{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/parallel-algorithms-for-computing-the-tensor","title":"Parallel algorithms for computing the tensor-train decomposition","arxiv_id":"2111.10448","date":"2021-11-19","proceeding":null,"authors":["Tianyi Shi","Maximilian Ruth","Alex Townsend"],"abstract":"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 $\\mathbb{R}^{n\\times\\dots\\times n}$, a two-sided sketching algorithm PSTT2 is shown to have a memory complexity of $\\mathcal{O}(n^{\\lfloor d/2 \\rfloor})$, improving upon $\\mathcal{O}(n^{d-1})$ from previous algorithms.","url_abs":"https://arxiv.org/abs/2111.10448v1","url_pdf":"https://arxiv.org/pdf/2111.10448v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"parallel-algorithms-for-computing-the-tensor","repo_url":"https://github.com/sidshi/parallel_tt_sketching","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}