Complex-valued neurons with phase-dependent activation functions

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. © 2010 Springer-Verlag.