{"paper":{"title":"Deterministic Coreset for Lp Subspace","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Anirban Dasgupta, Dan Feldman, Rachit Chhaya, Supratim Shit","submitted_at":"2026-01-01T14:31:16Z","abstract_excerpt":"We introduce the first iterative algorithm for constructing a $\\varepsilon$-coreset that guarantees deterministic $\\ell_p$ subspace embedding for any $p \\in [1,\\infty)$ and any $\\varepsilon > 0$. For a given full rank matrix $\\mathbf{X} \\in \\mathbb{R}^{n \\times d}$ where $n \\gg d$, $\\mathbf{X}' \\in \\mathbb{R}^{m \\times d}$ is an $(\\varepsilon,\\ell_p)$-subspace embedding of $\\mathbf{X}$, if for every $\\mathbf{q} \\in \\mathbb{R}^d$, $(1-\\varepsilon)\\|\\mathbf{Xq}\\|_{p}^{p} \\leq \\|\\mathbf{X'q}\\|_{p}^{p} \\leq (1+\\varepsilon)\\|\\mathbf{Xq}\\|_{p}^{p}$. Specifically, in this paper, $\\mathbf{X}'$ is a we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.00361","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.00361/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}