Learning in ultrametric committee machines

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Abstract

The problem of learning by examples in ultrametric committee machines (UCMs) is studied within the framework of statistical mechanics. Using the replica formalism we calculate the average generalization error in UCMs with L hidden layers and for a large enough number of units. In most of the regimes studied we find that the generalization error, as a function of the number of examples presented, develops a discontinuous drop at a critical value of the load parameter. We also find that when L>1 a number of teacher networks with the same number of hidden layers and different overlaps induce learning processes with the same critical points.

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Original languageEnglish
Pages (from-to)887-897
Number of pages11
JournalJournal of Statistical Physics
Volume149
Issue5
Early online date21 Nov 2012
DOIs
StatePublished - Nov 2012

Bibliographic note

The original publication is available at www.springerlink.com

    Keywords

  • multilayered networks, learning by examples

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