Superior Performance of Using Hyperbolic Sine Activation Functions in ZNN Illustrated via Time-Varying Matrix Square Roots Finding

Yunong Zhang1, Long Jin1 and Zhende Ke1

  1. School of Information Science and Technology, Sun Yat-sen University
    Guangzhou 510006, Guangdong, China
    zhynong@mail.sysu.edu.cn, spaformind@qq.com, kezhende@126.com

Abstract

A special class of recurrent neural network (RNN), termed Zhang neural network (ZNN) depicted in the implicit dynamics, has recently been proposed for online solution of time-varying matrix square roots. Such a ZNNmodel can be constructed by using monotonically-increasing odd activation functions to obtain the theoretical time-varying matrix square roots in an error-free manner. Different choices of activation function arrays may lead to different performance of the ZNN model. Generally speaking, ZNN model using hyperbolic sine activation functions may achieve better performance, as compared with those using other activation functions. In this paper, to pursue the superior convergence and robustness properties, hyperbolic sine activation functions are applied to the ZNN model for online solution of time-varying matrix square roots. Theoretical analysis and computer-simulation results further demonstrate the superior performance of the ZNN model using hyperbolic sine activation functions in the context of large model-implementation errors, in comparison with that using linear activation functions.

Key words

Zhang neural network, global exponential convergence, hyperbolic sine activation functions, time-varying matrix square roots, implementation errors

Digital Object Identifier (DOI)

https://doi.org/10.2298/CSIS120121043Z

Publication information

Volume 9, Issue 4 (December 2012)
Special Issue on Recent Advances in Systems and Informatics
Year of Publication: 2012
ISSN: 1820-0214 (Print) 2406-1018 (Online)
Publisher: ComSIS Consortium

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How to cite

Zhang, Y., Jin, L., Ke, Z.: Superior Performance of Using Hyperbolic Sine Activation Functions in ZNN Illustrated via Time-Varying Matrix Square Roots Finding. Computer Science and Information Systems, Vol. 9, No. 4, 1603-1626. (2012)