Complex-valued neural networks (CVNNs) are extensions of the classical neural networks, which have complex-valued weights, accept complex inputs and have more computational power than the classical ones. We present the structure and function of the phase-based neurons (PBNs), a simple type of CVNNs that uses as weights and biases complex numbers with magnitude 1, the phase being the only tunable parameter. We provide an adaptation method for PBNs and show that PBN based CVNNs have more computational power than classical artificial neural networks (ANNs), being able to implement some non-linearly-separable mappings, such as the XOR logical function. We show that the PBS has many features found in a class of biologically plausible neural networks called the phase based spiking neuron.

Keywords: Artificial neural networks, Complex-valued neural networks, Universal binary neuron, Phase-based neuron