{
  "id": "cond-mat/9906201",
  "version": "v1",
  "published": "1999-06-14T16:16:19.000Z",
  "updated": "1999-06-14T16:16:19.000Z",
  "title": "Correlations between hidden units in multilayer neural networks and replica symmetry breaking",
  "authors": [
    "D. Malzahn",
    "A. Engel"
  ],
  "comment": "9 pages, 3 figures, RevTex, accepted for publication in Phys. Rev. E",
  "doi": "10.1103/PhysRevE.60.2097",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "We consider feed-forward neural networks with one hidden layer, tree architecture and a fixed hidden-to-output Boolean function. Focusing on the saturation limit of the storage problem the influence of replica symmetry breaking on the distribution of local fields at the hidden units is investigated. These field distributions determine the probability for finding a specific activation pattern of the hidden units as well as the corresponding correlation coefficients and therefore quantify the division of labor among the hidden units. We find that although modifying the storage capacity and the distribution of local fields markedly replica symmetry breaking has only a minor effect on the correlation coefficients. Detailed numerical results are provided for the PARITY, COMMITTEE and AND machines with K=3 hidden units and nonoverlapping receptive fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-06-14T16:16:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hidden units",
      "multilayer neural networks",
      "markedly replica symmetry breaking",
      "correlation coefficients",
      "local fields markedly replica symmetry"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}