Enhanced artificial neural networks using complex numbers

The model of a simple perceptron using phase-encoded input and complex-valued weights is proposed. The aggregation function, activation function, and learning rule for the proposed neuron are derived and applied to two and three input Boolean logic functions. An improvement of 135% over the theoretical maximum of 104 linearly separable problems (of three variables) solvable by conventional perceptrons is achieved without additional logic, neuron stages, or higher order terms such as those required in polynomial logic gates. Such a network is very attractive for optical implementation since optical computations are naturally complex