{"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/faster-search-for-tensor-decomposition-over","title":"Faster search for tensor decomposition over finite fields","arxiv_id":"2502.12390","date":"2025-02-17","proceeding":null,"authors":["Jason Yang"],"abstract":"We present an $O^*(|\\mathbb{F}|^{\\min\\left\\{R,\\ \\sum_{d\\ge 2} n_d\\right\\} + (R-n_0)(\\sum_{d\\ne 0} n_d)})$-time algorithm for determining whether the rank of a concise tensor $T\\in\\mathbb{F}^{n_0\\times\\dots\\times n_{D-1}}$ is $\\le R$, assuming $n_0\\ge\\dots\\ge n_{D-1}$ and $R\\ge n_0$. For 3-dimensional tensors, we have a second algorithm running in $O^*(|\\mathbb{F}|^{n_0+n_2 + (R-n_0+1-r_*)(n_1+n_2)+r_*^2})$ time, where $r_*:=\\left\\lfloor\\frac{R}{n_0}\\right\\rfloor+1$. Both algorithms use polynomial space and improve on our previous work, which achieved running time $O^*(|\\mathbb{F}|^{n_0+(R-n_0)(\\sum_d n_d)})$.","url_abs":"https://arxiv.org/abs/2502.12390v1","url_pdf":"https://arxiv.org/pdf/2502.12390v1.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":"faster-search-for-tensor-decomposition-over","repo_url":"https://github.com/coolcomputery/tensor-cpd-search","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}