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Conference Papers Year : 2023

SoTT: a greedy construction of a sum of Tensor Trains

Abstract

Tensor Train is probably the tensor format most widely used in a number of fields, ranging from physics to machine learning. In this work, we focus on the compression problem of a given multi-way datum. It is known that in Tensor Train the order of the variables to be treated has to be fixed a priori, and this might have a non-negligible influence on the compression performances. We propose a compression method in which a given datum is compressed as a sum of Tensor Trains. Each term of a sum is a Tensor Train in which we do not fix a priori neither the order of variables nor the ranks: these are determined based on error and parsimony criteria, taken into account through the introduction of a trade-off function. We prove that, for finite dimensional data, the trade-off function chosen makes it possible to certify the approximation (in terms of accuracy) and get a precise convergence rate. Several encouraging numerical results were proposed on moderate order tensors (up to 6th order).
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Dates and versions

hal-04392369 , version 1 (13-01-2024)

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  • HAL Id : hal-04392369 , version 1

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Damiano Lombardi, Virginie Ehrlacher, Maria Fuente-Ruiz. SoTT: a greedy construction of a sum of Tensor Trains. ICOSAHOM 2023 - International Conference on Spectral and High Order Methods, Yonsei University, Seoul, Aug 2023, Seoul, South Korea. ⟨hal-04392369⟩
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