{
  "id": "1901.10267",
  "version": "v1",
  "published": "2019-01-29T13:19:47.000Z",
  "updated": "2019-01-29T13:19:47.000Z",
  "title": "Approximation of functions by neural networks",
  "authors": [
    "Andreas Thom"
  ],
  "comment": "4 pages, no figures",
  "categories": [
    "cs.LG",
    "stat.ML"
  ],
  "abstract": "We study the approximation of measurable functions on the hypercube by functions arising from affine neural networks. Our main achievement is an approximation of any measurable function $f \\colon W_n \\to [-1,1]$ up to a prescribed precision $\\varepsilon>0$ by a bounded number of neurons, depending only on $\\varepsilon$ and not on the function $f$ or $n \\in \\mathbb N$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-29T13:19:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "approximation",
      "affine neural networks",
      "measurable function",
      "main achievement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}