{
  "id": "1912.02302",
  "version": "v1",
  "published": "2019-12-04T23:19:58.000Z",
  "updated": "2019-12-04T23:19:58.000Z",
  "title": "Analysis of Deep Neural Networks with Quasi-optimal polynomial approximation rates",
  "authors": [
    "Joseph Daws",
    "Clayton Webster"
  ],
  "comment": "13 pages submitted to MSML 2020",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We show the existence of a deep neural network capable of approximating a wide class of high-dimensional approximations. The construction of the proposed neural network is based on a quasi-optimal polynomial approximation. We show that this network achieves an error rate that is sub-exponential in the number of polynomial functions, $M$, used in the polynomial approximation. The complexity of the network which achieves this sub-exponential rate is shown to be algebraic in $M$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-04T23:19:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65D15"
    ],
    "keywords": [
      "quasi-optimal polynomial approximation rates",
      "wide class",
      "high-dimensional approximations",
      "network achieves",
      "deep neural network capable"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}