successful application on the other hand, the field is currently hampered by a gap between theory and practice leaving fundamental questions unanswered: Can data-related and model-related uncertainty really be separated in practice? Which components of an uncertainty method are essential for real-world performance? Which uncertainty method works well for which application? In this work, we link this research gap to a lack of systematic and comprehensive evaluation of uncertainty methods. Specifically, we identify three key pitfalls in current literature and present an evaluation framework that bridges the research gap by providing 1) a controlled environment for studying data ambiguities as well as distribution shifts, 2) systematic ablations of relevant method components, and 3) test-beds for the five predominant uncertainty applications: OoD-detection, active learning, failure detection, calibration, and ambiguity modeling. Empirical results on simulated as well as real-world data demonstrate how the proposed framework is able to answer the predominant questions in the field revealing for instance that 1) separation of uncertainty types works on simulated data but does not necessarily translate to real-world data, 2) aggregation of scores is a crucial but currently neglected component of uncertainty methods, 3) While ensembles are performing most robustly across the different downstream tasks and settings, test-time augmentation often constitutes a light-weight alternative. Code is at: https://github.com/IML-DKFZ/values

The proliferation of open-source Large Language Models (LLMs) from various institutions has highlighted the urgent need for comprehensive evaluation methods. However, current evaluation platforms, such as the widely recognized HuggingFace open LLM leaderboard, neglect a crucial aspect -- uncertainty, which is vital for thoroughly assessing LLMs. To bridge this gap, we introduce a new benchmarking approach for LLMs that integrates uncertainty quantification. Our examination involves eight LLMs (LLM series) spanning five representative natural language processing tasks. Additionally, we introduce an uncertainty-aware evaluation metric, UAcc, which takes into account both prediction accuracy and prediction uncertainty. Our findings reveal that: I) LLMs with higher accuracy may exhibit lower certainty; II) Larger-scale LLMs may display greater uncertainty compared to their smaller counterparts; and III) Instruction-finetuning tends to increase the uncertainty of LLMs. By taking uncertainty into account, our new UAcc metric can either amplify or diminish the relative improvement of one LLM over another and may even change the relative ranking of two LLMs. These results underscore the significance of incorporating uncertainty in the evaluation of LLMs.

The prevalence and importance of algorithmic two-sided marketplaces has drawn attention to the issue of fairness in such settings. Algorithmic decisions are used in assigning students to schools, users to advertisers, and applicants to job interviews. These decisions should heed the preferences of individuals, and simultaneously be fair with respect to their merits (synonymous with fit, future performance, or need). Merits conditioned on observable features are always uncertain, a fact that is exacerbated by the widespread use of machine learning algorithms to infer merit from the observables. As our key contribution, we carefully axiomatize a notion of individual fairness in the two-sided marketplace setting which respects the uncertainty in the merits; indeed, it simultaneously recognizes uncertainty as the primary potential cause of unfairness and an approach to address it. We design a linear programming framework to find fair utility-maximizing distributions over allocations, and we show that the linear program is robust to perturbations in the estimated parameters of the uncertain merit distributions, a key property in combining the approach with machine learning techniques.

Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded framework to reason about model uncertainty, but usually come with a prohibitive computational cost. In this paper we develop a new theoretical framework casting dropout training in deep neural networks (NNs) as approximate Bayesian inference in deep Gaussian processes. A direct result of this theory gives us tools to model uncertainty with dropout NNs -- extracting information from existing models that has been thrown away so far. This mitigates the problem of representing uncertainty in deep learning without sacrificing either computational complexity or test accuracy. We perform an extensive study of the properties of dropout's uncertainty. Various network architectures and non-linearities are assessed on tasks of regression and classification, using MNIST as an example. We show a considerable improvement in predictive log-likelihood and RMSE compared to existing state-of-the-art methods, and finish by using dropout's uncertainty in deep reinforcement learning.

Quantifying uncertainty is important for actionable predictions in real-world applications. A crucial part of predictive uncertainty quantification is the estimation of epistemic uncertainty, which is defined as an integral of the product between a divergence function and the posterior. Current methods such as Deep Ensembles or MC dropout underperform at estimating the epistemic uncertainty, since they primarily consider the posterior when sampling models. We suggest Quantification of Uncertainty with Adversarial Models (QUAM) to better estimate the epistemic uncertainty. QUAM identifies regions where the whole product under the integral is large, not just the posterior. Consequently, QUAM has lower approximation error of the epistemic uncertainty compared to previous methods. Models for which the product is large correspond to adversarial models (not adversarial examples!). Adversarial models have both a high posterior as well as a high divergence between their predictions and that of a reference model. Our experiments show that QUAM excels in capturing epistemic uncertainty for deep learning models and outperforms previous methods on challenging tasks in the vision domain.

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.

It is well known that accurate probabilistic predictors can be trained through empirical risk minimisation with proper scoring rules as loss functions. While such learners capture so-called aleatoric uncertainty of predictions, various machine learning methods have recently been developed with the goal to let the learner also represent its epistemic uncertainty, i.e., the uncertainty caused by a lack of knowledge and data. An emerging branch of the literature proposes the use of a second-order learner that provides predictions in terms of distributions on probability distributions. However, recent work has revealed serious theoretical shortcomings for second-order predictors based on loss minimisation. In this paper, we generalise these findings and prove a more fundamental result: There seems to be no loss function that provides an incentive for a second-order learner to faithfully represent its epistemic uncertainty in the same manner as proper scoring rules do for standard (first-order) learners. As a main mathematical tool to prove this result, we introduce the generalised notion of second-order scoring rules.

Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions, or to model a diverse population without being overly reductive. For instance, epidemiological forecasts, cost estimates, and revenue predictions all benefit from being able to quantify the range of possible values accurately. As such, many models have been developed for this problem over many years of research in statistics, machine learning, and related fields. Rather than proposing yet another (new) algorithm for quantile regression we adopt a meta viewpoint: we investigate methods for aggregating any number of conditional quantile models, in order to improve accuracy and robustness. We consider weighted ensembles where weights may vary over not only individual models, but also over quantile levels, and feature values. All of the models we consider in this paper can be fit using modern deep learning toolkits, and hence are widely accessible (from an implementation point of view) and scalable. To improve the accuracy of the predicted quantiles (or equivalently, prediction intervals), we develop tools for ensuring that quantiles remain monotonically ordered, and apply conformal calibration methods. These can be used without any modification of the original library of base models. We also review some basic theory surrounding quantile aggregation and related scoring rules, and contribute a few new results to this literature (for example, the fact that post sorting or post isotonic regression can only improve the weighted interval score). Finally, we provide an extensive suite of empirical comparisons across 34 data sets from two different benchmark repositories.

Large language models (LLMs) excel in many tasks but struggle to accurately quantify uncertainty in their generated responses. This limitation makes it challenging to detect misinformation and ensure reliable decision-making. Existing uncertainty quantification (UQ) methods for LLMs are primarily prompt-wise rather than response-wise, often requiring multiple response samples, which incurs high computational costs. Moreover, LLMs have been shown to be overconfident, particularly when using reasoning steps to derive their answers. In this work, we propose CoT-UQ, a response-wise UQ framework that integrates LLMs' inherent reasoning capabilities through Chain-of-Thought (CoT) into the UQ process. CoT-UQ captures critical information during inference by extracting keywords from each reasoning step and assessing their importance to the final answer. This key reasoning information is then aggregated to produce a final uncertainty estimate. We conduct extensive experiments based on LLaMA Family with model sizes varying from 8B to 13B across logical and mathematical reasoning tasks. Experimental results demonstrate that CoT-UQ significantly outperforms existing UQ methods, achieving an average improvement of 5.9% AUROC compared to current UQ methods. The code is available at: https://github.com/ZBox1005/CoT-UQ.

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.

Recent advances in language models (LMs) have led to significant improvements in quality on complex NLP tasks, but at the expense of increased inference costs. Cascading offers a simple strategy to achieve more favorable cost-quality tradeoffs: here, a small model is invoked for most "easy" instances, while a few "hard" instances are deferred to the large model. While the principles underpinning cascading are well-studied for classification tasks - with deferral based on predicted class uncertainty favored theoretically and practically - a similar understanding is lacking for generative LM tasks. In this work, we initiate a systematic study of deferral rules for LM cascades. We begin by examining the natural extension of predicted class uncertainty to generative LM tasks, namely, the predicted sequence uncertainty. We show that this measure suffers from the length bias problem, either over- or under-emphasizing outputs based on their lengths. This is because LMs produce a sequence of uncertainty values, one for each output token; and moreover, the number of output tokens is variable across examples. To mitigate this issue, we propose to exploit the richer token-level uncertainty information implicit in generative LMs. We argue that naive predicted sequence uncertainty corresponds to a simple aggregation of these uncertainties. By contrast, we show that incorporating token-level uncertainty through learned post-hoc deferral rules can significantly outperform such simple aggregation strategies, via experiments on a range of natural language benchmarks with FLAN-T5 models. We further show that incorporating embeddings from the smaller model and intermediate layers of the larger model can give an additional boost in the overall cost-quality tradeoff.

A fundamental question in adversarial machine learning is whether a robust classifier exists for a given task. A line of research has made some progress towards this goal by studying the concentration of measure, but we argue standard concentration fails to fully characterize the intrinsic robustness of a classification problem since it ignores data labels which are essential to any classification task. Building on a novel definition of label uncertainty, we empirically demonstrate that error regions induced by state-of-the-art models tend to have much higher label uncertainty than randomly-selected subsets. This observation motivates us to adapt a concentration estimation algorithm to account for label uncertainty, resulting in more accurate intrinsic robustness measures for benchmark image classification problems.

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).

Conventional uncertainty-aware temporal difference (TD) learning methods often rely on simplistic assumptions, typically including a zero-mean Gaussian distribution for TD errors. Such oversimplification can lead to inaccurate error representations and compromised uncertainty estimation. In this paper, we introduce a novel framework for generalized Gaussian error modeling in deep reinforcement learning, applicable to both discrete and continuous control settings. Our framework enhances the flexibility of error distribution modeling by incorporating additional higher-order moment, particularly kurtosis, thereby improving the estimation and mitigation of data-dependent noise, i.e., aleatoric uncertainty. We examine the influence of the shape parameter of the generalized Gaussian distribution (GGD) on aleatoric uncertainty and provide a closed-form expression that demonstrates an inverse relationship between uncertainty and the shape parameter. Additionally, we propose a theoretically grounded weighting scheme to fully leverage the GGD. To address epistemic uncertainty, we enhance the batch inverse variance weighting by incorporating bias reduction and kurtosis considerations, resulting in improved robustness. Extensive experimental evaluations using policy gradient algorithms demonstrate the consistent efficacy of our method, showcasing significant performance improvements.

Multimodal semantic understanding often has to deal with uncertainty, which means the obtained messages tend to refer to multiple targets. Such uncertainty is problematic for our interpretation, including inter- and intra-modal uncertainty. Little effort has studied the modeling of this uncertainty, particularly in pre-training on unlabeled datasets and fine-tuning in task-specific downstream datasets. In this paper, we project the representations of all modalities as probabilistic distributions via a Probability Distribution Encoder (PDE) by utilizing sequence-level interactions. Compared to the existing deterministic methods, such uncertainty modeling can convey richer multimodal semantic information and more complex relationships. Furthermore, we integrate uncertainty modeling with popular pre-training frameworks and propose suitable pre-training tasks: Distribution-based Vision-Language Contrastive learning (D-VLC), Distribution-based Masked Language Modeling (D-MLM), and Distribution-based Image-Text Matching (D-ITM). The fine-tuned models are applied to challenging downstream tasks, including image-text retrieval, visual question answering, visual reasoning, and visual entailment, and achieve state-of-the-art results.

Numerous deep learning applications benefit from multi-task learning with multiple regression and classification objectives. In this paper we make the observation that the performance of such systems is strongly dependent on the relative weighting between each task's loss. Tuning these weights by hand is a difficult and expensive process, making multi-task learning prohibitive in practice. We propose a principled approach to multi-task deep learning which weighs multiple loss functions by considering the homoscedastic uncertainty of each task. This allows us to simultaneously learn various quantities with different units or scales in both classification and regression settings. We demonstrate our model learning per-pixel depth regression, semantic and instance segmentation from a monocular input image. Perhaps surprisingly, we show our model can learn multi-task weightings and outperform separate models trained individually on each task.

Leveraging human preferences for steering the behavior of Large Language Models (LLMs) has demonstrated notable success in recent years. Nonetheless, data selection and labeling are still a bottleneck for these systems, particularly at large scale. Hence, selecting the most informative points for acquiring human feedback may considerably reduce the cost of preference labeling and unleash the further development of LLMs. Bayesian Active Learning provides a principled framework for addressing this challenge and has demonstrated remarkable success in diverse settings. However, previous attempts to employ it for Preference Modeling did not meet such expectations. In this work, we identify that naive epistemic uncertainty estimation leads to the acquisition of redundant samples. We address this by proposing the Bayesian Active Learner for Preference Modeling (BAL-PM), a novel stochastic acquisition policy that not only targets points of high epistemic uncertainty according to the preference model but also seeks to maximize the entropy of the acquired prompt distribution in the feature space spanned by the employed LLM. Notably, our experiments demonstrate that BAL-PM requires 33% to 68% fewer preference labels in two popular human preference datasets and exceeds previous stochastic Bayesian acquisition policies.

Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually over-parameterized space. This paper investigates a new line of Bayesian deep learning by performing Bayesian inference on network structure. Instead of building structure from scratch inefficiently, we draw inspirations from neural architecture search to represent the network structure. We then develop an efficient stochastic variational inference approach which unifies the learning of both network structure and weights. Empirically, our method exhibits competitive predictive performance while preserving the benefits of Bayesian principles across challenging scenarios. We also provide convincing experimental justification for our modeling choice.

Large Language Models (LLMs) have recently been successfully applied to regression tasks -- such as time series forecasting and tabular prediction -- by leveraging their in-context learning abilities. However, their autoregressive decoding process may be ill-suited to continuous-valued outputs, where obtaining predictive distributions over numerical targets requires repeated sampling, leading to high computational cost and inference time. In this work, we investigate whether distributional properties of LLM predictions can be recovered without explicit autoregressive generation. To this end, we study a set of regression probes trained to predict statistical functionals (e.g., mean, median, quantiles) of the LLM's numerical output distribution directly from its internal representations. Our results suggest that LLM embeddings carry informative signals about summary statistics of their predictive distributions, including the numerical uncertainty. This investigation opens up new questions about how LLMs internally encode uncertainty in numerical tasks, and about the feasibility of lightweight alternatives to sampling-based approaches for uncertainty-aware numerical predictions.

As the issue of robustness in AI systems becomes vital, statistical learning techniques that are reliable even in presence of partly contaminated data have to be developed. Preference data, in the form of (complete) rankings in the simplest situations, are no exception and the demand for appropriate concepts and tools is all the more pressing given that technologies fed by or producing this type of data (e.g. search engines, recommending systems) are now massively deployed. However, the lack of vector space structure for the set of rankings (i.e. the symmetric group S_n) and the complex nature of statistics considered in ranking data analysis make the formulation of robustness objectives in this domain challenging. In this paper, we introduce notions of robustness, together with dedicated statistical methods, for Consensus Ranking the flagship problem in ranking data analysis, aiming at summarizing a probability distribution on S_n by a median ranking. Precisely, we propose specific extensions of the popular concept of breakdown point, tailored to consensus ranking, and address the related computational issues. Beyond the theoretical contributions, the relevance of the approach proposed is supported by an experimental study.

Accurately quantifying a large language model's (LLM) predictive uncertainty is crucial for judging the reliability of its answers. While most existing research focuses on short, directly answerable questions with closed-form outputs (e.g., multiple-choice), involving intermediate reasoning steps in LLM responses is increasingly important. This added complexity complicates uncertainty quantification (UQ) because the probabilities assigned to answer tokens are conditioned on a vast space of preceding reasoning tokens. Direct marginalization is infeasible, and the dependency inflates probability estimates, causing overconfidence in UQ. To address this, we propose UQAC, an efficient method that narrows the reasoning space to a tractable size for marginalization. UQAC iteratively constructs an "attention chain" of tokens deemed "semantically crucial" to the final answer via a backtracking procedure. Starting from the answer tokens, it uses attention weights to identify the most influential predecessors, then iterates this process until reaching the input tokens. Similarity filtering and probability thresholding further refine the resulting chain, allowing us to approximate the marginal probabilities of the answer tokens, which serve as the LLM's confidence. We validate UQAC on multiple reasoning benchmarks with advanced open-source LLMs, demonstrating that it consistently delivers reliable UQ estimates with high computational efficiency.

Bearing in mind the limited parametric knowledge of Large Language Models (LLMs), retrieval-augmented generation (RAG) which supplies them with the relevant external knowledge has served as an approach to mitigate the issue of hallucinations to a certain extent. However, uniformly retrieving supporting context makes response generation source-inefficient, as triggering the retriever is not always necessary, or even inaccurate, when a model gets distracted by noisy retrieved content and produces an unhelpful answer. Motivated by these issues, we introduce Semantic Uncertainty Guided Adaptive Retrieval (SUGAR), where we leverage context-based entropy to actively decide whether to retrieve and to further determine between single-step and multi-step retrieval. Our empirical results show that selective retrieval guided by semantic uncertainty estimation improves the performance across diverse question answering tasks, as well as achieves a more efficient inference.

Vision-language models (VLMs), such as CLIP and SigLIP, have found remarkable success in classification, retrieval, and generative tasks. For this, VLMs deterministically map images and text descriptions to a joint latent space in which their similarity is assessed using the cosine similarity. However, a deterministic mapping of inputs fails to capture uncertainties over concepts arising from domain shifts when used in downstream tasks. In this work, we propose post-hoc uncertainty estimation in VLMs that does not require additional training. Our method leverages a Bayesian posterior approximation over the last layers in VLMs and analytically quantifies uncertainties over cosine similarities. We demonstrate its effectiveness for uncertainty quantification and support set selection in active learning. Compared to baselines, we obtain improved and well-calibrated predictive uncertainties, interpretable uncertainty estimates, and sample-efficient active learning. Our results show promise for safety-critical applications of large-scale models.

Recent advances in Computer Vision have introduced the concept of pretrained representation uncertainty, enabling zero-shot uncertainty estimation. This holds significant potential for Earth Observation (EO), where trustworthiness is critical, yet the complexity of EO data poses challenges to uncertainty-aware methods. In this work, we investigate the generalization of representation uncertainty in EO, considering the domain's unique semantic characteristics. We pretrain uncertainties on large EO datasets and propose an evaluation framework to assess their zero-shot performance in multi-label classification and segmentation EO tasks. Our findings reveal that, unlike uncertainties pretrained on natural images, EO-pretraining exhibits strong generalization across unseen EO domains, geographic locations, and target granularities, while maintaining sensitivity to variations in ground sampling distance. We demonstrate the practical utility of pretrained uncertainties showcasing their alignment with task-specific uncertainties in downstream tasks, their sensitivity to real-world EO image noise, and their ability to generate spatial uncertainty estimates out-of-the-box. Initiating the discussion on representation uncertainty in EO, our study provides insights into its strengths and limitations, paving the way for future research in the field. Code and weights are available at: https://github.com/Orion-AI-Lab/EOUncertaintyGeneralization.

Classification on long-tailed distributed data is a challenging problem, which suffers from serious class-imbalance and accordingly unpromising performance especially on tail classes. Recently, the ensembling based methods achieve the state-of-the-art performance and show great potential. However, there are two limitations for current methods. First, their predictions are not trustworthy for failure-sensitive applications. This is especially harmful for the tail classes where the wrong predictions is basically frequent. Second, they assign unified numbers of experts to all samples, which is redundant for easy samples with excessive computational cost. To address these issues, we propose a Trustworthy Long-tailed Classification (TLC) method to jointly conduct classification and uncertainty estimation to identify hard samples in a multi-expert framework. Our TLC obtains the evidence-based uncertainty (EvU) and evidence for each expert, and then combines these uncertainties and evidences under the Dempster-Shafer Evidence Theory (DST). Moreover, we propose a dynamic expert engagement to reduce the number of engaged experts for easy samples and achieve efficiency while maintaining promising performances. Finally, we conduct comprehensive experiments on the tasks of classification, tail detection, OOD detection and failure prediction. The experimental results show that the proposed TLC outperforms existing methods and is trustworthy with reliable uncertainty.

In many applications of LLMs, natural language responses often have an underlying structure such as representing discrete labels, numerical values, or graphs. Yet, existing decoding and uncertainty estimation methods operate only in language space and largely disregard structural information. We address this by modeling LLM outputs directly in a task-dependent latent structure. By equipping this structure with a dissimilarity measure, we can compute Bayes-optimal responses. These are not selected from sampled generations but are newly synthesized by combining individual responses in the latent space. Across different tasks, Bayes-optimal responses consistently outperform standard decoding methods like beam search. Moreover, quantifying uncertainty via the induced Bayesian risk captures variations in terms of the latent structure and improves alignment with output quality and correctness. Our decision-theoretic framework is applicable to any problem that admits a latent response structure and enables reliable task-aware LLM predictions.

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).

As large language models continue to be widely developed, robust uncertainty quantification techniques will become crucial for their safe deployment in high-stakes scenarios. In this work, we explore how conformal prediction can be used to provide uncertainty quantification in language models for the specific task of multiple-choice question-answering. We find that the uncertainty estimates from conformal prediction are tightly correlated with prediction accuracy. This observation can be useful for downstream applications such as selective classification and filtering out low-quality predictions. We also investigate the exchangeability assumption required by conformal prediction to out-of-subject questions, which may be a more realistic scenario for many practical applications. Our work contributes towards more trustworthy and reliable usage of large language models in safety-critical situations, where robust guarantees of error rate are required.

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.

Monitoring machine learning models once they are deployed is challenging. It is even more challenging to decide when to retrain models in real-case scenarios when labeled data is beyond reach, and monitoring performance metrics becomes unfeasible. In this work, we use non-parametric bootstrapped uncertainty estimates and SHAP values to provide explainable uncertainty estimation as a technique that aims to monitor the deterioration of machine learning models in deployment environments, as well as determine the source of model deterioration when target labels are not available. Classical methods are purely aimed at detecting distribution shift, which can lead to false positives in the sense that the model has not deteriorated despite a shift in the data distribution. To estimate model uncertainty we construct prediction intervals using a novel bootstrap method, which improves upon the work of Kumar & Srivastava (2012). We show that both our model deterioration detection system as well as our uncertainty estimation method achieve better performance than the current state-of-the-art. Finally, we use explainable AI techniques to gain an understanding of the drivers of model deterioration. We release an open source Python package, doubt, which implements our proposed methods, as well as the code used to reproduce our experiments.

The quality of many modern machine learning models improves as model complexity increases, an effect that has been quantified, for predictive performance, with the non-monotonic double descent learning curve. Here, we address the overarching question: is there an analogous theory of double descent for models which estimate uncertainty? We provide a partially affirmative and partially negative answer in the setting of Gaussian processes (GP). Under standard assumptions, we prove that higher model quality for optimally-tuned GPs (including uncertainty prediction) under marginal likelihood is realized for larger input dimensions, and therefore exhibits a monotone error curve. After showing that marginal likelihood does not naturally exhibit double descent in the input dimension, we highlight related forms of posterior predictive loss that do exhibit non-monotonicity. Finally, we verify empirically that our results hold for real data, beyond our considered assumptions, and we explore consequences involving synthetic covariates.

We present UncertaintyRAG, a novel approach for long-context Retrieval-Augmented Generation (RAG) that utilizes Signal-to-Noise Ratio (SNR)-based span uncertainty to estimate similarity between text chunks. This span uncertainty enhances model calibration, improving robustness and mitigating semantic inconsistencies introduced by random chunking. Leveraging this insight, we propose an efficient unsupervised learning technique to train the retrieval model, alongside an effective data sampling and scaling strategy. UncertaintyRAG outperforms baselines by 2.03% on LLaMA-2-7B, achieving state-of-the-art results while using only 4% of the training data compared to other advanced open-source retrieval models under distribution shift settings. Our method demonstrates strong calibration through span uncertainty, leading to improved generalization and robustness in long-context RAG tasks. Additionally, UncertaintyRAG provides a lightweight retrieval model that can be integrated into any large language model with varying context window lengths, without the need for fine-tuning, showcasing the flexibility of our approach.

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.

Deploying large language models (LLMs) for long-context inference remains challenging due to their substantial memory and computational demands. While techniques such as Key-Value (KV) cache compression are designed to reduce memory usage, they often neglect the structured sparsity inherent in the relationship between hidden states and their corresponding KV cache. In this work, we explore the role of uncertainty as a potential indicator of sparsity within LLMs. We propose UNComp, an uncertainty-aware framework that leverages truncated matrix entropy to identify areas of low information content, thereby revealing sparsity patterns that can be used for adaptive compression. Unlike traditional methods that apply uniform compression, UNComp dynamically adjusts its approach to compression, guided by uncertainty measures that reflect the importance of various model components. Our analysis shows that sparsity patterns, when derived from uncertainty estimates, can be exploited to reveal special long-range dependencies, such as retrieval heads and retrieval layers. This perspective not only enhances our understanding of how compression can be optimized but also provides new insights into the inherent sparsity of LLMs during long-context inference. By focusing on uncertainty to analyze the sparsity pattern in detail, UNComp reduces the KV cache size to 4.74% of the original, achieves a 6% prefill speedup, and improves throughput by 6.4x - not only delivering strong lossless compression performance, but also validating the effectiveness of the underlying theoretical tool. We release the code at https://github.com/menik1126/UNComp.

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.

The increasing scale of large language models (LLMs) brings emergent abilities to various complex tasks requiring reasoning, such as arithmetic and commonsense reasoning. It is known that the effective design of task-specific prompts is critical for LLMs' ability to produce high-quality answers. In particular, an effective approach for complex question-and-answer tasks is example-based prompting with chain-of-thought (CoT) reasoning, which significantly improves the performance of LLMs. However, current CoT methods rely on a fixed set of human-annotated exemplars, which are not necessarily the most effective examples for different tasks. This paper proposes a new method, Active-Prompt, to adapt LLMs to different tasks with task-specific example prompts (annotated with human-designed CoT reasoning). For this purpose, we propose a solution to the key problem of determining which questions are the most important and helpful ones to annotate from a pool of task-specific queries. By borrowing ideas from the related problem of uncertainty-based active learning, we introduce several metrics to characterize the uncertainty so as to select the most uncertain questions for annotation. Experimental results demonstrate the superiority of our proposed method, achieving state-of-the-art on eight complex reasoning tasks. Further analyses of different uncertainty metrics, pool sizes, zero-shot learning, and accuracy-uncertainty relationship demonstrate the effectiveness of our method. Our code will be available at https://github.com/shizhediao/active-prompt.

Deep neural networks (DNNs) have been shown to perform well on exclusive, multi-class classification tasks. However, when different classes have similar visual features, it becomes challenging for human annotators to differentiate them. This scenario necessitates the use of composite class labels. In this paper, we propose a novel framework called Hyper-Evidential Neural Network (HENN) that explicitly models predictive uncertainty due to composite class labels in training data in the context of the belief theory called Subjective Logic (SL). By placing a grouped Dirichlet distribution on the class probabilities, we treat predictions of a neural network as parameters of hyper-subjective opinions and learn the network that collects both single and composite evidence leading to these hyper-opinions by a deterministic DNN from data. We introduce a new uncertainty type called vagueness originally designed for hyper-opinions in SL to quantify composite classification uncertainty for DNNs. Our results demonstrate that HENN outperforms its state-of-the-art counterparts based on four image datasets. The code and datasets are available at: https://github.com/Hugo101/HyperEvidentialNN.

3D Visual Question Answering (3D VQA) is crucial for enabling models to perceive the physical world and perform spatial reasoning. In 3D VQA, the free-form nature of answers often leads to improper annotations that can confuse or mislead models when training on the entire dataset. While other text generation tasks can mitigate this issue by learning on large-scale datasets, the scarcity of 3D scene data enlarges the negative effect of misleading annotations. Although active learning strategies can select valuable instances for training, they fail to identify and resolve misleading labels, which the oracle inevitably provides in practice. To address this issue, we propose a multi-turn interactive active learning strategy. This strategy selects data based on models' semantic uncertainty to form a solid knowledge foundation more effectively and actively requests reannotation from an oracle to resolve potentially misleading labels. For uncertainty assessment, we utilize a variance-based metric that takes semantic relationships between terms into consideration, thus avoiding the uniform inter-class similarity assumption of previous assessment metrics. Extensive experiments exhibit better model performance and a substantial reduction in training costs, with a halving of training costs for achieving relatively high accuracy. The code is available at https://github.com/fz-zsl/AQuA.

Uncertainty learning and quantification of models are crucial tasks to enhance the trustworthiness of the models. Importantly, the recent surge of generative language models (GLMs) emphasizes the need for reliable uncertainty quantification due to the concerns on generating hallucinated facts. In this paper, we propose to learn neural prediction set models that comes with the probably approximately correct (PAC) guarantee for quantifying the uncertainty of GLMs. Unlike existing prediction set models, which are parameterized by a scalar value, we propose to parameterize prediction sets via neural networks, which achieves more precise uncertainty quantification but still satisfies the PAC guarantee. We demonstrate the efficacy of our method on four types of language datasets and six types of models by showing that our method improves the quantified uncertainty by 63% on average, compared to a standard baseline method.

We present a scheme to obtain an inexpensive and reliable estimate of the uncertainty associated with the predictions of a machine-learning model of atomic and molecular properties. The scheme is based on resampling, with multiple models being generated based on sub-sampling of the same training data. The accuracy of the uncertainty prediction can be benchmarked by maximum likelihood estimation, which can also be used to correct for correlations between resampled models, and to improve the performance of the uncertainty estimation by a cross-validation procedure. In the case of sparse Gaussian Process Regression models, this resampled estimator can be evaluated at negligible cost. We demonstrate the reliability of these estimates for the prediction of molecular energetics, and for the estimation of nuclear chemical shieldings in molecular crystals. Extension to estimate the uncertainty in energy differences, forces, or other correlated predictions is straightforward. This method can be easily applied to other machine learning schemes, and will be beneficial to make data-driven predictions more reliable, and to facilitate training-set optimization and active-learning strategies.

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.

Estimating the difficulty of multiple-choice questions would be great help for educators who must spend substantial time creating and piloting stimuli for their tests, and for learners who want to practice. Supervised approaches to difficulty estimation have yielded to date mixed results. In this contribution we leverage an aspect of generative large models which might be seen as a weakness when answering questions, namely their uncertainty, and exploit it towards exploring correlations between two different metrics of uncertainty, and the actual student response distribution. While we observe some present but weak correlations, we also discover that the models' behaviour is different in the case of correct vs wrong answers, and that correlations differ substantially according to the different question types which are included in our fine-grained, previously unused dataset of 451 questions from a Biopsychology course. In discussing our findings, we also suggest potential avenues to further leverage model uncertainty as an additional proxy for item difficulty.

Large Language Models (LLMs) are employed across various high-stakes domains, where the reliability of their outputs is crucial. One commonly used method to assess the reliability of LLMs' responses is uncertainty estimation, which gauges the likelihood of their answers being correct. While many studies focus on improving the accuracy of uncertainty estimations for LLMs, our research investigates the fragility of uncertainty estimation and explores potential attacks. We demonstrate that an attacker can embed a backdoor in LLMs, which, when activated by a specific trigger in the input, manipulates the model's uncertainty without affecting the final output. Specifically, the proposed backdoor attack method can alter an LLM's output probability distribution, causing the probability distribution to converge towards an attacker-predefined distribution while ensuring that the top-1 prediction remains unchanged. Our experimental results demonstrate that this attack effectively undermines the model's self-evaluation reliability in multiple-choice questions. For instance, we achieved a 100 attack success rate (ASR) across three different triggering strategies in four models. Further, we investigate whether this manipulation generalizes across different prompts and domains. This work highlights a significant threat to the reliability of LLMs and underscores the need for future defenses against such attacks. The code is available at https://github.com/qcznlp/uncertainty_attack.