{"paper":{"title":"A Random Matrix Approach to Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.PR","authors_text":"Cosme Louart, Romain Couillet, Zhenyu Liao","submitted_at":"2017-02-17T16:16:01Z","abstract_excerpt":"This article studies the Gram random matrix model $G=\\frac1T\\Sigma^{\\rm T}\\Sigma$, $\\Sigma=\\sigma(WX)$, classically found in the analysis of random feature maps and random neural networks, where $X=[x_1,\\ldots,x_T]\\in{\\mathbb R}^{p\\times T}$ is a (data) matrix of bounded norm, $W\\in{\\mathbb R}^{n\\times p}$ is a matrix of independent zero-mean unit variance entries, and $\\sigma:{\\mathbb R}\\to{\\mathbb R}$ is a Lipschitz continuous (activation) function --- $\\sigma(WX)$ being understood entry-wise. By means of a key concentration of measure lemma arising from non-asymptotic random matrix argument"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05419","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"}