The Computational Power of Complex-Valued Neuron

Abstract

There exist some problems that cannot be solved with conventional usual 2-layered real-valued neural networks (i.e., a single realvalued neuron) such as the XOR problem and the detection of symmetry. In this paper, it will be proved that such problems can be solved by a 2-layered complex-valued neural network (i.e., a single complex-valued neuron) with the orthogonal decision boundaries. Furthermore, it will be shown that the fading equalization problem can be successfully solved by the 2-layered complex-valued neural network with the highest generalization ability.