{
  "id": "2304.10552",
  "version": "v1",
  "published": "2023-04-20T08:45:16.000Z",
  "updated": "2023-04-20T08:45:16.000Z",
  "title": "Interpolation property of shallow neural networks",
  "authors": [
    "Vlad-Raul Constantinescu",
    "Ionel Popescu"
  ],
  "categories": [
    "cs.LG",
    "math.OC",
    "math.PR",
    "stat.ML"
  ],
  "abstract": "We study the geometry of global minima of the loss landscape of overparametrized neural networks. In most optimization problems, the loss function is convex, in which case we only have a global minima, or nonconvex, with a discrete number of global minima. In this paper, we prove that in the overparametrized regime, a shallow neural network can interpolate any data set, i.e. the loss function has a global minimum value equal to zero as long as the activation function is not a polynomial of small degree. Additionally, if such a global minimum exists, then the locus of global minima has infinitely many points. Furthermore, we give a characterization of the Hessian of the loss function evaluated at the global minima, and in the last section, we provide a practical probabilistic method of finding the interpolation point.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-20T08:45:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "shallow neural network",
      "interpolation property",
      "loss function",
      "global minimum value equal",
      "interpolation point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}