Complex- and Real-Valued Neural Network Architectures

Nils Moenning, Suresh Manandhar

Abstract: Complex-value neural networks are not a new concept, however, the use of real-values has often been favoured over complex-values due to difficulties in training and accuracy of results. Existing literature ignores the number of parameters used. We compared complex- and real-valued neural networks using five activation functions. We found that when real and complex neural networks are compared using simple classification tasks, complex neural networks perform equal to or slightly worse than real-value neural networks. However, when specialised architecture is used, complex-valued neural networks outperform real-valued neural networks. Therefore, complex–valued neural networks should be used when the input data is also complex or it can be meaningfully to the complex plane, or when the network architecture uses the structure defined by using complex numbers.

TL;DR: Comparison of complex- and real-valued multi-layer perceptron with respect to the number of real-valued parameters.

Keywords: complex numbers, complex-valued, neural, network, multi-layer, perceptron, architecture