{
  "id": "2108.12615",
  "version": "v1",
  "published": "2021-08-28T10:08:38.000Z",
  "updated": "2021-08-28T10:08:38.000Z",
  "title": "Limiting free energy of multi-layer generalized linear models",
  "authors": [
    "Hong-Bin Chen",
    "Jiaming Xia"
  ],
  "comment": "43 pages",
  "categories": [
    "math.PR",
    "cond-mat.dis-nn",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "We compute the high-dimensional limit of the free energy associated with a multi-layer generalized linear model. Under certain technical assumptions, we identify the limit in terms of a variational formula. The approach is to first show that the limit is a solution to a Hamilton-Jacobi equation whose initial condition is related to the limiting free energy of a model with one fewer layer. Then, we conclude by an iteration.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-28T10:08:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B44",
      "82D30"
    ],
    "keywords": [
      "multi-layer generalized linear model",
      "limiting free energy",
      "high-dimensional limit",
      "variational formula",
      "hamilton-jacobi equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}