{
  "id": "2303.05262",
  "version": "v2",
  "published": "2023-03-09T13:56:04.000Z",
  "updated": "2023-04-17T09:24:33.000Z",
  "title": "Fredholm integral equations for function approximation and the training of neural networks",
  "authors": [
    "Patrick Gelß",
    "Aizhan Issagali",
    "Ralf Kornhuber"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We present a novel and mathematically transparent approach to function approximation and the training of large, high-dimensional neural networks, based on the approximate least-squares solution of associated Fredholm integral equations of the first kind by Ritz-Galerkin discretization, Tikhonov regularization and tensor-train methods. Practical application to supervised learning problems of regression and classification type confirm that the resulting algorithms are competitive with state-of-the-art neural network-based methods.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-04-17T09:24:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "function approximation",
      "associated fredholm integral equations",
      "state-of-the-art neural network-based methods",
      "classification type confirm",
      "approximate least-squares solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}