{
  "id": "1805.06523",
  "version": "v1",
  "published": "2018-05-16T20:53:21.000Z",
  "updated": "2018-05-16T20:53:21.000Z",
  "title": "End-to-end Learning of a Convolutional Neural Network via Deep Tensor Decomposition",
  "authors": [
    "Samet Oymak",
    "Mahdi Soltanolkotabi"
  ],
  "comment": "29 pages, 12 figures",
  "categories": [
    "cs.LG",
    "math.OC",
    "stat.ML"
  ],
  "abstract": "In this paper we study the problem of learning the weights of a deep convolutional neural network. We consider a network where convolutions are carried out over non-overlapping patches with a single kernel in each layer. We develop an algorithm for simultaneously learning all the kernels from the training data. Our approach dubbed Deep Tensor Decomposition (DeepTD) is based on a rank-1 tensor decomposition. We theoretically investigate DeepTD under a realizable model for the training data where the inputs are chosen i.i.d. from a Gaussian distribution and the labels are generated according to planted convolutional kernels. We show that DeepTD is data-efficient and provably works as soon as the sample size exceeds the total number of convolutional weights in the network. We carry out a variety of numerical experiments to investigate the effectiveness of DeepTD and verify our theoretical findings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-16T20:53:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "end-to-end learning",
      "approach dubbed deep tensor decomposition",
      "deep convolutional neural network",
      "training data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}