{
  "id": "1509.07385",
  "version": "v1",
  "published": "2015-09-24T14:20:29.000Z",
  "updated": "2015-09-24T14:20:29.000Z",
  "title": "Provable approximation properties for deep neural networks",
  "authors": [
    "Uri Shaham",
    "Alexander Cloninger",
    "Ronald R. Coifman"
  ],
  "categories": [
    "stat.ML",
    "cs.LG",
    "cs.NE"
  ],
  "abstract": "We discuss approximation of functions using deep neural nets. Given a function $f$ on a $d$-dimensional manifold $\\Gamma \\subset \\mathbb{R}^m$, we construct a sparsely-connected depth-4 neural network and bound its error in approximating $f$. The size of the network depends on dimension and curvature of the manifold $\\Gamma$, the complexity of $f$, in terms of its wavelet description, and only weakly on the ambient dimension $m$. Essentially, our network computes wavelet functions, which are computed from Rectified Linear Units (ReLU)",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-24T14:20:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "deep neural networks",
      "provable approximation properties",
      "deep neural nets",
      "rectified linear units",
      "dimensional manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150907385S"
    }
  }
}