{"paper":{"title":"Learning Two Layer Rectified Neural Networks in Polynomial Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Ainesh Bakshi, David P. Woodruff, Rajesh Jayaram","submitted_at":"2018-11-05T18:03:56Z","abstract_excerpt":"Consider the following fundamental learning problem: given input examples $x \\in \\mathbb{R}^d$ and their vector-valued labels, as defined by an underlying generative neural network, recover the weight matrices of this network. We consider two-layer networks, mapping $\\mathbb{R}^d$ to $\\mathbb{R}^m$, with $k$ non-linear activation units $f(\\cdot)$, where $f(x) = \\max \\{x , 0\\}$ is the ReLU. Such a network is specified by two weight matrices, $\\mathbf{U}^* \\in \\mathbb{R}^{m \\times k}, \\mathbf{V}^* \\in \\mathbb{R}^{k \\times d}$, such that the label of an example $x \\in \\mathbb{R}^{d}$ is given by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01885","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"}