Artificial Neural Networks Using Complex Numbers and Phase Encoded Weights - Electronic and Optical Implementations

The model of a simple perception using phase-encoded inputs and complex-valued weights is proposed. The aggregation function, activation function, and learning rule for the proposed neuron are derived and applied to Boolean logic functions. The complex-valued neuron (CVN) is shown to be superior to traditional perceptrons. Optical and analog circuit implementations are discussed and the CVN is shown to be very attractive for optical implementation since optical computations are naturally complex. The cost of the CVN is less in all cases than the traditional neuron when implemented optically. However, on those implementations dependent on standard serial computers, CVN will be more cost effective only in those applications where its increased power can offset the requirement for additional neurons.