{"paper":{"title":"Deep Network with Approximation Error Being Reciprocal of Width to Power of Square Root of Depth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","stat.ML"],"primary_cat":"cs.LG","authors_text":"Haizhao Yang, Shijun Zhang, Zuowei Shen","submitted_at":"2020-06-22T13:27:33Z","abstract_excerpt":"A new network with super approximation power is introduced. This network is built with Floor ($\\lfloor x\\rfloor$) or ReLU ($\\max\\{0,x\\}$) activation function in each neuron and hence we call such networks Floor-ReLU networks. For any hyper-parameters $N\\in\\mathbb{N}^+$ and $L\\in\\mathbb{N}^+$, it is shown that Floor-ReLU networks with width $\\max\\{d,\\, 5N+13\\}$ and depth $64dL+3$ can uniformly approximate a H\\\"older function $f$ on $[0,1]^d$ with an approximation error $3\\lambda d^{\\alpha/2}N^{-\\alpha\\sqrt{L}}$, where $\\alpha \\in(0,1]$ and $\\lambda$ are the H\\\"older order and constant, respecti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.12231","kind":"arxiv","version":6},"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/2006.12231/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"}