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Ускоренные безградиентные методы оптимизации с неевклидовым проксимальным оператором
Автоматика и телемеханика. 2019. № 8. С. 149–156.
Gasnikov A.
In press
Derkacheva A., Sakirkina M., Kraev G. et al., /. 2026.
Comprehensive data on natural hazards and their consequences are crucial for effective for risk assessment, adaptation planning, and emergency response. However, many countries face challenges with fragmented, inconsistent, and inaccessible data, particularly regarding local-scale events. To address this data gap in Russia, we developed an end-to-end processing pipeline that scrapes news from various online sources, ...
Added: April 28, 2026
Qin X., Deng Y., Shchur L. et al., / Series arXiv "math". 2026. No. 2603.02962.
We perform a Monte Carlo analysis of the Ising model on many three-dimensional lattices. By means of finite-size scaling we obtain the critical points and determine the scaling dimensions. As expected, the critical exponents agree with the three-dimensional Ising universality class for all models. The irrelevant field, as revealed by the correction-to-scaling amplitudes, appears to ...
Added: April 20, 2026
Pilé I., Deng Y., Shchur L., / Series arXiv "math". 2026. No. 2604.10254.
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Svendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for two models in different universality classes: the Ising model and the Potts model with three components. The overlap of two ...
Added: April 20, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 2026
Petrovanov I., Sergeev A., / Series Computer Science "arxiv.org". 2025. No. 2512.18332.
Transport coding reduces message delay in packet-switched networks by introducing controlled redundancy at the transport layer: original packets are encoded into coded packets, and the message is reconstructed after the first successful deliveries, effectively shifting latency from the maximum packet delay to the -th order statistic. We present a concise, reproducible discrete-event implementation of transport coding in OMNeT++, including ...
Added: December 24, 2025
Hessian-based lightweight neural network for brain vessel segmentation on a minimal training dataset
Меньшиков И. А., Бернадотт А. К., Elvimov N. S., / Series arXie "Statistical mechanics". 2025.
Accurate segmentation of blood vessels in brain magnetic resonance angiography (MRA) is essential for successful surgical procedures, such as aneurysm repair or bypass surgery. Currently, annotation is primarily performed through manual segmentation or classical methods, such as the Frangi filter, which often lack sufficient accuracy. Neural networks have emerged as powerful tools for medical image ...
Added: December 1, 2025
Чернышов Д. П., Satanin A., Shchur L., / Series arXiv "math". 2025.
We investigate the boundary separating regular and chaotic dynamics in the generalized Chirikov map, an extension of the standard map with phase-shifted secondary kicks. Lyapunov maps were computed across the parameter space (K,K(α, τ)) and used to train a convolutional neural network (ResNet18) for binary classification of dynamical regimes. The model reproduces the known critical ...
Added: November 21, 2025
Rubchinskiy A., Chubarova D., / Series WP7 "Математические методы анализа решений в экономике, бизнесе и политике". 2025. No. WP7/2025/01.
The article examines one of the most famous examples of socio-economic systems, characterized by significant uncertainty – the S&P-500 stock market, where shares of 500 largest US companies are traded. No assumptions are made about the probabilistic characteristics of the stock market. A flexible algorithm for daily trading has been developed, based on both known fixed data ...
Added: November 9, 2025
Meshchaninov V., Strashnov, P., Shevtsov A. et al., / Cornell University. Серия CoRR, arXiv:2403.03726 "Computing Research Repository,". 2025.
Protein design requires a deep understanding of the inherent complexities of the protein universe. While many efforts lean towards conditional generation or focus on specific families of proteins, the foundational task of unconditional generation remains underexplored and undervalued. Here, we explore this pivotal domain, introducing DiMA, a model that leverages continuous diffusion on embeddings derived ...
Added: October 5, 2025
Shabalin A., Meshchaninov V., Vetrov D., / Series cs.CL, arXiv:2505.18853 "Computation and Language". 2025.
Diffusion models have achieved state-of-the-art performance in generating images, audio, and video, but their adaptation to text remains challenging due to its discrete nature. Prior approaches either apply Gaussian diffusion in continuous latent spaces, which inherits semantic structure but struggles with token decoding, or operate in categorical simplex space, which respect discreteness but disregard semantic ...
Added: October 5, 2025
Абрамов А. С., Chernyshev V. L., Mikhaylets E. et al., / Series Social Science Research Network "Social Science Research Network". 2025.
Computer vision is one of the most relevant modern research areas with broad practical applications. However, traditional solutions based on deep learning have signicant limitations and can be misleading. Topological data analysis, on the other hand, is a modern approach to solving similar problems using mathematically deterministic methods of algebraic topology that reduce the risk ...
Added: September 23, 2025
Kochetkov Y., / Series arXiv.org e-print archive "arXiv.math". 2025. No. 07600.
We demonstrate in an elementary way how to construct a frieze pattern of width m-3 from a partition of a convex m-gon
by not intersecting diagonals. ...
Added: September 17, 2025
Kochetkov Y., / Series arXiv.org e-print archive "arXiv.math". 2025. No. 20584.
We give a new proof of the following statement: the Catalan number C_n is divisible
by n+2, if n is odd and n<> 3k+1. ...
Added: September 9, 2025
Ivanashev Y., / Series Computer Science "arxiv.org". 2025.
Added: July 29, 2025
Gladin E., Sadiev A., Gasnikov A. et al., , in: Mathematical Optimization Theory and Operations Research: 20th International Conference, MOTOR 2021, Irkutsk, Russia, July 5–10, 2021, Proceedings.: Cham: Springer, 2021. P. 19–40.
In this paper, we consider two types of problems that have some similarity in their structure, namely, min-min problems and min-max saddle-point problems. Our approach is based on considering the outer minimization problem as a minimization problem with an inexact oracle. This inexact oracle is calculated via an inexact solution of the inner problem, which ...
Added: November 29, 2024
Gladin E., Alkousa M., Gasnikov A., Automation and Remote Control 2021 Vol. 82 P. 1679–1691
The article deals with some approaches to solving convex problems of the min-min type with smoothness and strong convexity in only one of the two groups of variables. It is shown that the proposed approaches based on Vaidya’s method, the fast gradient method, and the accelerated gradient method with variance reduction have linear convergence. It ...
Added: November 29, 2024
Gladin E., Gasnikov A., Ermakova E., Mathematical notes 2022 Vol. 112 No. 1 P. 183–190
The paper deals with a general problem of convex stochastic optimization in a space of small dimension (for example, 100 variables). It is known that for deterministic problems of convex optimization in small dimensions, the methods of centers of gravity type (for example, Vaidya’s method) provide the best convergence. For stochastic optimization problems, the question ...
Added: November 29, 2024
Gladin E., Gasnikov A., Dvurechensky P., Journal of Optimization Theory and Applications 2025 Vol. 204 No. 1 Article 1
Accuracy certificates for convex minimization problems allow for online verification of the accuracy of approximate solutions and provide a theoretically valid online stopping criterion. When solving the Lagrange dual problem, accuracy certificates produce a simple way to recover an approximate primal solution and estimate its accuracy. In this paper, we generalize accuracy certificates for the ...
Added: November 29, 2024
Gladin E., Зайнуллина К. Э., Компьютерные исследования и моделирование 2021 Т. 13 № 6 С. 1137–1147
The article considers minimization of the expectation of convex function. Problems of this type often arise in machine learning and a variety of other applications. In practice, stochastic gradient descent (SGD) and similar procedures are usually used to solve such problems. We propose to use the ellipsoid method with mini-batching, which converges linearly and can ...
Added: November 29, 2024
Rudenko V., Yudin N., Васин А. А., Компьютерные исследования и моделирование 2023 Т. 15 № 2 С. 329–353
This article reviews both historical achievements and modern results in the field of Markov Decision Process (MDP) and convex optimization. This review is the first attempt to cover the field of reinforcement learning in Russian in the context of convex optimization. The fundamental Bellman equation and the criteria of optimality of policy — strategies based on it, ...
Added: November 29, 2024
Yudin N., Компьютерные исследования и моделирование 2021 Т. 13 № 4 С. 697–723
In this paper, we introduce a new version of Gauss-Newton method for solving a system of nonlinear equations based on ideas of the residual upper bound for a system of nonlinear equations and a quadratic regularization term. The introduced Gauss-Newton method in practice virtually forms the whole parameterized family of the methods solving systems of ...
Added: November 28, 2024
Puchkin N., Gorbunov E., Kutuzov N. et al., , in: Proceedings of The 27th International Conference on Artificial Intelligence and Statistics (AISTATS 2024), 2-4 May 2024, Palau de Congressos, Valencia, Spain. PMLR: Volume 238Vol. 238.: Valencia: PMLR, 2024. P. 856–864.
We consider stochastic optimization problems with heavy-tailed noise with structured density. For such problems, we show that it is possible to get faster rates of convergence than 𝑂(𝐾^{−2(𝛼−1)/𝛼}), when the stochastic gradients have finite 𝛼-th moment, 𝛼∈(1,2]. In particular, our analysis allows the noise norm to have an unbounded expectation. To achieve these results, we stabilize stochastic gradients, ...
Added: April 22, 2024
Beznosikov A., Richtarik P., Diskin M. et al., , in: Thirty-Sixth Conference on Neural Information Processing Systems : NeurIPS 2022.: Curran Associates, Inc., 2022. P. 14013–14029.
Added: January 27, 2023