815 citations · 3.2k across the 142 of their papers we have counts for
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Tensor Train Decomposition for Adversarial Attacks on Computer Vision Models
Andrei Chertkov, Ivan Oseledets
Deep neural networks (DNNs) are widely used today, but they are vulnerable to adversarial attacks. To develop effective methods of defense, it is important to understand the potent…
On the structure of the Schur complement matrix for the Stokes equation
Vladislav Pimanov, Ekaterina Muravleva, Ivan Oseledets +1
In this paper, we investigate the structure of the Schur complement matrix for the fully-staggered finite-difference discretization of the stationary Stokes equation. Specifically,…
On the efficient preconditioning of the Stokes equations in tight geometries
Vladislav Pimanov, Oleg Iliev, Ivan Oseledets +1
If the Stokes equations are properly discretized, it is known that the Schur complement matrix is spectrally equivalent to the identity matrix. Moreover, in the case of simple geom…
Adaptive Cross Tubal Tensor Approximation
Salman Ahmadi-Asl, Anh Huy Phan, Andrzej Cichocki +4
In this paper, we propose a new adaptive cross algorithm for computing a low tubal rank approximation of third-order tensors, with less memory and lower computational complexity th…
General Covariance Data Augmentation for Neural PDE Solvers
Vladimir Fanaskov, Tianchi Yu, Alexander Rudikov +1
The growing body of research shows how to replace classical partial differential equation (PDE) integrators with neural networks. The popular strategy is to generate the input-outp…
PROTES: Probabilistic Optimization with Tensor Sampling
Anastasia Batsheva, Andrei Chertkov, Gleb Ryzhakov +1
We developed a new method PROTES for black-box optimization, which is based on the probabilistic sampling from a probability density function given in the low-parametric tensor tra…