Doklady Mathematics最新文献

{"title":"Sampling of Semiorthogonal Matrices for the Muon Algorithm","authors":"E. D. Petrov,&nbsp;G. V. Evseev,&nbsp;A. V. Antonov,&nbsp;A. S. Veprikov,&nbsp;N. A. Bushkov,&nbsp;S. V. Moiseev,&nbsp;A. N. Beznosikov","doi":"10.1134/S1064562425700565","DOIUrl":"10.1134/S1064562425700565","url":null,"abstract":"<p>Fine-tuning of large language models (LLMs) is widely used in contemporary deployment and development of LLMs, enabling the adaptation of pretrained models to specific tasks with limited labeled data. Traditional first-order stochastic optimization methods, such as SGD and Adam, although widely applied in practice, do not always guarantee optimal convergence. Currently, matrix-oriented optimization algorithms are actively being developed, surpassing classical methods by better exploiting the internal structure of model parameters. One such method is Muon, which projects gradients onto the space of semiorthogonal matrices, providing stable and rapid convergence with reduced sensitivity to hyperparameters. To further reduce memory requirements, zero-order algorithms are considered, which estimate gradients solely through forward passes without employing backpropagation. This work focuses on the study of orthogonal matrix sampling methods for the Muon algorithm within the framework of zero-order optimization during LLM fine-tuning. Various sampling strategies are compared, and their impact on fine-tuning quality and computational efficiency is evaluated. The results of this study can inform future research on zero-order optimization methods in the context of LLM fine-tuning.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"112 3","pages":"572 - 580"},"PeriodicalIF":0.6,"publicationDate":"2026-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Automation of Input Control of Transistors Using Deep Learning Models and Analysis of Their Latent Space","authors":"A. S. Chernova,&nbsp;F. P. Meshchaninov,&nbsp;D. A. Zhevnenko,&nbsp; E. S. Gornev","doi":"10.1134/S1064562425700644","DOIUrl":"10.1134/S1064562425700644","url":null,"abstract":"<p>Reliable automation of the input control of transistors in microelectronics requires detection of deviations in multichannel volt–ampere characteristics; however, threshold and simple statistical methods are poorly generalized to new and experimental structures and do not detect previously unseen defects and ignore nonlinear interchannel dependences. We offer a framework for detecting anomalies based on neural network models trained on the results of monitoring normal devices. Within the framework, we compare the family of autoencoders (MLP/LSTM/CAE) and specialized methods (USAD, GBAD), as well as explore the obtained latent spaces for interpreting the work of neural networks. The developed framework was verified on the basis of 14 200 180 nm VAC field-effect transistors with expert marking. The GBAD (F1 = 0.857) and regularized CAE (F1 = 0.857) models showed the best results in the test. The results set reproducible baselines for detecting anomalies in multichannel <i>I–V</i> transistor data and highlight the advantage of explicit modeling of the interchannel structure and latent representation analysis to enhance portability and interpretability.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"112 3","pages":"489 - 498"},"PeriodicalIF":0.6,"publicationDate":"2026-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ExtraSAGA: Variance Reduction Hybrid Method for Variational Inequalities","authors":"G. Chirkov,&nbsp;Yu. Kabikov,&nbsp;D. Medyakov,&nbsp;G. Molodtsov,&nbsp;A. Shestakov,&nbsp;A. Beznosikov","doi":"10.1134/S1064562425700607","DOIUrl":"10.1134/S1064562425700607","url":null,"abstract":"<p>Variational inequalities (VIs) serve as a powerful tool for various problems. This setting can be applied to a wide range of optimization, machine learning (ML), and other challenges. At the same time, large volumes of data are essential for high performance in ML tasks, which are addressed through stochastic approaches. However, widely used SGD method suffers from a non-decreasing variance of the stochastic gradient. To resolve this issue, variance reduction techniques were developed. This approach is well-studied for minimization but less extensively for VIs. In this paper, we modify the SAGA method, known for its effectiveness in stochastic minimization, by integrating Extragradient to address VI problems. We provide a theoretical analysis of the proposed method and conduct experiments, including bilinear problems and image denoising tasks.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"112 3","pages":"527 - 540"},"PeriodicalIF":0.6,"publicationDate":"2026-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S1064562425700607.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Where Semantics Meets Space: A Layer-Wise Analysis of Frozen Encoders for Efficient Polyp Segmentation","authors":"A. Taha,&nbsp;R. Lukmanov","doi":"10.1134/S1064562425700541","DOIUrl":"10.1134/S1064562425700541","url":null,"abstract":"<p>While deep encoder-decoder models dominate endoscopic segmentation, their reliance on full fine-tuning or training from scratch is computationally expensive and data-intensive. This paper challenges this by demonstrating that an extremely efficient model—a frozen foundation model encoder with a shallow decoder—can achieve state-of-the-art performance. Our core contribution is a systematic, layer-wise analysis to identify the single most effective feature source within the encoder’s hierarchy, challenging the common practice of using the final, most abstract layer. We identify a distinct performance peak at an intermediate layer (Layer 12), with an optimal trade-off between high-level semantic understanding and the high-resolution spatial fidelity crucial for segmentation. Despite training only 650k parameters, our method surpasses existing benchmarks on the challenging multi-center PolypGen dataset with a Dice score of 0.972. This work provides an evidence-based methodology for efficient feature extraction, significantly lowering the computational and data barriers for developing high-performance clinical AI tools.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"112 3","pages":"592 - 599"},"PeriodicalIF":0.6,"publicationDate":"2026-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Erratum to: MMRFiGN: An Ensemble Graph Segmentation Model for Imbalanced High-Resolution Images Informed by Multicomponent Markov Random Fields","authors":"A. K. Gorshenin,&nbsp;A. M. Dostovalova","doi":"10.1134/S1064562425330038","DOIUrl":"10.1134/S1064562425330038","url":null,"abstract":"","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"112 3","pages":"635 - 635"},"PeriodicalIF":0.6,"publicationDate":"2026-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S1064562425330038.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Medical Intelligence Solution for Population-Based Oncology Prevention","authors":"P. Philonenko,&nbsp;V. Kokh,&nbsp;P. Blinov","doi":"10.1134/S1064562425700620","DOIUrl":"10.1134/S1064562425700620","url":null,"abstract":"<p><i>Objective</i>.</p><p>To develop a scalable AI solution for population-based cancer prevention that enables effective detection of malignant neoplasms (cancer) using the minimal necessary dataset from electronic health records (EHRs) – medical diagnosis and procedure codes. This system addresses the resource limitations of traditional cancer screening methods while maintaining high efficiency in patient risk stratification.</p><p>The proposed method is based on a combination of gradient boosting with survival models. Over 700 predictors were constructed from raw EHR events, including sociodemographic characteristics, visit patterns, clinical history, and event frequencies by diagnosis groups. A key feature involves using population-based (Kaplan-Meier estimates) and individual (AFT model) risk characteristics as additional predictors for gradient boosting. Validation was conducted on data from over 2.5 million adult patients across 5 regions of the Russian Federation under the supervision of certified oncologists.</p><p>Our method achieves an Average Precision (AP) metric of 0.228, outperforming modern deep learning and large language model solutions with the best AP of 0.193. When forming a risk group comprising 1% of the population, the proposed method can identify 3.7–5.4 times more patients with cancer using the same screening volume. In a 12-month retrospective study, our method increased the number of detected cancer cases by +91% and expanded regional cancer coverage by 36 percentage points compared to current preventive health examination processes. The proposed AI-based system demonstrates high scalability: processing data for a city of one million takes less than three hours and requires no high-performance servers.</p><p>This research presents a system for scalable population-based cancer prevention using exclusively medical diagnosis and procedure codes from EHRs. The system naturally integrates into existing medical workflows by directing at-risk patients to primary care physicians for decisions regarding oncologist referrals and additional examinations. Minimal data and computational resource requirements make the solution accessible for implementation across diverse healthcare systems, including remote regions with limited resources, opening new opportunities for enhancing population-based cancer prevention effectiveness.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"112 3","pages":"506 - 517"},"PeriodicalIF":0.6,"publicationDate":"2026-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S1064562425700620.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Diffusion Models for Synthetic Tabular Data Generation","authors":"E. Telesheva,&nbsp;M. Hushchyn","doi":"10.1134/S1064562425700553","DOIUrl":"10.1134/S1064562425700553","url":null,"abstract":"<p>The problem of generating high-quality synthetic data is crucial for many data science tasks. A generated dataset can cut the costs on the augmentation of the existing data with additional instances, for example, in physics, or help with its privacy protection, for instance, in banking. However, generating a tabular dataset is challenging, as the data contains both numerical and categorical features. In this paper, we investigate modern approaches for tabular data generation, evaluate several modifications of the state-of-the-art model and whether they affect the quality of synthesized datasets. The modifications include the use of Gaussian diffusion models for both numerical and categorical features and Gaussian noise for the regularization during the training procedure. Comprehensive experiments and estimation of the tabular data generation quality metrics on five publicly available datasets prove that the proposed modified model retains a similar quality of synthesized data compared to the original model while requiring less time to generate synthetic samples. Code is available at GitHub: https://github.com/hushchyn-mikhail/tabular_data_generation.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"112 3","pages":"581 - 591"},"PeriodicalIF":0.6,"publicationDate":"2026-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generating Russian-Language Image Descriptions in Both Formal and Conversational Styles via a Neural-Network Ensemble","authors":"M. A. Privalov,&nbsp;A. S. Kozharinov","doi":"10.1134/S1064562425700528","DOIUrl":"10.1134/S1064562425700528","url":null,"abstract":"<p>The paper proposes a solution for generating image captions in both formal and conversational registers. This study is motivated by the need for educational tools to assist non-native speakers in mastering colloquial Russian. The methodology employs a multimodal encoder–decoder ensemble architecture, in which a pre-trained ResNet-152 Convolutional Neural Network serves as the encoder, and an LSTM network functions as the decoder. The captioning performance is further enhanced by incorporating the Bahdanau attention mechanism. To facilitate training, the authors constructed a proprietary dataset derived from MS COCO, which was translated and stylistically adapted via the GigaChat large language model. During ensemble construction, ruCLIPScore is utilized to select the most effective model configurations. Experimental results indicate that the ensemble significantly outperforms its individual constituent models according to ruCLIPScore and can produce captions with stylistic diversity across registers.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"112 3","pages":"624 - 632"},"PeriodicalIF":0.6,"publicationDate":"2026-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimization with Markovian Noise: Towards Optimal Rates in Strong Growth Case","authors":"S. Chebykin,&nbsp;B. Prokhorov,&nbsp;A. Beznosikov","doi":"10.1134/S1064562425700462","DOIUrl":"10.1134/S1064562425700462","url":null,"abstract":"<p>This paper investigates stochastic optimization problems under Markovian noise and the strong growth condition, motivated by overparameterized ML models. We present an improved analysis of the Accelerated Gradient Descent algorithm from [1] in the strongly convex case, showing that in low-noise regimes, the effect of Markovianity can be ignored. Furthermore, we derive the first lower bound that simultaneously depends on the Markov chain’s mixing time and the problem’s noise level, establishing the near-optimality of our results.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"112 2","pages":"392 - 399"},"PeriodicalIF":0.6,"publicationDate":"2026-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S1064562425700462.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Beyond Familiar Domains: A Study of the Generalization Ability of Machine-Generated Image Detectors","authors":"K. D. Varlamova,&nbsp;D. D. Dorin,&nbsp;A. V. Grabovoy","doi":"10.1134/S1064562425700516","DOIUrl":"10.1134/S1064562425700516","url":null,"abstract":"<p>Modern generative models produce images that are nearly indistinguishable from human-created ones, posing serious challenges for content verification. As machine-generated content is increasingly integrated into professional workflows, the task of reliably detecting it becomes critically important. Existing detectors of machine-generated images do not generalize well to new generative models and visual domains. This paper investigates the ability of current detectors of machine-generated images to recognize new generative models and images from various domains not represented in the training data. The objects of the study include popular architectures, such as a combination of a pretrained CLIP with an MLP classifier and a model based on a mixture of experts. Particular attention is paid to analyzing the current limitations and reliability of both closed and open solutions, especially in the context of emerging new generative methods and specific types of images. Experimental results demonstrate significant limitations of existing approaches: models exhibit low generalization ability not only to new generators, but also when working with images from new domains.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"112 2","pages":"343 - 353"},"PeriodicalIF":0.6,"publicationDate":"2026-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}