{"paper":{"title":"Fast, Parallel, Query-Efficient Binary Classification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.LG"],"primary_cat":"math.OC","authors_text":"Aaron Sidford, Ishani Karmarkar, Liam O'Carroll","submitted_at":"2026-07-05T00:18:56Z","abstract_excerpt":"We study the fundamental classification problem of computing a separating hyperplane for a binary-labeled dataset of size $n$ with normalized $d$-dimensional features. Letting $\\Phi \\in \\mathbb{R}^{n \\times d}$ denote the feature matrix and $\\gamma$ the margin of the maximum-margin separating hyperplane, we present a randomized algorithm that solves this problem in $\\tilde{O}(\\gamma^{-2/3}\\, \\operatorname{nnz}(\\Phi) + \\gamma^{-2(\\omega+1)/3})$-sequential running time (work), $\\tilde{O}(\\gamma^{-2/3})$-parallel (computational) depth, and accesses $\\Phi$ only through $\\tilde{O}(\\gamma^{-2/3})$-m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04062","kind":"arxiv","version":1},"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/2607.04062/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"}