Doklady Mathematics最新文献

The goals, objectives, and structure of the ontology of the Common Digital Space of Scientific Knowledge (CDSSK) are considered. The CDSSK is an integrated information structure that combines state scientific information systems presented on the Internet (the Great Russian Encyclopedia, the National Electronic Library, the State Catalog of Geographical Names, etc.) with industry information systems, databases, and electronic libraries (MathNet, Socionet, Scientific Heritage of Russia, etc.). CDSSK can be considered as an information basis for solving artificial intelligence problems. The article presents the unified structure of the CDSSK ontology developed at the Joint Supercomputer Center of the Russian Academy of Sciences and its modeling on an example of ten subject classes and eight auxiliary classes of objects of the CDSSK universal subspace.

For prediction tasks using tabular data, it is possible to extract additional information about the target variable by examining the relationships between the objects. Specifically, if it is possible to receive agraph in which the objects are represented as vertices and the relationships are expressed as edges, then it is likely that the graph structure contains valuable information. Recent research has indicated that jointly training graph neural networks and gradient boostings on this type of data can increase the accuracy of predictions. This article proposes new methods for learning on tabular data that incorporates a graph structure, in an attempt to combine modern multilayer techniques for processing tabular data and graph neural networks. In addition, we discuss ways to mitigate the computational complexity of the proposed models and conduct experiments in both inductive and transductive settings. Our findings demonstrate tha the proposed approaches provide comparable quality to modern methods.

The paper introduces a novel methodology for predicting intentions in dialog systems through a graph-based approach. This methodology involves constructing graph structures that represent dialogs, thus capturing contextual information effectively. By analyzing results from various open and closed domain datasets, the authors demonstrate the substantial enhancement in intention prediction accuracy achieved by combining graph models with text encoders. The primary focus of the study revolves around assessing the impact of diverse graph architectures and encoders on the performance of the proposed technique. Through empirical evaluation, the experimental outcomes affirm the superiority of graph neural networks in terms of both (Recall@k) (MAR) metric and computational resources when compared to alternative methods. This research uncovers a novel avenue for intention prediction in dialog systems by leveraging graph-based representations.

This article provides a survey of the results of several research studies [12–14, 26], in which open questions related to the high-probability convergence analysis of stochastic first-order optimization methods under mild assumptions on the noise were gradually addressed. In the beginning, we introduce the concept of gradient clipping, which plays a pivotal role in the development of stochastic methods for successful operation in the case of heavy-tailed distributions. Next, we examine the importance of obtaining the high-probability convergence guarantees and their connection with in-expectation convergence guarantees. The concluding sections of the article are dedicated to presenting the primary findings related to minimization problems and the results of numerical experiments.

Differential equation discovery, a machine learning subfield, is used to develop interpretable models, particularly, in nature-related applications. By expertly incorporating the general parametric form of the equation of motion and appropriate differential terms, algorithms can autonomously uncover equations from data. This paper explores the prerequisites and tools for independent equation discovery without expert input, eliminating the need for equation form assumptions. We focus on addressing the challenge of assessing the adequacy of discovered equations when the correct equation is unknown, with the aim of providing insights for reliable equation discovery without prior knowledge of the equation form.

This article is the author’s review of the singularity in which events in the field of artificial intelligence (AI) are developing. A general view is offered on the role of revolutions in information technology as they expand the human personality. The current stage of personal expansion is considered, covering the last decade, especially 2023. The most important and common socially significant documents expressing concern about AI, as well as those that assert an optimistic view of events, are considered: ethical principles, important directions, requirements, and restrictions. It takes a closer look at the pending European AI Act (AIA) and how different groups are reacting to it. Cultural and historical factors are highlighted that can counteract the negative and catastrophic developments that may result from AI. Possible mechanisms for preserving genuine knowledge among professionals and disseminating it among the general public are analyzed.

We consider a system of second-order semilinear elliptic equations in a multidimensional domain with an arbitrarily curved boundary contained in a narrow layer along the unperturbed boundary. The Dirichlet or Neumann condition is imposed on the curved boundary. In the case of the Neumann condition, rather natural and weak conditions are additionally imposed on the structure of the curving. Under these conditions, we show that the homogenized problem is one for the same system of equations in the unperturbed problem with a boundary condition of the same kind as on the perturbed boundary. The main result is operator (W_{2}^{1})- and L₂- estimates.

This paper is dedicated to the development of a novel method for coordination analysis (CA) in English using the neural (deep learning) methods. An efficient solution for the task allows identifying potentially valuable links and relationships between specific parts of a sentence, making the extraction of coordinate structures an important text preprocessing tool. In this study, a number of ideas for approaching the task within the framework of one-stage detectors were tested. The achieved results are comparable in quality to the current most advanced CA methods while allowing to process more than three-fold more sentences per unit time.

Recent advances in text generative models make it possible to create artificial texts that look like human-written texts. A large number of methods for detecting texts obtained using large language models have already been developed. However, improvement of detection methods occurs simultaneously with the improvement of generation methods. Therefore, it is necessary to explore new generative models and modernize existing approaches to their detection. In this paper, we present a large analysis of existing detection methods, as well as a study of lexical, syntactic, and stylistic features of the generated fragments. Taking into account the developments, we have tested the most qualitative, in our opinion, methods of detecting machine-generated documents for their further application in the scientific domain. Experiments were conducted for Russian and English languages on the collected datasets. The developed methods improved the detection quality to a value of 0.968 on the F1-score metric for Russian and 0.825 for English, respectively. The described techniques can be applied to detect generated fragments in scientific, research, and graduate papers.