Exceptional reducibility of complex-valued neural networks

Authors:
Masaki Kobayashi
Affiliations:
Interdisciplinary Graduate School of Medicine and Engineering, University of Yamanashi, Takeda, Kofu, Yamanashi, Japan
Venue:
IEEE Transactions on Neural Networks
Year:
2010

Citing 6
Cited 1

Original Contribution: Uniqueness of the weights for minimal feedforward nets with a given input-output map

Neural Networks
An extension of the back-propagation algorithm to complex numbers

Neural Networks
Local minima and plateaus in hierarchical structures of multilayer perceptions

Neural Networks
Complex-Valued Neural Networks: Theories and Applications (Series on Innovative Intelligence, 5)

Complex-Valued Neural Networks: Theories and Applications (Series on Innovative Intelligence, 5)
Complex-Valued Neural Networks (Studies in Computational Intelligence)

Complex-Valued Neural Networks (Studies in Computational Intelligence)
Complex-valued Neural Networks: Utilizing High-dimensional Parameters

Complex-valued Neural Networks: Utilizing High-dimensional Parameters

Local minima in hierarchical structures of complex-valued neural networks

Neural Networks

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Abstract

A neural network is referred to as minimal if it cannot reduce the number of hidden neurons that maintain the input-output map. The condition in which the number of hidden neurons can be reduced is referred to as reducibility. Real-valued neural networks have only three simple types of reducibility. It can be naturally extended to complex-valued neural networks without bias terms of hidden neurons. However, general complex-valued neural networks have another type of reducibility, referred to herein as exceptional reducibility. In this paper, another type of reducibility is presented, and a method by which to minimize complex-valued neural networks is proposed.