Previous Research: Complex-valued Deep Learning

Complex-valued data is ubiquitous in physics and signal processing applications, and complex-valued representations in deep learning have appealing theoretical properties. While these aspects have long been recognized, complex-valued deep learning lags far behind its real-valued counterpart.  Existing methods ignore the rich geometry of complex-valued data, instead opting to use the same techniques and architectures as real-valued data, with undesirable consequences such as decreased robustness, larger model sizes, and poor generalization.  We focus on understanding the unique mathematical structure of complex-valued data and derive the necessary architectures in a principled manner. Our method achieves better robustness and generalization than the state-of-the-art with significantly fewer parameters.