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

Published: 01 Feb 2023, Last Modified: 27 Feb 2023ICLR 2023 posterReaders: Everyone
Keywords: Tensor approximation, Discrete multivariate functions, Tensor train decomposition, TT-Tucker format, Game theory, Combinatorial problems
TL;DR: A method to build tensor train representation for a wide class of tensors for which an analytical dependence on the indices is given.
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.
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