{
  "id": "2103.16355",
  "version": "v1",
  "published": "2021-03-30T13:54:33.000Z",
  "updated": "2021-03-30T13:54:33.000Z",
  "title": "Nonlinear Weighted Directed Acyclic Graph and A Priori Estimates for Neural Networks",
  "authors": [
    "Yuqing Li",
    "Tao Luo",
    "Chao Ma"
  ],
  "categories": [
    "cs.LG",
    "stat.ML"
  ],
  "abstract": "In an attempt to better understand structural benefits and generalization power of deep neural networks, we firstly present a novel graph theoretical formulation of neural network models, including fully connected, residual network~(ResNet) and densely connected networks~(DenseNet). Secondly, we extend the error analysis of the population risk for two layer network~\\cite{ew2019prioriTwo} and ResNet~\\cite{e2019prioriRes} to DenseNet, and show further that for neural networks satisfying certain mild conditions, similar estimates can be obtained. These estimates are a priori in nature since they depend sorely on the information prior to the training process, in particular, the bounds for the estimation errors are independent of the input dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-30T13:54:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C62",
      "41A46",
      "41A63",
      "62J02"
    ],
    "keywords": [
      "nonlinear weighted directed acyclic graph",
      "priori estimates",
      "better understand structural benefits",
      "deep neural networks",
      "novel graph theoretical formulation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}