Hybrid real- and complex-valued neural network architecture

Abstract We propose a hybrid real- and complex-valued neural network (HNN) architecture, designed to combine the computational efficiency of real-valued processing with the ability to effectively handle complex-valued data. We illustrate the limitations of using a real-valued neural network (RVNN) for inherently complex-valued problems by showing how it learns to perform complex-valued convolution; learning twice as many weights as necessary. To create the HNN, we use building blocks containing both real- and complex-valued paths, where information between domains is exchanged through domain conversion functions. We also introduce novel complex-valued activation functions, with better generalisation and parameterisation efficiency. HNN-specific architecture search techniques are described to navigate the larger solution space. Experiments with the AudioMNIST dataset demonstrate that the HNN reduces cross-entropy loss and consumes fewer parameters compared to an RVNN for all cases considered. Further experiments for audio denoising also show performance gains using HNNs with a reduced model complexity when compared to its real- or complex-valued counterparts. Such results highlight the potential for the use of partially complex-valued processing in neural networks and applications of HNNs in many signal processing domains.