{
  "id": "2309.07367",
  "version": "v1",
  "published": "2023-09-14T01:00:05.000Z",
  "updated": "2023-09-14T01:00:05.000Z",
  "title": "The kernel-balanced equation for deep neural networks",
  "authors": [
    "Kenichi Nakazato"
  ],
  "categories": [
    "cond-mat.dis-nn",
    "cs.AI",
    "cs.LG"
  ],
  "abstract": "Deep neural networks have shown many fruitful applications in this decade. A network can get the generalized function through training with a finite dataset. The degree of generalization is a realization of the proximity scale in the data space. Specifically, the scale is not clear if the dataset is complicated. Here we consider a network for the distribution estimation of the dataset. We show the estimation is unstable and the instability depends on the data density and training duration. We derive the kernel-balanced equation, which gives a short phenomenological description of the solution. The equation tells us the reason for the instability and the mechanism of the scale. The network outputs a local average of the dataset as a prediction and the scale of averaging is determined along the equation. The scale gradually decreases along training and finally results in instability in our case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-14T01:00:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "deep neural networks",
      "kernel-balanced equation",
      "instability",
      "scale gradually decreases",
      "data space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}