{"paper":{"title":"Reliably Learning the ReLU in Polynomial Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Adam Klivans, Justin Thaler, Surbhi Goel, Varun Kanade","submitted_at":"2016-11-30T16:42:23Z","abstract_excerpt":"We give the first dimension-efficient algorithms for learning Rectified Linear Units (ReLUs), which are functions of the form $\\mathbf{x} \\mapsto \\max(0, \\mathbf{w} \\cdot \\mathbf{x})$ with $\\mathbf{w} \\in \\mathbb{S}^{n-1}$. Our algorithm works in the challenging Reliable Agnostic learning model of Kalai, Kanade, and Mansour (2009) where the learner is given access to a distribution $\\cal{D}$ on labeled examples but the labeling may be arbitrary. We construct a hypothesis that simultaneously minimizes the false-positive rate and the loss on inputs given positive labels by $\\cal{D}$, for any con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.10258","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":""},"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"}