Large Language Models (LLMs) have become indispensable tools across various applications, making it more important than ever to ensure the quality and the trustworthiness of their outputs.This has led to growing interest in uncertainty quantification (UQ) methods for assessing the reliability of LLM outputs.Many existing UQ techniques rely on token probabilities, which inadvertently introduces a bias with respect to the length of the output.While some methods attempt to account for this, we demonstrate that such biases persist even in lengthnormalized approaches.To address the problem, here we propose UNCERTAINTY-LINE (Length-INvariant Estimation), a simple debiasing procedure that regresses uncertainty scores on output length and uses the residuals as corrected, length-invariant estimates.Our method is post-hoc, model-agnostic, and applicable to a range of UQ measures.Through extensive evaluation on machine translation, summarization, and question-answering tasks, we demonstrate that UNCERTAINTY-LINE consistently improves over even nominally lengthnormalized UQ methods uncertainty estimates across multiple metrics and models.We release our code publicly.1 * These authors contributed equally. 1 https://github.com/stat-ml/uncertainty-line

Artem Vazhentsev, Ekaterina Fadeeva, Rui Xing, Gleb Kuzmin, Ivan Lazichny, Alexander Panchenko, Preslav Nakov, Timothy Baldwin, Maxim Panov, Artem Shelmanov. Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing. 2025.

There are various measures of predictive uncertainty in the literature, but their relationships to each other remain unclear. This paper uses a decomposition of statistical pointwise risk into components associated with different sources of predictive uncertainty: namely, aleatoric uncertainty (inherent data variability) and epistemic uncertainty (model-related uncertainty). Together with Bayesian methods applied as approximations, we build a framework that allows one to generate different predictive uncertainty measures. We validate measures, derived from our framework on image datasets by evaluating its performance in detecting out-of-distribution and misclassified instances using the AUROC metric. The experimental results confirm that the measures derived from our framework are useful for the considered downstream tasks.

We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $\textup{P}_{Y \mid X}$. Existing methods, such as conformalized quantile regression and probabilistic conformal prediction, usually provide only a marginal coverage guarantee. In contrast, our approach extends these frameworks to achieve approximately conditional coverage, which is crucial for many practical applications. Our prediction sets adapt to the behavior of the predictive distribution, making them effective even under high heteroscedasticity. While exact conditional guarantees are infeasible without assumptions on the underlying data distribution, we derive non-asymptotic bounds that depend on the total variation distance of the conditional distribution and its estimate. Using extensive simulations, we show that our method consistently outperforms existing approaches in terms of conditional coverage, leading to more reliable statistical inference in a variety of applications.

We present a new method for generating confidence sets within the split conformal prediction framework. Our method performs a trainable transformation of any given conformity score to improve conditional coverage while ensuring exact marginal coverage. The transformation is based on an estimate of the conditional quantile of conformity scores. The resulting method is particularly beneficial for constructing adaptive confidence sets in multi-output problems where standard conformal quantile regression approaches have limited applicability. We develop a theoretical bound that captures the influence of the accuracy of the quantile estimate on the approximate conditional validity, unlike classical bounds for conformal prediction methods that only offer marginal coverage. We experimentally show that our method is highly adaptive to the local data structure and outperforms existing methods in terms of conditional coverage, improving the reliability of statistical inference in various applications.

Artem Vazhentsev, Lyudmila Rvanova, Ivan Lazichny, Alexander Panchenko, Maxim Panov, Timothy Baldwin, Artem Shelmanov. Proceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers). 2025.

Uncertainty quantification for Large Language Models (LLMs) encompasses a diverse range of approaches, with two major families being particularly prominent: (i) information-based, which estimate model confidence from token-level probabilities, and (ii) consistency-based, which assess the semantic agreement among multiple outputs generated using repeated sampling. While several recent methods have sought to combine these two paradigms to improve uncertainty quantification performance, they often fail to consistently outperform simpler baselines. In this work, we revisit the foundations of uncertainty estimation through the lens of Minimum Bayes Risk decoding, establishing a direct link between uncertainty and the optimal decision-making process of LLMs. Building on these findings, we propose CoCoA, a unified framework that integrates model confidence with output consistency, yielding a family of efficient and robust uncertainty quantification methods. We evaluate CoCoA across diverse tasks, including question answering, abstractive text summarization, and machine translation, and demonstrate sizable improvements over state-of-the-art uncertainty quantification approaches.

The success of Deep Neural Network (DNN) models significantly depends on the quality of provided annotations. In medical image segmentation, for example, having multiple expert annotations for each data point is standard to minimize subjective annotation bias. Then, the goal of estimation is to filter out the label noise and recover the ground-truth masks, which are not explicitly given. This paper proposes a probabilistic model for noisy observations that allows us to build confident classification and segmentation models. We explicitly model label noise to accomplish this and introduce a new information-based regularization that pushes the network to recover the ground-truth labels. In addition, we adjust the loss function for the segmentation task by prioritizing learning in high-confidence regions where all the annotators agree on labeling. We evaluate the proposed method on a series of classification tasks such as noisy versions of MNIST, CIFAR-10, and Fashion-MNIST datasets, as well as CIFAR-10N, a real-world dataset with noisy human annotations. Additionally, for the segmentation task, we consider several medical imaging datasets, such as LIDC and RIGA, that reflect real-world inter-variability among multiple annotators. Our experiments show that our algorithm outperforms state-of-the-art solutions for the considered classification and segmentation problems.

Abstract The rapid proliferation of large language models (LLMs) has stimulated researchers to seek effective and efficient approaches to deal with LLM hallucinations and low-quality outputs. Uncertainty quantification (UQ) is a key element of machine learning applications in dealing with such challenges. However, research to date on UQ for LLMs has been fragmented in terms of techniques and evaluation methodologies. In this work, we address this issue by introducing a novel benchmark that implements a collection of state-of-the-art UQ baselines and offers an environment for controllable and consistent evaluation of novel UQ techniques over various text generation tasks. Our benchmark also supports the assessment of confidence normalization methods in terms of their ability to provide interpretable scores. Using our benchmark, we conduct a large-scale empirical investigation of UQ and normalization techniques across eleven tasks, identifying the most effective approaches.

Conformal prediction (CP) stands out as a robust framework for uncertainty quantification, which is crucial for ensuring the reliability of predictions. However, common CP methods heavily rely on the data exchangeability, a condition often violated in practice. Existing approaches for tackling non-exchangeability lead to methods that are not computable beyond the simplest examples. In this work, we introduce a new efficient approach to CP that produces provably valid confidence sets for fairly general non-exchangeable data distributions. We illustrate the general theory with applications to the challenging setting of federated learning under data heterogeneity between agents. Our method allows constructing provably valid personalized prediction sets for agents in a fully federated way. The effectiveness of the proposed method is demonstrated in a series of experiments on real-world datasets.

The asymptotically precise estimation of the generalization of kernel methods has recently received attention due to the parallels between neural networks and their associated kernels. However, prior works derive such estimates for training by kernel ridge regression (KRR), whereas neural networks are typically trained with gradient descent (GD). In the present work, we consider the training of kernels with a family of \emph{spectral algorithms} specified by profile $h(\lambda)$, and including KRR and GD as special cases. Then, we derive the generalization error as a functional of learning profile $h(\lambda)$ for two data models: high-dimensional Gaussian and low-dimensional translation-invariant model. Under power-law assumptions on the spectrum of the kernel and target, we use our framework to (i) give full loss asymptotics for both noisy and noiseless observations (ii) show that the loss localizes on certain spectral scales, giving a new perspective on the KRR saturation phenomenon (iii) conjecture, and demonstrate for the considered data models, the universality of the loss w.r.t. non-spectral details of the problem, but only in case of noisy observation.

Artem Vazhentsev, Gleb Kuzmin, Akim Tsvigun, Alexander Panchenko, Maxim Panov, Mikhail Burtsev, Artem Shelmanov. Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2023.

The performance of modern deep learning-based systems dramatically depends on the quality of input objects. For example, face recognition quality is lower for blurry or corrupted inputs. Moreover, it is difficult to predict the influence of input quality on the resulting accuracy in more complex scenarios. We propose a deep metric learning framework that allows for direct estimation of the uncertainty with almost no additional computational cost. The developed ScaleFace algorithm uses trainable scale values that modify similarities in the space of embeddings. These input-dependent scale values represent a measure of confidence in the recognition result, thereby providing provably reasonable uncertainty estimation. We present results from comprehensive experiments on open-set classification tasks, including face recognition, which demonstrate the superior performance of ScaleFace compared to other uncertainty-aware face recognition approaches. We also extend our study to the task of text-to-image retrieval, showing that the proposed approach outperforms competitors by significant margins.

Federated Learning (FL) is a machine learning framework where many clients collaboratively train models while keeping the training data decentralized. Despite recent advances in FL, the uncertainty quantification topic (UQ) remains partially addressed. Among UQ methods, conformal prediction (CP) approaches provides distribution-free guarantees under minimal assumptions. We develop a new federated conformal prediction method based on quantile regression and take into account privacy constraints. This method takes advantage of importance weighting to effectively address the label shift between agents and provides theoretical guarantees for both valid coverage of the prediction sets and differential privacy. Extensive experimental studies demonstrate that this method outperforms current competitors.

Gleb Kuzmin, Artem Vazhentsev, Artem Shelmanov, Xudong Han, Simon Suster, Maxim Panov, Alexander Panchenko, Timothy Baldwin. Proceedings of the 13th International Joint Conference on Natural Language Processing and the 3rd Conference of the Asia-Pacific Chapter of the Association for Computational Linguistics (Volume 1: Long Papers). 2023.

In deep active learning, it is especially important to choose multiple examples to markup at each step to work efficiently, especially on large datasets. At the same time, existing solutions to this problem in the Bayesian setup, such as BatchBALD, have significant limitations in selecting a large number of examples, associated with the exponential complexity of computing mutual information for joint random variables. We, therefore, present the Large BatchBALD algorithm, which gives a well-grounded approximation to the BatchBALD method that aims to achieve comparable quality while being more computationally efficient. We provide a complexity analysis of the algorithm, showing a reduction in computation time, especially for large batches. Furthermore, we present an extensive set of experimental results on image and text data, both on toy datasets and larger ones such as CIFAR-100.

Under a simplified data model, this paper provides a theoretical analysis of learning from data that have an underlying low-rank tensor structure in both supervised and unsupervised settings. For the supervised setting, we provide an analysis of a Ridge classifier (with high regularization parameter) with and without knowledge of the low-rank structure of the data. Our results quantify analytically the gain in misclassification errors achieved by exploiting the low-rank structure for denoising purposes, as opposed to treating data as mere vectors. We further provide a similar analysis in the context of clustering, thereby quantifying the exact performance gap between tensor methods and standard approaches which treat data as simple vectors.

Artem Vazhentsev, Gleb Kuzmin, Artem Shelmanov, Akim Tsvigun, Evgenii Tsymbalov, Kirill Fedyanin, Maxim Panov, Alexander Panchenko, Gleb Gusev, Mikhail Burtsev, Manvel Avetisian, Leonid Zhukov. Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2022.

A memory efficient approach to ensembling neural networks is to share most weights among the ensembled models by means of a single reference network. We refer to this strategy as Embedded Ensembling (EE); its particular examples are BatchEnsembles and Monte-Carlo dropout ensembles. In this paper we perform a systematic theoretical and empirical analysis of embedded ensembles with different number of models. Theoretically, we use a Neural-Tangent-Kernel-based approach to derive the wide network limit of the gradient descent dynamics. In this limit, we identify two ensemble regimes - independent and collective - depending on the architecture and initialization strategy of ensemble models. We prove that in the independent regime the embedded ensemble behaves as an ensemble of independent models. We confirm our theoretical prediction with a wide range of experiments with finite networks, and further study empirically various effects such as transition between the two regimes, scaling of ensemble performance with the network width and number of models, and dependence of performance on a number of architecture and hyperparameter choices.

This paper proposes a fast and scalable method for uncertainty quantification of machine learning models' predictions. First, we show the principled way to measure the uncertainty of predictions for a classifier based on Nadaraya-Watson's nonparametric estimate of the conditional label distribution. Importantly, the approach allows to disentangle explicitly \textit{aleatoric} and \textit{epistemic} uncertainties. The resulting method works directly in the feature space. However, one can apply it to any neural network by considering an embedding of the data induced by the network. We demonstrate the strong performance of the method in uncertainty estimation tasks on text classification problems and a variety of real-world image datasets, such as MNIST, SVHN, CIFAR-100 and several versions of ImageNet.

Artem Shelmanov, Evgenii Tsymbalov, Dmitri Puzyrev, Kirill Fedyanin, Alexander Panchenko, Maxim Panov. Proceedings of the 16th Conference of the European Chapter of the Association for Computational Linguistics: Main Volume. 2021.

Variational auto-encoders (VAE) are popular deep latent variable models which are trained by maximizing an Evidence Lower Bound (ELBO). To obtain tighter ELBO and hence better variational approximations, it has been proposed to use importance sampling to get a lower variance estimate of the evidence. However, importance sampling is known to perform poorly in high dimensions. While it has been suggested many times in the literature to use more sophisticated algorithms such as Annealed Importance Sampling (AIS) and its Sequential Importance Sampling (SIS) extensions, the potential benefits brought by these advanced techniques have never been realized for VAE: the AIS estimate cannot be easily differentiated, while SIS requires the specification of carefully chosen backward Markov kernels. In this paper, we address both issues and demonstrate the performance of the resulting Monte Carlo VAEs on a variety of applications.

Estimation of probability density function from samples is one of the central problems in statistics and machine learning. Modern neural network-based models can learn high dimensional distributions but have problems with hyperparameter selection and are often prone to instabilities during training and inference. We propose a new efficient tensor train-based model for density estimation (TTDE). Such density parametrization allows exact sampling, calculation of cumulative and marginal density functions, and partition function. It also has very intuitive hyperparameters. We develop an efficient non-adversarial training procedure for TTDE based on the Riemannian optimization. Experimental results demonstrate the competitive performance of the proposed method in density estimation and sampling tasks, while TTDE significantly outperforms competitors in training speed.

Each day bank clients conduct numerous operations, such as purchasing goods or transferring money to other clients. These interactions can be interpreted as a graph dynamically changing over time. This work focuses on the task of predicting new interactions in the network of bank clients and treats it as a link prediction problem. We propose an architecture for the graph convolutional network to efficiently solve the link prediction problem for this type of data. Our model uses recurrent neural networks to leverage the time-series data in both nodes and edges and effectively scales to the graphs with millions of nodes. We evaluate the model on the data provided for several years by a large European bank. The obtained results show that the model outperforms the existing approaches. The current paper is an extended abstract for the work [5].

In this paper, we discuss how modern deep learning approaches can be applied to the credit scoring of bank clients. We show that information about connections between clients based on money transfers between them allows us to significantly improve the quality of credit scoring compared to the approaches using information about the target client solely. As a final solution, we develop a new graph neural network model EWS-GCN that combines ideas of graph convolutional and recurrent neural networks via attention mechanism. The resulting model allows for robust training and efficient processing of large-scale data. We also demonstrate that our model outperforms the state-of-the-art graph neural networks achieving excellent results.

Modern methods for data visualization via dimensionality reduction, such as t-SNE, usually have performance issues that prohibit their application to large amounts of high-dimensional data. In this work, we propose NCVis – a high-performance dimensionality reduction method built on a sound statistical basis of noise contrastive estimation. We show that NCVis outperforms state-of-the-art techniques in terms of speed while preserving the representation quality of other methods. In particular, the proposed approach successfully proceeds a large dataset of more than 1 million news headlines in several minutes and presents the underlying structure in a human-readable way. Moreover, it provides results consistent with classical methods like t-SNE on more straightforward datasets like images of hand-written digits. We believe that the broader usage of such software can significantly simplify the large-scale data analysis and lower the entry barrier to this area.

The existing approaches to intrinsic dimension estimation usually are not reliable when the data are nonlinearly embedded in the high dimensional space. In this work, we show that the explicit accounting to geometric properties of unknown support leads to the polynomial correction to the standard maximum likelihood estimate of intrinsic dimension for flat manifolds. The proposed algorithm (GeoMLE) realizes the correction by regression of standard MLEs based on distances to nearest neighbors for different sizes of neighborhoods. Moreover, the proposed approach also efficiently handles the case of nonuniform sampling of the manifold. We perform a series of experiments on various synthetic and real-world datasets. The results show that our algorithm achieves state-of-the-art performance, while also being robust to noise in the data and competitive computationally.

Aerial drones can be used for a number of monitoring and control applications. Most of existing drone control platforms are quite primitive in terms of body-machine interface. They are usually a variation of a hand-held remote controller or ground control station. However, in a number of line-of-sight scenarios it would be more convenient to use the human gestures and voice for the drone control. In this work, we present an approach for instantaneous control of drones based on human voice and gestures. The proposed solution includes wearable sensors and embedded artificial intelligence. We use a microphone and an Inertial Measurement Unit (IMU) for capturing the human voice and the hand movements. Primary control is implemented by a voice recognition unit based on Recurrent Neural Network (RNN) while the secondary control is implemented by the gesture recognition system based on Convolutional Neural Network (CNN). For implementing the embedded intelligence, we use a low-power embedded system with a graphical processing unit able to run pre-trained neural networks on board of the drone. As a result, the system can perform different speech and gesture recognition tasks real-time.

Active learning methods for neural networks are usually based on greedy criteria, which ultimately give a single new design point for the evaluation. Such an approach requires either some heuristics to sample a batch of design points at one active learning iteration, or retraining the neural network after adding each data point, which is computationally inefficient. Moreover, uncertainty estimates for neural networks sometimes are overconfident for the points lying far from the training sample. In this work, we propose to approximate Bayesian neural networks (BNN) by Gaussian processes (GP), which allows us to update the uncertainty estimates of predictions efficiently without retraining the neural network while avoiding overconfident uncertainty prediction for out-of-sample points. In a series of experiments on real-world data, including large-scale problems of chemical and physical modeling, we show the superiority of the proposed approach over the state-of-the-art methods.

Bitcoin is digital assets infrastructure powering the first worldwide decentralized cryptocurrency of the same name. All history of Bitcoins owning and transferring (addresses and transactions) is available as a public ledger called blockchain. But real-world owners of addresses are not known in general. That's why Bitcoin is called pseudo-anonymous. However, some addresses can be grouped by their ownership using behavior patterns and publicly available information from off-chain sources. Blockchain-based common behavior pattern analysis (common spending and one-time change heuristics) is widely used for Bitcoin clustering as votes for addresses association, while offchain information (tags) is mostly used to verify results. In this paper, we propose to use off-chain information as votes for address separation and to consider it together with blockchain information during the clustering model construction step. Both blockchain and off-chain information are not reliable, and our approach aims to filter out errors in input data. The results of the study show the feasibility of a proposed approached for Bitcoin address clustering. It can be useful for the users to avoid insecure Bitcoin usage patterns and for the investigators to conduct a more advanced de-anonymizing analysis.