PARALLEL ALGORITHMS FOR COMPUTING THE TENSOR-TRAIN DECOMPOSITION

doi:10.1137/21M146079X

PARALLEL ALGORITHMS FOR COMPUTING THE TENSOR-TRAIN DECOMPOSITION

2023-06-07

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DOI：10.1137/21M146079X

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The tensor-train (TT) decomposition expresses a tensor in a data-sparse format used in molecular simulations, high-order correlation functions, and optimization. In this paper, we propose four parallelizable algorithms that compute the TT format from various tensor inputs: (1) Parallel-TTSVD for traditional format, (2) PSTT and its variants for streaming data, (3) Tucker2TT for Tucker format, and (4) TT-fADI for solutions of Sylvester tensor equations. We provide theoretical guarantees of accuracy, parallelization methods, scaling analysis, and numerical results. For example, for a d-dimension tensor in R-nx center dot center dot center dot xn, a two-sided sketching algorithm PSTT2 is shown to have a memory complexity of O(n((sic)d/2(sic))), improving upon O(n(d-1)) from previous algorithms.

Keywords:

tensor-train

parallel computing

low numerical rank

dimension reduction

Sylvester tensor equations

PARALLEL ALGORITHMS FOR COMPUTING THE TENSOR-TRAIN DECOMPOSITION

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