{"paper":{"title":"Learning a Single Neuron with Adversarial Label Noise via Gradient Descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.LG","authors_text":"Christos Tzamos, Ilias Diakonikolas, Nikos Zarifis, Vasilis Kontonis","submitted_at":"2022-06-17T17:55:43Z","abstract_excerpt":"We study the fundamental problem of learning a single neuron, i.e., a function of the form $\\mathbf{x}\\mapsto\\sigma(\\mathbf{w}\\cdot\\mathbf{x})$ for monotone activations $\\sigma:\\mathbb{R}\\mapsto\\mathbb{R}$, with respect to the $L_2^2$-loss in the presence of adversarial label noise. Specifically, we are given labeled examples from a distribution $D$ on $(\\mathbf{x}, y)\\in\\mathbb{R}^d \\times \\mathbb{R}$ such that there exists $\\mathbf{w}^\\ast\\in\\mathbb{R}^d$ achieving $F(\\mathbf{w}^\\ast)=\\epsilon$, where $F(\\mathbf{w})=\\mathbf{E}_{(\\mathbf{x},y)\\sim D}[(\\sigma(\\mathbf{w}\\cdot \\mathbf{x})-y)^2]$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.08918","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/2206.08918/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"}