Theory and Implementation of Complex-Valued Neural Networks

2023/02/16 by José Agustín Barrachina, Barrachina, Jose Agustin, Chengfang Ren +7 · 3 citations
Computer Science · Engineering · #Neural Networks and Applications #Computational Physics and Python Applications #Fault Detection and Control Systems

paper · pdf · doi:10.48550/arxiv.2302.08286

Abstract

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.

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