On the appropriateness of complex-valued neural networks for speech enhancement

Although complex-valued neural networks (CVNNs) â?? networks which can operate with complex arithmetic â?? have been around for a while, they have not been given reconsideration since the breakthrough of deep network architectures. This paper presents a critical assessment whether the novel tool set of deep neural networks (DNNs) should be extended to complex-valued arithmetic. Indeed, with DNNs making inroads in speech enhancement tasks, the use of complex-valued input data, specifically the short-time Fourier transform coefficients, is an obvious consideration. In particular when it comes to performing tasks that heavily rely on phase information, such as acoustic beamforming, complex-valued algorithms are omnipresent. In this contribution we recapitulate backpropagation in CVNNs, develop complex-valued network elements, such as the split-rectified non-linearity, and compare real- and complex-valued networks on a beamforming task. We find that CVNNs hardly provide a performance gain and conclude that the effort of developing the complex-valued counterparts of the building blocks of modern deep or recurrent neural networks can hardly be justified.