{"paper":{"title":"Fitting ReLUs via SGD and Quantized SGD","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC","cs.IT","math.IT","stat.ML"],"primary_cat":"cs.LG","authors_text":"A. Salman Avestimehr, Mahdi Soltanolkotabi, Seyed Mohammadreza Mousavi Kalan","submitted_at":"2019-01-19T21:21:54Z","abstract_excerpt":"In this paper we focus on the problem of finding the optimal weights of the shallowest of neural networks consisting of a single Rectified Linear Unit (ReLU). These functions are of the form $\\mathbf{x}\\rightarrow \\max(0,\\langle\\mathbf{w},\\mathbf{x}\\rangle)$ with $\\mathbf{w}\\in\\mathbb{R}^d$ denoting the weight vector. We focus on a planted model where the inputs are chosen i.i.d. from a Gaussian distribution and the labels are generated according to a planted weight vector. We first show that mini-batch stochastic gradient descent when suitably initialized, converges at a geometric rate to the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.06587","kind":"arxiv","version":2},"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"}