{
  "id": "1211.3024",
  "version": "v1",
  "published": "2012-11-13T15:44:13.000Z",
  "updated": "2012-11-13T15:44:13.000Z",
  "title": "Generalization learning in a perceptron with binary synapses",
  "authors": [
    "Carlo Baldassi"
  ],
  "comment": "16 pages, 4 figures",
  "journal": "Journal of Statistical Physics 136 (2009) 902-916",
  "doi": "10.1007/s10955-009-9822-1",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "We consider the generalization problem for a perceptron with binary synapses, implementing the Stochastic Belief-Propagation-Inspired (SBPI) learning algorithm which we proposed earlier, and perform a mean-field calculation to obtain a differential equation which describes the behaviour of the device in the limit of a large number of synapses N. We show that the solving time of SBPI is of order N*sqrt(log(N)), while the similar, well-known clipped perceptron (CP) algorithm does not converge to a solution at all in the time frame we considered. The analysis gives some insight into the ongoing process and shows that, in this context, the SBPI algorithm is equivalent to a new, simpler algorithm, which only differs from the CP algorithm by the addition of a stochastic, unsupervised meta-plastic reinforcement process, whose rate of application must be less than sqrt(2/(\\pi * N)) for the learning to be achieved effectively. The analytical results are confirmed by simulations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-13T15:44:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "F.2.2",
      "I.2.6",
      "I.5.1"
    ],
    "keywords": [
      "binary synapses",
      "generalization learning",
      "unsupervised meta-plastic reinforcement process",
      "generalization problem",
      "stochastic"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Statistical Physics",
      "year": 2009,
      "month": "Sep",
      "volume": 136,
      "number": 5,
      "pages": 902
    },
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009JSP...136..902B"
    }
  }
}