{
  "id": "2212.02223",
  "version": "v1",
  "published": "2022-11-30T05:36:23.000Z",
  "updated": "2022-11-30T05:36:23.000Z",
  "title": "Limitations on approximation by deep and shallow neural networks",
  "authors": [
    "Guergana Petrova",
    "Przemysław Wojtaszczyk"
  ],
  "categories": [
    "stat.ML",
    "cs.LG",
    "math.FA"
  ],
  "abstract": "We prove Carl's type inequalities for the error of approximation of compact sets K by deep and shallow neural networks. This in turn gives lower bounds on how well we can approximate the functions in K when requiring the approximants to come from outputs of such networks. Our results are obtained as a byproduct of the study of the recently introduced Lipschitz widths.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-30T05:36:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "shallow neural networks",
      "approximation",
      "limitations",
      "carls type inequalities",
      "compact sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}