{
  "id": "1209.5941",
  "version": "v2",
  "published": "2012-09-26T13:44:42.000Z",
  "updated": "2012-10-05T15:59:24.000Z",
  "title": "Stability of the replica symmetric solution in diluted perceptron learning",
  "authors": [
    "Alejandro Lage-Castellanos",
    "Andrea Pagnani",
    "Gretel Quintero Angulo"
  ],
  "comment": "Stability of the solution in arXiv:0907.3241, 13 pages, (some typos corrected)",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "We study the role played by the dilution in the average behavior of a perceptron model with continuous coupling with the replica method. We analyze the stability of the replica symmetric solution as a function of the dilution field for the generalization and memorization problems. Thanks to a Gardner like stability analysis we show that at any fixed ratio $\\alpha$ between the number of patterns M and the dimension N of the perceptron ($\\alpha=M/N$), there exists a critical dilution field $h_c$ above which the replica symmetric ansatz becomes unstable.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-05T15:59:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "replica symmetric solution",
      "diluted perceptron learning",
      "replica symmetric ansatz",
      "replica method",
      "perceptron model"
    ],
    "publication": {
      "doi": "10.1088/1742-5468/2013/02/L02002",
      "journal": "Journal of Statistical Mechanics: Theory and Experiment",
      "year": 2013,
      "month": "Feb",
      "volume": 2013,
      "number": 2
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013JSMTE..02..000L"
    }
  }
}