Constructive TT-representation of the tensors given as index interaction functions with applications

Gleb Ryzhakov; Ivan Oseledets

ICLR 2023poster4 citations

Constructive TT-representation of the tensors given as index interaction functions with applications

Abstract

This paper presents a method to build explicit tensor-train (TT) representations. We show that a wide class of tensors can be explicitly represented with sparse TT-cores, obtaining, in many cases, optimal TT-ranks. Numerical experiments show that our method outperforms the existing ones in several practical applications, including game theory problems. Theoretical estimations of the number of operations show that in some problems, such as permanent calculation, our methods are close to the known optimal asymptotics, which are obtained by a completely different type of methods.

Tensor approximationDiscrete multivariate functionsTensor train decompositionTT-Tucker formatGame theoryCombinatorial problems

BibTeX

@inproceedings{
ryzhakov2023constructive,
title={Constructive {TT}-representation of the tensors given as index interaction functions with applications},
author={Gleb Ryzhakov and Ivan Oseledets},
booktitle={The Eleventh International Conference on Learning Representations },
year={2023},
url={https://openreview.net/forum?id=yLzLfM-Esnu}
}