{
  "id": "1508.01084",
  "version": "v1",
  "published": "2015-08-05T14:18:17.000Z",
  "updated": "2015-08-05T14:18:17.000Z",
  "title": "Deep Convolutional Networks are Hierarchical Kernel Machines",
  "authors": [
    "Fabio Anselmi",
    "Lorenzo Rosasco",
    "Cheston Tan",
    "Tomaso Poggio"
  ],
  "categories": [
    "cs.LG",
    "cs.NE"
  ],
  "abstract": "In i-theory a typical layer of a hierarchical architecture consists of HW modules pooling the dot products of the inputs to the layer with the transformations of a few templates under a group. Such layers include as special cases the convolutional layers of Deep Convolutional Networks (DCNs) as well as the non-convolutional layers (when the group contains only the identity). Rectifying nonlinearities -- which are used by present-day DCNs -- are one of the several nonlinearities admitted by i-theory for the HW module. We discuss here the equivalence between group averages of linear combinations of rectifying nonlinearities and an associated kernel. This property implies that present-day DCNs can be exactly equivalent to a hierarchy of kernel machines with pooling and non-pooling layers. Finally, we describe a conjecture for theoretically understanding hierarchies of such modules. A main consequence of the conjecture is that hierarchies of trained HW modules minimize memory requirements while computing a selective and invariant representation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-05T14:18:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "deep convolutional networks",
      "hierarchical kernel machines",
      "hw modules minimize memory requirements",
      "present-day dcns"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150801084A"
    }
  }
}