{
  "id": "2011.11307",
  "version": "v1",
  "published": "2020-11-23T10:08:53.000Z",
  "updated": "2020-11-23T10:08:53.000Z",
  "title": "Restricted Boltzmann Machine, recent advances and mean-field theory",
  "authors": [
    "Aurélien Decelle",
    "Cyril Furtlehner"
  ],
  "comment": "44 pages, 13 figures. Accepted for CPB",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech",
    "cs.LG"
  ],
  "abstract": "This review deals with Restricted Boltzmann Machine (RBM) under the light of statistical physics. The RBM is a classical family of Machine learning (ML) models which played a central role in the development of deep learning. Viewing it as a Spin Glass model and exhibiting various links with other models of statistical physics, we gather recent results dealing with mean-field theory in this context. First the functioning of the RBM can be analyzed via the phase diagrams obtained for various statistical ensembles of RBM leading in particular to identify a {\\it compositional phase} where a small number of features or modes are combined to form complex patterns. Then we discuss recent works either able to devise mean-field based learning algorithms; either able to reproduce generic aspects of the learning process from some {\\it ensemble dynamics equations} or/and from linear stability arguments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-23T10:08:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "restricted boltzmann machine",
      "mean-field theory",
      "statistical physics",
      "reproduce generic aspects",
      "form complex patterns"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}