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.

翻译：本文详细阐述了复值神经网络的理论基础，包括Wirtinger微积分、复数反向传播算法，以及复数层、复数激活函数、复数权重初始化等基础模块。我们还展示了未正确适配复数域权重初始化带来的影响。本文重点介绍了如何利用cvnn工具箱在Python中实现这些模块。此外，我们基于实值数据进行了仿真实验，通过希尔伯特变换将其转换至复数域，从而验证了复值神经网络对非复数数据亦具有潜在应用价值。