Maxim Panov

Artem Vazhentsev, Ekaterina Fadeeva, Rui Xing et al.

Uncertainty quantification (UQ) has emerged as a promising approach for detecting hallucinations and low-quality output of Large Language Models (LLMs). However, obtaining proper uncertainty scores is complicated by the conditional dependency between the generation steps of an autoregressive LLM because it is hard to model it explicitly. Here, we propose to learn this dependency from attention-based features. In particular, we train a regression model that leverages LLM attention maps, probabilities on the current generation step, and recurrently computed uncertainty scores from previously generated tokens. To incorporate the recurrent features, we also suggest a two-staged training procedure. Our experimental evaluation on ten datasets and three LLMs shows that the proposed method is highly effective for selective generation, achieving substantial improvements over rivaling unsupervised and supervised approaches.

Ekaterina Fadeeva, Maiya Goloburda, Aleksandr Rubashevskii et al.

Consistency-based methods have emerged as an effective approach to uncertainty quantification (UQ) in large language models. These methods typically rely on several generations obtained via multinomial sampling, measuring their agreement level. However, in short-form QA, multinomial sampling is prone to producing duplicates due to peaked distributions, and its stochasticity introduces considerable variance in uncertainty estimates across runs. We introduce a new family of methods that employ beam search to generate candidates for consistency-based UQ, yielding improved performance and reduced variance compared to multinomial sampling. We also provide a theoretical lower bound on the beam set probability mass under which beam search achieves a smaller error than multinomial sampling. We empirically evaluate our approach on six QA datasets and find that its consistent improvements over multinomial sampling lead to state-of-the-art UQ performance.

Fedor Noskov, Alexander Fishkov, Maxim Panov

Prediction with the possibility of abstention (or selective prediction) is an important problem for error-critical machine learning applications. While well-studied in the classification setup, selective approaches to regression are much less developed. In this work, we consider the nonparametric heteroskedastic regression problem and develop an abstention procedure via testing the hypothesis on the value of the conditional variance at a given point. Unlike existing methods, the proposed one allows to account not only for the value of the variance itself but also for the uncertainty of the corresponding variance predictor. We prove non-asymptotic bounds on the risk of the resulting estimator and show the existence of several different convergence regimes. Theoretical analysis is illustrated with a series of experiments on simulated and real-world data.

Fedor Noskov, Maxim Panov

Community detection is one of the most critical problems in modern network science. Its applications can be found in various fields, from protein modeling to social network analysis. Recently, many papers appeared studying the problem of overlapping community detection, where each node of a network may belong to several communities. In this work, we consider Mixed-Membership Stochastic Block Model (MMSB) first proposed by Airoldi et al. MMSB provides quite a general setting for modeling overlapping community structure in graphs. The central question of this paper is to reconstruct relations between communities given an observed network. We compare different approaches and establish the minimax lower bound on the estimation error. Then, we propose a new estimator that matches this lower bound. Theoretical results are proved under fairly general conditions on the considered model. Finally, we illustrate the theory in a series of experiments.

Roman Vashurin, Ekaterina Fadeeva, Artem Vazhentsev et al.

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. Code: https://github.com/IINemo/lm-polygraph Benchmark: https://huggingface.co/LM-Polygraph

Roman Vashurin, Maiya Goloburda, Albina Ilina et al.

Uncertainty quantification (UQ) methods for Large Language Models (LLMs) encompass a variety of approaches, with two major types being particularly prominent: information-based, which focus on model confidence expressed as token probabilities, and consistency-based, which assess the semantic relationship between multiple outputs generated using repeated sampling. Several recent methods have combined these two approaches to boost UQ performance. However, they sometimes fail to outperform much simpler baseline methods. Our work discusses the fundamental approach to constructing uncertainty measures that directly links uncertainty with the minimum Bayes risks achieved by LLM decoding. Building on these findings, we propose a novel approach to integrating model confidence with output consistency, resulting in a family of efficient and robust UQ methods. Our investigation reveals distinctive characteristics of LLMs as probabilistic models, which help to explain why these UQ methods underperform in certain tasks. Based on these findings, we propose a new way of synthesizing model confidence and output consistency, leading to a family of efficient and robust UQ methods. We evaluate our approach across various tasks such as question answering, abstractive summarization, and machine translation, demonstrating sizable improvements over state-of-the-art UQ approaches.

Ekaterina Fadeeva, Aleksandr Rubashevskii, Roman Vashurin et al.

Large Language Models (LLMs) enhanced with external knowledge retrieval, an approach known as Retrieval-Augmented Generation (RAG), have shown strong performance in open-domain question answering. However, RAG systems remain susceptible to hallucinations: factually incorrect outputs that may arise either from inconsistencies in the model's internal knowledge or incorrect use of the retrieved context. Existing approaches often conflate factuality with faithfulness to the retrieved context, misclassifying factually correct statements as hallucinations if they are not directly supported by the retrieval. In this paper, we introduce FRANQ (Faithfulness-based Retrieval Augmented UNcertainty Quantification), a novel method for hallucination detection in RAG outputs. FRANQ applies different Uncertainty Quantification (UQ) techniques to estimate factuality based on whether a statement is faithful to the retrieved context or not. To evaluate FRANQ and other UQ techniques for RAG, we present a new long-form Question Answering (QA) dataset annotated for both factuality and faithfulness, combining automated labeling with manual validation of challenging examples. Extensive experiments on long- and short-form QA across multiple datasets and LLMs show that FRANQ achieves more accurate detection of factual errors in RAG-generated responses compared to existing methods.

Roman Vashurin, Maiya Goloburda, Preslav Nakov et al.

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 length-normalized 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 length-normalized UQ methods uncertainty estimates across multiple metrics and models.

Georgii S. Novikov, Maxim E. Panov, Ivan V. Oseledets

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.

Achille Thin, Nikita Kotelevskii, Arnaud Doucet et al.

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.

Achille Thin, Nikita Kotelevskii, Christophe Andrieu et al.

Markov Chain Monte Carlo (MCMC) is a class of algorithms to sample complex and high-dimensional probability distributions. The Metropolis-Hastings (MH) algorithm, the workhorse of MCMC, provides a simple recipe to construct reversible Markov kernels. Reversibility is a tractable property that implies a less tractable but essential property here, invariance. Reversibility is however not necessarily desirable when considering performance. This has prompted recent interest in designing kernels breaking this property. At the same time, an active stream of research has focused on the design of novel versions of the MH kernel, some nonreversible, relying on the use of complex invertible deterministic transforms. While standard implementations of the MH kernel are well understood, the aforementioned developments have not received the same systematic treatment to ensure their validity. This paper fills the gap by developing general tools to ensure that a class of nonreversible Markov kernels, possibly relying on complex transforms, has the desired invariance property and leads to convergent algorithms. This leads to a set of simple and practically verifiable conditions.

Achille Thin, Nikita Kotelevskii, Jean-Stanislas Denain et al.

In this contribution, we propose a new computationally efficient method to combine Variational Inference (VI) with Markov Chain Monte Carlo (MCMC). This approach can be used with generic MCMC kernels, but is especially well suited to \textit{MetFlow}, a novel family of MCMC algorithms we introduce, in which proposals are obtained using Normalizing Flows. The marginal distribution produced by such MCMC algorithms is a mixture of flow-based distributions, thus drastically increasing the expressivity of the variational family. Unlike previous methods following this direction, our approach is amenable to the reparametrization trick and does not rely on computationally expensive reverse kernels. Extensive numerical experiments show clear computational and performance improvements over state-of-the-art methods.

Aleksandr Artemenkov, Maxim Panov

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.

Marina Gomtsyan, Nikita Mokrov, Maxim Panov et al.

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 numerous experiments on different synthetic and real-world datasets. The results show that our algorithm achieves state-of-the-art performance, while also being computationally efficient and robust to noise in the data.

Evgenii Tsymbalov, Sergei Makarychev, Alexander Shapeev et al.

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, 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 superiority of the proposed approach over the state-of-the-art methods.

Stanislav Tsepa, Maxim Panov

The problem of unsupervised learning node embeddings in graphs is one of the important directions in modern network science. In this work we propose a novel framework, which is aimed to find embeddings by \textit{discriminating distributions of similarities (DDoS)} between nodes in the graph. The general idea is implemented by maximizing the \textit{earth mover distance} between distributions of decoded similarities of similar and dissimilar nodes. The resulting algorithm generates embeddings which give a state-of-the-art performance in the problem of link prediction in real-world graphs.

Evgenii Tsymbalov, Maxim Panov, Alexander Shapeev

Active learning is relevant and challenging for high-dimensional regression models when the annotation of the samples is expensive. Yet most of the existing sampling methods cannot be applied to large-scale problems, consuming too much time for data processing. In this paper, we propose a fast active learning algorithm for regression, tailored for neural network models. It is based on uncertainty estimation from stochastic dropout output of the network. Experiments on both synthetic and real-world datasets show comparable or better performance (depending on the accuracy metric) as compared to the baselines. This approach can be generalized to other deep learning architectures. It can be used to systematically improve a machine-learning model as it offers a computationally efficient way of sampling additional data.

Ivan Nazarov, Boris Shirokikh, Maria Burkina et al.

We consider the problem of matrix completion with side information (\textit{inductive matrix completion}). In real-world applications many side-channel features are typically non-informative making feature selection an important part of the problem. We incorporate feature selection into inductive matrix completion by proposing a matrix factorization framework with group-lasso regularization on side feature parameter matrices. We demonstrate, that the theoretical sample complexity for the proposed method is much lower compared to its competitors in sparse problems, and propose an efficient optimization algorithm for the resulting low-rank matrix completion problem with sparsifying regularizers. Experiments on synthetic and real-world datasets show that the proposed approach outperforms other methods.

Mikhail Belyaev, Evgeny Burnaev, Ermek Kapushev et al.

We describe GTApprox - a new tool for medium-scale surrogate modeling in industrial design. Compared to existing software, GTApprox brings several innovations: a few novel approximation algorithms, several advanced methods of automated model selection, novel options in the form of hints. We demonstrate the efficiency of GTApprox on a large collection of test problems. In addition, we describe several applications of GTApprox to real engineering problems.