Noise, regularizers, and unrealizable scenarios in online learning from restricted training sets

Yuan-Sheng Xiong, David Saad

Research output: Contribution to journalArticle

Abstract

We study the dynamics of on-line learning in multilayer neural networks where training examples are sampled with repetition and where the number of examples scales with the number of network weights. The analysis is carried out using the dynamical replica method aimed at obtaining a closed set of coupled equations for a set of macroscopic variables from which both training and generalization errors can be calculated. We focus on scenarios whereby training examples are corrupted by additive Gaussian output noise and regularizers are introduced to improve the network performance. The dependence of the dynamics on the noise level, with and without regularizers, is examined, as well as that of the asymptotic values obtained for both training and generalization errors. We also demonstrate the ability of the method to approximate the learning dynamics in structurally unrealizable scenarios. The theoretical results show good agreement with those obtained by computer simulations.
Original languageEnglish
Article number011919
Pages (from-to)1-18
Number of pages18
JournalPhysical Review E
Volume64
Issue number1
DOIs
Publication statusPublished - 27 Jun 2001

Bibliographical note

Copyright of the American Physical Society

Keywords

  • on-line learning
  • multilayer neural networks
  • dynamical replica method
  • network performance
  • noise level

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