Learning dynamics of a single polar variable complex-valued neuron

Neural Computation
Tohru Nitta

Abstract

This letter investigates the characteristics of the complex-valued neuron model with parameters represented by polar coordinates (called polar variable complex-valued neuron). The parameters of the polar variable complex-valued neuron are unidentifiable. The plateau phenomenon can occur during learning of the polar variable complex-valued neuron. Furthermore, computer simulations suggest that a single polar variable complex-valued neuron has the following characteristics in the case of using the steepest gradient-descent method with square error: (1) unidentifiable parameters (singular points) degrade the learning speed and (2) a plateau can occur during learning. When the weight is attracted to the singular point, the learning tends to become stuck. However, computer simulations also show that the steepest gradient-descent method with amplitude-phase error and the complex-valued natural gradient method could reduce the effects of the singular points. The learning dynamics near singular points depends on the error functions and the training algorithms used.

References

Feb 17, 2000·Journal of Chromatography. B, Biomedical Sciences and Applications·F Hatzack, S K Rasmussen
Nov 30, 2007·Neural Computation·Haikun WeiShun-Ichi Amari
Aug 15, 2008·IEEE Transactions on Neural Networks·Florent CousseauShun-Ichi Amari
Aug 1, 2009·IEEE Transactions on Neural Networks·Gouhei Tanaka, Kazuyuki Aihara
Mar 8, 2013·Neural Networks : the Official Journal of the International Neural Network Society·Tohru Nitta
May 9, 2014·IEEE Transactions on Neural Networks and Learning Systems·Ramasamy SavithaNarasimhan Sundararajan

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