{
  "id": "cond-mat/9907390",
  "version": "v1",
  "published": "1999-07-26T13:05:44.000Z",
  "updated": "1999-07-26T13:05:44.000Z",
  "title": "Q-Ising neural network dynamics: a comparative review of various architectures",
  "authors": [
    "D. Bolle",
    "G. Jongen",
    "G. M. Shim"
  ],
  "comment": "To appear in the proceedings of the Int. Conf. on Math. Phys. and Stochastic Analysis (Lisbon, October, 1998), ed. S. Albevero et all (World Scientific)",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "This contribution reviews the parallel dynamics of Q-Ising neural networks for various architectures: extremely diluted asymmetric, layered feedforward, extremely diluted symmetric, and fully connected. Using a probabilistic signal-to-noise ratio analysis, taking into account all feedback correlations, which are strongly dependent upon these architectures the evolution of the distribution of the local field is found. This leads to a recursive scheme determining the complete time evolution of the order parameters of the network. Arbitrary Q and mainly zero temperature are considered. For the asymmetrically diluted and the layered feedforward network a closed-form solution is obtained while for the symmetrically diluted and fully connected architecture the feedback correlations prevent such a closed-form solution. For these symmetric networks equilibrium fixed-point equations can be derived under certain conditions on the noise in the system. They are the same as those obtained in a thermodynamic replica-symmetric mean-field theory approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-07-26T13:05:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "q-ising neural network dynamics",
      "comparative review",
      "architecture",
      "thermodynamic replica-symmetric mean-field theory approach",
      "symmetric networks equilibrium fixed-point equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999cond.mat..7390B"
    }
  }
}