Hybrid Real- and Complex-valued Neural Network Architecture

We propose a \emph{hybrid} real- and complex-valued \emph{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 real-valued neural networks (RVNNs) for inherently complex-valued problems by showing how it learnt to perform complex-valued convolution, but with notable inefficiencies stemming from its real-valued constraints. To create the HNN, we propose to 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 higher 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 less parameters compared to an RVNN for all considered cases. Such results highlight the potential for the use of partially complex-valued processing in neural networks and applications for HNNs in many signal processing domains.