A New Tensor Network: Tubal Tensor Train and Its Applications
Abstract
We introduce the tubal tensor train (TTT) decomposition, a tensor-network model that combines the t-product algebra of the tensor singular value decomposition (T-SVD) with the low-order core structure of the tensor train (TT) format. For an order- tensor with a distinguished tube mode, the proposed representation consists of two third-order boundary cores and fourth-order interior cores linked through the t-product. As a result, for bounded tubal ranks, the storage scales linearly with the number of modes, in contrast to direct high-order extensions of T-SVD. We present two computational strategies: a sequential fixed-rank construction, called TTT-SVD, and a Fourier-slice alternating scheme based on the alternating two-cores update (ATCU). We also state a TT-SVD-type error bound for TTT-SVD and illustrate the practical performance of the proposed model on image compression, video compression, tensor completion, and hyperspectral imaging.
Cite
@article{arxiv.2603.10503,
title = {A New Tensor Network: Tubal Tensor Train and Its Applications},
author = {Salman Ahmadi-Asl and Valentin Leplat and Anh-Huy Phan and Andrzej Cichocki},
journal= {arXiv preprint arXiv:2603.10503},
year = {2026}
}