{"paper":{"title":"Deep Network Approximation Characterized by Number of Neurons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA"],"primary_cat":"math.NA","authors_text":"Haizhao Yang, Shijun Zhang, Zuowei Shen","submitted_at":"2019-06-13T06:15:15Z","abstract_excerpt":"This paper quantitatively characterizes the approximation power of deep feed-forward neural networks (FNNs) in terms of the number of neurons. It is shown by construction that ReLU FNNs with width $\\mathcal{O}\\big(\\max\\{d\\lfloor N^{1/d}\\rfloor,\\, N+1\\}\\big)$ and depth $\\mathcal{O}(L)$ can approximate an arbitrary H\\\"older continuous function of order $\\alpha\\in (0,1]$ on $[0,1]^d$ with a nearly tight approximation rate $\\mathcal{O}\\big(\\sqrt{d} N^{-2\\alpha/d}L^{-2\\alpha/d}\\big)$ measured in $L^p$-norm for any $N,L\\in \\mathbb{N}^+$ and $p\\in[1,\\infty]$. More generally for an arbitrary continuou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.05497","kind":"arxiv","version":5},"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/1906.05497/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"}