Learning dynamics of neural networks with singularity - Standard gradient vs. natural gradient

Hyeyoung Park*, Masato Inoue, Masato Okada

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

3 Citations (Scopus)


In hierarchical models, such as neural networks, there exist complex singular structures. The singularity is known to affect estimation performances and learning dynamics of the models. Recently, there have been a number of studies on properties of obtained estimators for the models, but there are few studies on the dynamical properties of learning used for obtaining the estimators. Using two-layer neural networks, we investigate influences of singularities on dynamics of standard gradient learning and natural gradient learning under various learning conditions. In the standard gradient learning, we found a quasi-plateau phenomenon, which is severer than the well known plateau in some cases. The slow convergence due to the quasi-plateau and plateau becomes extremely serious when an optimal point is in a neighborhood of a singularity. In the natural gradient learning, however, the quasi-plateau and plateau are not observed and convergence speed is hardly affected by singularity.

Original languageEnglish
Pages (from-to)282-291
Number of pages10
JournalLecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science)
Publication statusPublished - 2004
Externally publishedYes
Event8th Pacific Rim International Conference on Artificial Intelligence, PRICAI 2004: Trends in Artificial Intelligence - Auckland, New Zealand
Duration: 2004 Aug 92004 Aug 13

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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