Theory and Implementation of Complex-Valued Neural Networks
This work provides a foundational guide for researchers and practitioners interested in applying CVNNs, even to non-complex data, though it is incremental in building on existing complex-valued methods.
The paper explains the theory and implementation of Complex-Valued Neural Networks (CVNNs), including key concepts like Wirtinger calculus and complex backpropagation, and demonstrates their potential on real-valued data using the Hilbert Transform, showing improved performance in simulations.
This work explains in detail the theory behind Complex-Valued Neural Network (CVNN), including Wirtinger calculus, complex backpropagation, and basic modules such as complex layers, complex activation functions, or complex weight initialization. We also show the impact of not adapting the weight initialization correctly to the complex domain. This work presents a strong focus on the implementation of such modules on Python using cvnn toolbox. We also perform simulations on real-valued data, casting to the complex domain by means of the Hilbert Transform, and verifying the potential interest of CVNN even for non-complex data.