The Science and Information (SAI) Organization
  • Home
  • About Us
  • Journals
  • Conferences
  • Contact Us

Publication Links

  • IJACSA
  • Author Guidelines
  • Publication Policies
  • Digital Archiving Policy
  • Promote your Publication
  • Metadata Harvesting (OAI2)

IJACSA

  • About the Journal
  • Call for Papers
  • Editorial Board
  • Author Guidelines
  • Submit your Paper
  • Current Issue
  • Archives
  • Indexing
  • Fees/ APC
  • Reviewers
  • Apply as a Reviewer

IJARAI

  • About the Journal
  • Archives
  • Indexing & Archiving

Special Issues

  • Home
  • Archives
  • Proposals
  • Guest Editors
  • SUSAI-EE 2025
  • ICONS-BA 2025
  • IoT-BLOCK 2025

Future of Information and Communication Conference (FICC)

  • Home
  • Call for Papers
  • Submit your Paper/Poster
  • Register
  • Venue
  • Contact

Computing Conference

  • Home
  • Call for Papers
  • Submit your Paper/Poster
  • Register
  • Venue
  • Contact

Intelligent Systems Conference (IntelliSys)

  • Home
  • Call for Papers
  • Submit your Paper/Poster
  • Register
  • Venue
  • Contact

Future Technologies Conference (FTC)

  • Home
  • Call for Papers
  • Submit your Paper/Poster
  • Register
  • Venue
  • Contact
  • Home
  • Call for Papers
  • Editorial Board
  • Guidelines
  • Submit
  • Current Issue
  • Archives
  • Indexing
  • Fees
  • Reviewers
  • Subscribe

DOI: 10.14569/IJACSA.2013.040911
PDF

Construction of Neural Networks that Do Not Have Critical Points Based on Hierarchical Structure

Author 1: Tohru Nitta

International Journal of Advanced Computer Science and Applications(IJACSA), Volume 4 Issue 9, 2013.

  • Abstract and Keywords
  • How to Cite this Article
  • {} BibTeX Source

Abstract: a critical point is a point at which the derivatives of an error function are all zero. It has been shown in the literature that critical points caused by the hierarchical structure of a real-valued neural network (NN) can be local minima or saddle points, although most critical points caused by the hierarchical structure are saddle points in the case of complex-valued neural networks. Several studies have demonstrated that singularity of those kinds has a negative effect on learning dynamics in neural networks. As described in this paper, the decomposition of high-dimensional neural networks into low-dimensional neural networks equivalent to the original neural networks yields neural networks that have no critical point based on the hierarchical structure. Concretely, the following three cases are shown: (a) A 2-2-2 real-valued NN is constructed from a 1-1-1 complex-valued NN. (b) A 4-4-4 real-valued NN is constructed from a 1-1-1 quaternionic NN. (c) A 2-2-2 complex-valued NN is constructed from a 1-1-1 quaternionic NN. Those NNs described above do not suffer from a negative effect by singular points during learning comparatively because they have no critical point based on a hierarchical structure.

Keywords: critical point; singular point; redundancy; complex number; quaternion

Tohru Nitta, “Construction of Neural Networks that Do Not Have Critical Points Based on Hierarchical Structure” International Journal of Advanced Computer Science and Applications(IJACSA), 4(9), 2013. http://dx.doi.org/10.14569/IJACSA.2013.040911

@article{Nitta2013,
title = {Construction of Neural Networks that Do Not Have Critical Points Based on Hierarchical Structure},
journal = {International Journal of Advanced Computer Science and Applications},
doi = {10.14569/IJACSA.2013.040911},
url = {http://dx.doi.org/10.14569/IJACSA.2013.040911},
year = {2013},
publisher = {The Science and Information Organization},
volume = {4},
number = {9},
author = {Tohru Nitta}
}



Copyright Statement: This is an open access article licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, even commercially as long as the original work is properly cited.

IJACSA

Upcoming Conferences

IntelliSys 2025

28-29 August 2025

  • Amsterdam, The Netherlands

Future Technologies Conference 2025

6-7 November 2025

  • Munich, Germany

Healthcare Conference 2026

21-22 May 2026

  • Amsterdam, The Netherlands

Computing Conference 2026

9-10 July 2026

  • London, United Kingdom

IntelliSys 2026

3-4 September 2026

  • Amsterdam, The Netherlands

Computer Vision Conference 2026

15-16 October 2026

  • Berlin, Germany
The Science and Information (SAI) Organization
BACK TO TOP

Computer Science Journal

  • About the Journal
  • Call for Papers
  • Submit Paper
  • Indexing

Our Conferences

  • Computing Conference
  • Intelligent Systems Conference
  • Future Technologies Conference
  • Communication Conference

Help & Support

  • Contact Us
  • About Us
  • Terms and Conditions
  • Privacy Policy

© The Science and Information (SAI) Organization Limited. All rights reserved. Registered in England and Wales. Company Number 8933205. thesai.org