{"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/entrywise-tensor-train-approximation-of-large","title":"Entrywise tensor-train approximation of large tensors via random embeddings","arxiv_id":"2403.11768","date":"2024-03-18","proceeding":null,"authors":["Stanislav Budzinskiy"],"abstract":"The theory of low-rank tensor-train approximation is well understood when the approximation error is measured in the Frobenius norm. The entrywise maximum norm is equally important but is significantly weaker for large tensors, making the estimates obtained via the Frobenius norm and norm equivalence pessimistic or even meaningless. In this article, we derive a direct estimate of the entrywise approximation error that is applicable in some of these cases. The estimate is given in terms of the higher-order generalization of the matrix factorization norm, and its proof is based on the tensor-structured Hanson--Wright inequality. The theoretical results are accompanied by numerical experiments carried out with the method of alternating projections.","url_abs":"https://arxiv.org/abs/2403.11768v3","url_pdf":"https://arxiv.org/pdf/2403.11768v3.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":"entrywise-tensor-train-approximation-of-large","repo_url":"https://github.com/sbudzinskiy/lrap","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2403.11768","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}