?
Towards Practical Control of Singular Values of Convolutional Layers
P. 10918–10930.
In book
Curran Associates, Inc., 2022.
Alexander Molozhavenko, Rakhuba M., Computational and Applied Mathematics 2026 Vol. 45 No. 6 Article 221
This paper studies tensors that admit decomposition in the Extended Tensor Train (ETT) format, with a key focus on the case where some decomposition factors are constrained to be equal. This factor sharing introduces additional challenges, as it breaks the multilinear structure of the decomposition. Nevertheless, we show that Riemannian optimization methods can naturally handle ...
Added: December 22, 2025
Derkacheva A., Frost G., Epstein H. et al., Journal of Ecology 2025 Vol. 113 No. 10 P. 2813–2831
Tundra shrub expansion is a central form of change in warming Arctic ecosystems, but the pace of shrubification varies across spatial scales, complicating efforts to understand its drivers and consequences. Here, we apply convolutional neural networks (CNNs) to very-high resolution satellite image pairs acquired 10–15 years apart (circa 2005–2019) to identify spatio-temporal patterns of tall shrub ...
Added: August 4, 2025
Yusupov V., Rakhuba M., Frolov E., , in: Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, 3-5 May 2025, Splash Beach Resort in Mai Khao, Thailand, PMLR: vol. 258Vol. 258.: PMLR, 2025. P. 4924–4932.
Added: May 25, 2025
Frolov E., Oseledets I., Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery 2017 Vol. 7 No. 3
Added: November 16, 2023
Frolov E., Oseledets I., IEEE Access 2023 Vol. 11 P. 6357–6371
Self-attentive transformer models have recently been shown to solve the next item recommendation task very efficiently. The learned attention weights capture sequential dynamics in user behavior and generalize well. Motivated by the special structure of learned parameter space, we question if it is possible to mimic it with an alternative and more lightweight approach. We ...
Added: November 16, 2023
Chertenkov V., Burovskiy E., Shchur L., / Series "stat-mech". 2023. No. 2305:0334.
We analyze the problem of supervised learning of ferromagnetic phase transitions from the statistical physics perspective. We consider two systems in two universality classes, the two-dimensional Ising model and two-dimensional Baxter-Wu model, and perform careful finite-size analysis of the results of the supervised learning of the phases of each model. We find that the variance ...
Added: May 8, 2023
Churaev E., Andrey V. Savchenko, , in: 2022 VIII International Conference on Information Technology and Nanotechnology (ITNT).: IEEE, 2022. P. 1–5.
In this paper, the multi-user video-based facial emotion recognition is examined in the presence of a small data set with the emotions of end users. By using the idea of speaker-dependent speech recognition, we propose a novel approach to solve this task if labeled video data from end users is available. During the training stage, ...
Added: September 25, 2022
Marcati C., Rakhuba M., Christoph S., / Series math "arxiv.org". 2020.
We analyze rates of approximation by quantized, tensor-structured representations of functions with isolated point singularities in ℝ3. We consider functions in countably normed Sobolev spaces with radial weights and analytic- or Gevrey-type control of weighted semi-norms. Several classes of boundary value and eigenvalue problems from science and engineering are discussed whose solutions belong to the countably ...
Added: October 20, 2020
Kazeev V., Oseledets I., Rakhuba M. et al., / Series math "arxiv.org". 2020.
Homogenization in terms of multiscale limits transforms a multiscale problem with n+1 asymptotically separated microscales posed on a physical domain D⊂ℝd into a one-scale problem posed on a product domain of dimension (n+1)d by introducing n so-called "fast variables". This procedure allows to convert n+1 scales in d physical dimensions into a single-scale structure in (n+1)d dimensions. We prove here that both the original, physical multiscale problem and the ...
Added: October 20, 2020
Marcati C., Rakhuba M., Ulander J., / Series math "arxiv.org". 2020. No. 2010.06919.
We derive rank bounds on the quantized tensor train (QTT) compressed approximation of singularly perturbed reaction diffusion partial differential equations (PDEs) in one dimension. Specifically, we show that, independently of the scale of the singular perturbation parameter, a numerical solution with accuracy 0<ϵ<1 can be represented in QTT format with a number of parameters that depends only ...
Added: October 20, 2020
Obukhov A., Rakhuba M., Kanakis M. et al., , in: International Conference on Machine Learning (ICML 2020)Vol. 119.: PMLR, 2020. P. 7392–7404.
Added: October 20, 2020