Doklady Mathematics最新文献

Identifying the right user to target is a common problem for different Internet platforms. Although numerous systems address this task, they are heavily tailored for specific environments and settings. It is challenging for practitioners to apply these findings to their problems. The reason is that most systems are designed for settings with millions of highly active users and with personal information, as is the case in social networks or other services with high virality. There exists a gap in the literature for systems that are for medium-sized data and where the only data available are the event sequences of a user. It motivates us to present Look-A-Liker (LAL) as an unsupervised deep cluster system. It uses temporal point processes to identify similar users for targeting tasks. We use data from the leading Internet marketplace for the gastronomic sector for experiments. LAL generalizes beyond proprietary data. Using event sequences of users, it is possible to obtain state-of-the-art results compared to novel methods such as Transformer architectures and multimodal learning. Our approach produces the up to 20% ROC AUC score improvement on real-world datasets from 0.803 to 0.959. Although LAL focuses on hundreds of thousands of sequences, we show how it quickly expands to millions of user sequences. We provide a fully reproducible implementation with code and datasets in https://github.com/adasegroup/sequence_clusterers.

We propose to study neural networks’ loss surfaces by methods of topological data analysis. We suggest to apply barcodes of Morse complexes to explore topology of loss surfaces. An algorithm for calculations of the loss function’s barcodes of local minima is described. We have conducted experiments for calculating barcodes of local minima for benchmark functions and for loss surfaces of small neural networks. Our experiments confirm our two principal observations for neural networks’ loss surfaces. First, the barcodes of local minima are located in a small lower part of the range of values of neural networks’ loss function. Secondly, increase of the neural network’s depth and width lowers the barcodes of local minima. This has some natural implications for the neural network’s learning and for its generalization properties.

Distributed optimization is an important direction of research in modern optimization theory. Its applications include large scale machine learning, distributed signal processing and many others. The paper studies decentralized min-max optimization for saddle point problems. Saddle point problems arise in training adversarial networks and in robust machine learning. The focus of the work is optimization over (slowly) time-varying networks. The topology of the network changes from time to time, and the velocity of changes is limited. We show that, analogically to decentralized optimization, it is sufficient to change only two edges per iteration in order to slow down convergence to the arbitrary time-varying case. At the same time, we investigate several classes of time-varying graphs for which the communication complexity can be reduced.

Neovascular age-related macular degeneration (n-AMD) is a form of AMD that is responsible for most cases of severe vision loss. Anti-VEGF therapy, which is the gold standard for the treatment of this pathology, is accompanied by OCT monitoring. However, this process is hampered by the lack of methods for accurately quantifying OCT images. The aim of this study is to develop and evaluate the accuracy of the automated calculation of the quantitative characteristics of PED, SRF, and IRF biomarkers. A neural network with U-NET architecture was trained on a manually annotated dataset that included 385 OCT images. The dice coefficient measured on the validation dataset was 0.9, 0.72, and 0.69 for PED, SRF, and IRF. The results of the quantitative calculation of these biomarkers did not statistically differ from the measurements of an ophthalmologist. Comparison of groups with respect to the anatomical outcome of therapy showed that PED height, extent, and square are different for groups with adherence and non-adherence PED; and PED height, PED square, and IRF square are different for groups with nonadherence and tear PED. Thus, the algorithm for the quantitative calculation of biomarkers provides more information for assessing the results of therapy, which can improve the outcomes of treatment in patients with n-AMD.

To provide secure information exchange in communication channels, the correctness of the operation of the relevant information protection systems must be preliminary studied. The mathematical algorithms used in such systems are correct and can theoretically provide the correct statistical properties of the output stream compared to the input. However, at the stage of implementation (programming) of these protection algorithms or at the stages of assembling the final equipment (using hardware, making adjustments) and its operation in real conditions, it is possible to introduce distortions that violate the operation of certain elements of information security tools (for example, a random number generator). As a result, by the nature of the transmitted signal, it becomes possible to determine that the output stream for a number of characteristics is steadily different from the ideal encrypted stream, which in theory should have come from the equipment and appeared at the output of the communication channel. In this situation, it is necessary to understand how the introduction of certain distortions affects the degree of security of the system being created. For this purpose, the parameters of various message sources are described, which simulate receiving an output stream with distortions. At the same time, the degree of security of the corresponding communication channel is proposed to be determined by estimating the proportion of the input stream that can be restored from the output using side information resulting from the introduction of appropriate distortions in the operation of the system.

The growing recognition of environmental, social, and governance (ESG) factors in financial decision-making has spurred the need for effective and comprehensive ESG risk assessment tools. In this study, we introduce an open-source Natural Language Processing (NLP) model, “ESGify”^1,2, based on MPNet-base architecture and aimed to classify texts within the frames of ESG risks. We also present a hierarchical and detailed methodology for ESG risk classification, leveraging the expertise of ESG professionals and global best practices. Anchored by a manually annotated multilabel dataset of 2000 news articles and domain adaptation with texts of sustainability reports, ESGify is developed to automate ESG risk classification following the established methodology. We compare augmentation techniques based on back translation and Large Language Models (LLMs) to improve the model quality and achieve 0.5 F1-weighted model quality in the dataset with 47 classes. This result outperforms ChatGPT 3.5 with a simple prompt. The model weights and documentation is hosted on Github https://github.com/sb-ai-lab/ESGify under the Apache 2.0 license.

The problem of predicting the position of a person on future frames of a video stream is solved, and in-depth experimental studies on the application of traditional and SOTA blocks for this task are carried out. An original architecture of KeyFNet and its modifications based on transform blocks is presented, which is able to predict coordinates in the video stream for 30, 60, 90, and 120 frames ahead with high accuracy. The novelty lies in the application of a combined algorithm based on multiple FNet blocks with fast Fourier transform as an attention mechanism concatenating the coordinates of key points. Experiments on Human3.6M and on our own real data confirmed the effectiveness of the proposed approach based on FNet blocks, compared to the traditional approach based on LSTM. The proposed algorithm matches the accuracy of advanced models, but outperforms them in terms of speed, uses less computational resources, and thus can be applied in collaborative robotic solutions.

The concept of intermediate asymptotics for the solution of an evolution equation with initial data and a related solution obtained without initial conditions was introduced by G.N. Barenblatt and Ya.B. Zeldovich in the context of extending the concept of strict determinism in statistical physics and quantum mechanics. Here, according to V.P. Maslov, to axiomatize the mathematical theory, we need to know the conditions satisfied by the initial data of the problem. We show that the correct solvability of a problem without initial conditions for fractional differential equations in a Banach space is a necessary, but not sufficient, condition for intermediate asymptotics. Examples of intermediate asymptotics are given.

We consider a competitive facility location problem with two competing parties operating in a situation of uncertain demand scenarios. The problem of finding the best solutions for the parties is formulated as a discrete bilevel mathematical programming problem. A procedure for computing an upper bound for the objective function on solution subsets is suggested. The procedure could be employed in implicit enumeration schemes capable of computing an optimal solution for the problem under study. Within the procedure, additional constraints (cuts) iteratively augment the high-point relaxation of the initial bilevel problem, which strengthens the relaxation and improves the upper bound’s quality. A new procedure for generating such cuts is proposed, which allows us to construct the strongest cuts without enumerating the parameters encoding them.

New cases of integrable fifth-order dynamical systems that are homogeneous with respect to some of the variables are obtained, in which a system on the tangent bundle of a two-dimensional manifold can be distinguished. In this case, the force field is divided into an internal (conservative) and an external one, which has dissipation of different signs. The external field is introduced using some unimodular transformation and generalizes previously considered fields. Complete sets of both first integrals and invariant differential forms are given.