Ivan V. Oseledets

Ruituo Wu, Jiani Liu, Ce Zhu et al.

Efficient probability density estimation is a core challenge in statistical machine learning. Tensor-based probabilistic graph methods address interpretability and stability concerns encountered in neural network approaches. However, a substantial number of potential tensor permutations can lead to a tensor network with the same structure but varying expressive capabilities. In this paper, we take tensor ring decomposition for density estimator, which significantly reduces the number of permutation candidates while enhancing expressive capability compared with existing used decompositions. Additionally, a mixture model that incorporates multiple permutation candidates with adaptive weights is further designed, resulting in increased expressive flexibility and comprehensiveness. Different from the prevailing directions of tensor network structure/permutation search, our approach provides a new viewpoint inspired by ensemble learning. This approach acknowledges that suboptimal permutations can offer distinctive information besides that of optimal permutations. Experiments show the superiority of the proposed approach in estimating probability density for moderately dimensional datasets and sampling to capture intricate details.

Ivan A. Kazakov, Iana V. Kulichenko, Egor E. Kovalev et al.

We present an experimental study of a fiber Bragg grating (FBG) interrogator based on a silicon oxynitride (SiON) photonic integrated arrayed waveguide grating (AWG). While AWG-based interrogators are compact and scalable, their practical performance is limited by non-ideal spectral responses. To address this, two calibration strategies within a 2.4 nm spectral region were compared: (1) a segmented analytical model based on a sigmoid fitting function, and (2) a machine learning (ML)-based regression model. The analytical method achieves a root mean square error (RMSE) of 7.11 pm within the calibrated range, while the ML approach based on exponential regression achieves 3.17 pm. Moreover, the ML model demonstrates generalization across an extended 2.9 nm wavelength span, maintaining sub-5 pm accuracy without re-fitting. Residual and error distribution analyses further illustrate the trade-offs between the two approaches. ML-based calibration provides a robust, data-driven alternative to analytical methods, delivering enhanced accuracy for non-ideal channel responses, reduced manual calibration effort, and improved scalability across diverse FBG sensor configurations.

Georgii S. Novikov, Maxim E. Panov, Ivan V. Oseledets

Estimation of probability density function from samples is one of the central problems in statistics and machine learning. Modern neural network-based models can learn high dimensional distributions but have problems with hyperparameter selection and are often prone to instabilities during training and inference. We propose a new efficient tensor train-based model for density estimation (TTDE). Such density parametrization allows exact sampling, calculation of cumulative and marginal density functions, and partition function. It also has very intuitive hyperparameters. We develop an efficient non-adversarial training procedure for TTDE based on the Riemannian optimization. Experimental results demonstrate the competitive performance of the proposed method in density estimation and sampling tasks, while TTDE significantly outperforms competitors in training speed.

Anna Petrovskaia, Raghavendra B. Jana, Ivan V. Oseledets

Remote sensing images are used for a variety of analyses, from agricultural monitoring, to disaster relief, to resource planning, among others. The images can be corrupted due to a number of reasons, including instrument errors and natural obstacles such as clouds. We present here a novel approach for reconstruction of missing information in such cases using only the corrupted image as the input. The Deep Image Prior methodology eliminates the need for a pre-trained network or an image database. It is shown that the approach easily beats the performance of traditional single-image methods.

Artem L. Pavlov, Azat Davletshin, Alexey Kharlamov et al.

With the advancements of various autonomous car projects aiming to achieve SAE Level 5, real-time detection of traffic signs in real-life scenarios has become a highly relevant problem for the industry. Even though a great progress has been achieved in this field, there is still no clear consensus on what the state-of-the-art in this field is. Moreover, it is important to develop and test systems in various regions and conditions. This is why the "Ice Vision" competition has focused on the detection of Russian traffic signs in winter conditions. The IceVisionSet dataset used for this competition features real-world collection of lossless frame sequences with traffic sign annotations. The sequences were collected in varying conditions, including: different weather, camera exposure, illumination and moving speeds. In this work we describe the competition and present the solutions of the 3 top teams.

Daria Sushnikova, Ivan V. Oseledets

In this paper we consider linear systems with dense-matrices which arise from numerical solution of boundary integral equations. Such matrices can be well-approximated with $\mathcal{H}^2$-matrices. We propose several new preconditioners for such matrices that are based on the equivalent \emph{sparse extended form} of $\mathcal{H}^2$-matrices. In the numerical experiments we show that the most efficient approach is based on the so-called reverse-Schur preconditioning technique.

Zheng Zhang, Xiu Yang, Ivan V. Oseledets et al.

Hierarchical uncertainty quantification can reduce the computational cost of stochastic circuit simulation by employing spectral methods at different levels. This paper presents an efficient framework to simulate hierarchically some challenging stochastic circuits/systems that include high-dimensional subsystems. Due to the high parameter dimensionality, it is challenging to both extract surrogate models at the low level of the design hierarchy and to handle them in the high-level simulation. In this paper, we develop an efficient ANOVA-based stochastic circuit/MEMS simulator to extract efficiently the surrogate models at the low level. In order to avoid the curse of dimensionality, we employ tensor-train decomposition at the high level to construct the basis functions and Gauss quadrature points. As a demonstration, we verify our algorithm on a stochastic oscillator with four MEMS capacitors and 184 random parameters. This challenging example is simulated efficiently by our simulator at the cost of only 10 minutes in MATLAB on a regular personal computer.