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Complex-Valued Neurons with Phase-Dependent Activation Functions

  • Igor Aizenberg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6114)

Abstract

In this paper, we observe two artificial neurons with complex-valued weights. There are a multi-valued neuron and a universal binary neuron. Both neurons have activation functions depending on the argument (phase) of the weighted sum. A multi-valued neuron may learn multiple-valued threshold functions. A universal binary neuron may learn arbitrary (not only linearly-separable) Boolean functions. It is shown that a multi-valued neuron with a periodic activation function may learn non-threshold functions by their projection to the space corresponding to the larger valued logic. A feedforward neural network with multi-valued neurons and its learning are also considered.

Keywords

complex-valued neural networks derivative-free learning multi-valued neuron 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Igor Aizenberg
    • 1
  1. 1.Department of Computer ScienceTexas A&M University-TexarkanaTexarkanaUSA

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