Fetching the paper…

Reading the bibliography…

2022

Optimization of Functions Given in the Tensor Train Format

Chertkov, Andrei, Ryzhakov, Gleb, Novikov, Georgii et al.

Original
PDF
Post on X

Understand

Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine learning.

In this work, we propose a new algorithm for TT-tensor optimization, which leads to very accurate approximations for the minimum and maximum tensor element.
The method consists in sequential tensor multiplications of the TT-cores with an intelligent selection of candidates for the optimum.
We propose the probabilistic interpretation of the method, and make estimates on its complexity and convergence.

Optimization of Functions Given in the Tensor Train Format · Around

Built on

I. Oseledets, and E. Tyrtyshnikov, TT-cross approximation for multidimensional arrays, Linear Algebra and its Applications, pp. 70–88, 2010
2010
Earlier work this paper cites.
I. Oseledets, Tensor-train decomposition, SIAM Journal on Scientific Computing, vol. 33, 2011
2011
Earlier work this paper cites.
M. Jamil and X.-S. Yang, A literature survey of benchmark functions for global optimization problems, Journal of Mathematical Modelling and Numerical Optimisation, v. 4, pp. 150–194, 2013
2013
Earlier work this paper cites.
A. Cichocki, N. Lee, I. Oseledets, A.-H. Phan, Q. Zhao, and D. Mandic, Tensor networks for dimensionality reduction and large-scale optimization: Part 1 low-rank tensor decompositions, Foundations and Trends in Machine Learning, v. 9, pp. 249–429, 2016
2016
Earlier work this paper cites.

Similar

S. Dolgov, and R. Scheichl, A hybrid alternating least squares–TT-cross algorithm for parametric PDEs, SIAM/ASA Journal on Uncertainty Quantification, v. 7(1), pp. 260-291, 2019
2019
Cited alongside, same era.
M. B. Soley, P. Bergold, and V. S. Batista, Iterative power algorithm for global optimization with quantics tensor trains, Journal of Chemical Theory and Computation, v. 17, pp. 3280–3291, 2021
2021
Cited alongside, same era.
A. Chertkov, G. Ryzhakov, and I. Oseledets, Black box approximation in the tensor train format initialized by ANOVA decomposition, arXiv preprint, arXiv:2208.03380, 2022
Original
2022
Cited alongside, same era.
K. Sozykin, A. Chertkov, R. Schutski, A.-H. Phan, A. Cichocki, and I. Oseledets, TTOpt: A maximum volume quantized tensor train-based optimization and its application to reinforcement learning, arXiv preprint, arXiv:2205.00293, 2022
Original
2022
Cited alongside, same era.

Then

A. Nikitin, A. Chertkov, R. Ballester-Ripoll, I. Oseledets, and E. Frolov, Are quantum computers practical yet? a case for feature selection in recommender systems using tensor networks, arXiv preprint, arXiv:2205.04490, 2022
Original
2022
Closest in time.
C. Selvanayagam, P. L. T. Duong, B. Wilkerson, and N. Raghavan, Global optimization of surface warpage for inverse design of ultra-thin electronic packages using tensor train decomposition, IEEE Access, v. 10, pp. 48589–48602, 2022
2022
Closest in time.
S. Shetty, T. Lembono, T. Loew, and S. Calinon, Tensor train for global optimization problems in robotics, arXiv preprint, arXiv:2206.05077, 2022
Original
2022
Closest in time.
B. Zhu, Z.Gu, Y. Qian, F. Lau, and Z. Tian, Leveraging Transferability and Improved Beam Search in Textual Adversarial Attacks, Neurocomputing, 2022
2022
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…