{
  "id": "cond-mat/9608092",
  "version": "v2",
  "published": "1996-08-21T08:02:36.000Z",
  "updated": "1997-01-13T12:01:27.000Z",
  "title": "Multifractality and percolation in the coupling space of perceptrons",
  "authors": [
    "M. Weigt",
    "A. Engel"
  ],
  "comment": "13 pages, revtex, 4 eps figures, version accepted for publication in Phys. Rev. E",
  "journal": "Phys. Rev. E55, 4552 (1997)",
  "doi": "10.1103/PhysRevE.55.4552",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "The coupling space of perceptrons with continuous as well as with binary weights gets partitioned into a disordered multifractal by a set of $p=\\gamma N$ random input patterns. The multifractal spectrum $f(\\alpha)$ can be calculated analytically using the replica formalism. The storage capacity and the generalization behaviour of the perceptron are shown to be related to properties of $f(\\alpha)$ which are correctly described within the replica symmetric ansatz. Replica symmetry breaking is interpreted geometrically as a transition from percolating to non-percolating cells. The existence of empty cells gives rise to singularities in the multifractal spectrum. The analytical results for binary couplings are corroborated by numerical studies.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1997-01-13T12:01:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "coupling space",
      "perceptron",
      "multifractality",
      "percolation",
      "multifractal spectrum"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}