title: Learning dynamics of a single polar variable complex-valued neuron.
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.
authors.affiliation: National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki, 305-8568 Japan tohru-nitta@aist.go.jp.
authors.forename: Tohru
authors.initials: T
authors.lastname: Nitta