Solving the XOR problem and the detection of symmetry using a single complex-valued neuron.

Abstract

This letter presents some results on the computational power of complex-valued neurons. The main results may be summarized as follows. The XOR problem and the detection of symmetry problem which cannot be solved with a single real-valued neuron (i.e. a two-layered real-valued neural network), can be solved with a single complex-valued neuron (i.e. a two-layered complex-valued neural network) with the orthogonal decision boundaries, which reveals the potent computational power of complex-valued neurons. Furthermore, the fading equalization problem can be successfully solved with a single complex-valued neuron with the highest generalization ability.