{
  "id": "2205.14421",
  "version": "v1",
  "published": "2022-05-28T13:09:43.000Z",
  "updated": "2022-05-28T13:09:43.000Z",
  "title": "Approximation of Functionals by Neural Network without Curse of Dimensionality",
  "authors": [
    "Yahong Yang",
    "Yang Xiang"
  ],
  "categories": [
    "math.NA",
    "cs.LG",
    "cs.NA",
    "math.OC"
  ],
  "abstract": "In this paper, we establish a neural network to approximate functionals, which are maps from infinite dimensional spaces to finite dimensional spaces. The approximation error of the neural network is $O(1/\\sqrt{m})$ where $m$ is the size of networks, which overcomes the curse of dimensionality. The key idea of the approximation is to define a Barron space of functionals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-28T13:09:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "neural network",
      "dimensionality",
      "infinite dimensional spaces",
      "approximate functionals",
      "approximation error"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}