A New Tensor Network: Tubal Tensor Train and Its Applications
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914386165104640 |
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| author | Ahmadi-Asl, Salman Leplat, Valentin Phan, Anh-Huy Cichocki, Andrzej |
| author_facet | Ahmadi-Asl, Salman Leplat, Valentin Phan, Anh-Huy Cichocki, Andrzej |
| contents | 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-$(N+1)$ tensor with a distinguished tube mode, the proposed representation consists of two third-order boundary cores and $N-2$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10503 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A New Tensor Network: Tubal Tensor Train and Its Applications Ahmadi-Asl, Salman Leplat, Valentin Phan, Anh-Huy Cichocki, Andrzej Numerical Analysis Machine Learning 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-$(N+1)$ tensor with a distinguished tube mode, the proposed representation consists of two third-order boundary cores and $N-2$ 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. |
| title | A New Tensor Network: Tubal Tensor Train and Its Applications |
| topic | Numerical Analysis Machine Learning |
| url | https://arxiv.org/abs/2603.10503 |