Archives of Neuroscience

Published by: Kowsar

Complex-Valued Neurocomputing and Singular Points

Tohru Nitta 1 , *
Author Information
1 Human Informatics Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Japan
Article information
  • Archives of Neuroscience: October 01, 2015, 2 (4); e27461
  • Published Online: October 10, 2015
  • Article Type: Review Article
  • Received: March 2, 2015
  • Accepted: March 3, 2015
  • DOI: 10.5812/archneurosci.27461

To Cite: Nitta T. Complex-Valued Neurocomputing and Singular Points, Arch Neurosci. 2015 ; 2(4):e27461. doi: 10.5812/archneurosci.27461.

Abstract
Copyright © 2015, Tehran University of Medical Sciences. This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/) which permits copy and redistribute the material just in noncommercial usages, provided the original work is properly cited.
1. Context
2. Evidence Acquisition
3. Results
4. Conclusions
Acknowledgements
Footnote
References
  • 1. Bengio Y. Learning deep architectures for AI. 2009; : 1-127
  • 2. Nitta T. Complex-Valued Neural Networks: Utilizing High-Dimensional Parameters. 2009; : 504
  • 3. Schaffer ES, Ostojic S, Abbott LF. A complex-valued firing-rate model that approximates the dynamics of spiking networks. PLoS Comput Biol. 2013; 9(10)[DOI][PubMed]
  • 4. Amari S, Park H, Ozeki T. Singularities affect dynamics of learning in neuromanifolds. Neural Comput. 2006; 18(5): 1007-65[DOI][PubMed]
  • 5. Wei H, Zhang J, Cousseau F, Ozeki T, Amari S. Dynamics of learning near singularities in layered networks. Neural Comput. 2008; 20(3): 813-43[DOI][PubMed]
  • 6. Cousseau F, Ozeki T, Amari S. Dynamics of learning in multilayer perceptrons near singularities. IEEE Trans Neural Netw. 2008; 19(8): 1313-28[DOI][PubMed]
  • 7. Nitta T. On the Singularity of a Single Complex-Valued Neuron [in Japanese]. IEICE Trans Inf SystD. 2010; (8): 1614-21
  • 8. Nitta T. Plateau in a Polar Variable Complex-Valued Neuron. ICAART2014 the 6th International Conference on Agents and Artificial Intelligence. : 526-31
  • 9. Nitta T. Learning dynamics of a single polar variable complex-valued neuron. Neural Comput. 2015; 27(5): 1120-41[DOI][PubMed]
  • 10. Savitha R, Suresh S, Sundararajan N. Projection-based fast learning fully complex-valued relaxation neural network. IEEE Trans Neural Netw Learn Syst. 2013; 24(4): 529-41[DOI][PubMed]
  • 11. Nitta T. Natural Gradient Descent for Training Stochastic Complex-Valued Neural Networks. Int J Adv Comput Sci Appl. 2014; 5(7): 193-8[DOI]
  • 12. Nitta T. Local minima in hierarchical structures of complex-valued neural networks. Neural Netw. 2013; 43: 1-7[DOI][PubMed]
  • 13. Fukumizu K, Amari S. Local minima and plateaus in hierarchical structures of multilayer perceptrons. Neural Netw. 2000; 13(3): 317-27[DOI]
  • 14. Kobayashi M. Exceptional reducibility of complex-valued neural networks. IEEE Trans Neural Netw. 2010; 21(7): 1060-72[DOI][PubMed]
  • 15. Nitta T. Learning Dynamics of the Complex-Valued Neural Network in the Neighborhood of Singular Points. J Comput Commun. 2014; 2(1): 27-32[DOI]
  • 16. Nitta T. Construction of Neural Networks that Do Not Have Critical Points Based on Hierarchical Structure. Int J Adv Comput Sci Appl. 2013; 4(9): 68-73[DOI]
  • 17. Gürlebeck K, Habetha K, Sprößig W. Holomorphic functions in the plane and n-dimensional space. 2008;
Creative Commons License Except where otherwise noted, this work is licensed under Creative Commons Attribution Non Commercial 4.0 International License .
Readers' Comments