## How to Improve Neural Networks by Using Complex Numbers?## What are Convolutional Neural Networks?
Convolutional Neural Networks are used for the ## Complex Numbers or Functions in Convolutional Neural NetworksIt is obvious that the initial layers of the neural network extract minimal features from the images, like the colour and edges of the images. We can say it extracts the low level features of the images, and the The neural networks that use Let's see some features of the complex-valued neural networks. - The complex-valued neural networks have two
**hypersurfaces dividing the decision region into four equal sections**. - The complex-valued neural networks can represent
**two dimensional information**as the parameters of input and output signals are complex numbers. - The complex-valued neural networks
**learn faster than traditional real-valued neural networks**. It used a**backpropagation algorithm**for the learning process. - It
**needs fewer parameters**than the real-valued neural networks. It is about half of the parameters, including the weights and thresholds. - The complex-valued networks are much
**more flexible towards noise and interference**produced while preprocessing the images, which makes it more efficient for fields like signal processing.
## Training of the neural networks with complex numbersComplex valued neural networks use The complex-valued neural networks are trained with the As we ## Applications and Use Cases of the Complex-valued Neural NetworksAccording to various studies, in neural networks that use complex numbers for the preprocessing and training, the complex part of the parameter is treated individually as real numbers. The complex values neural networks are assumed as two dimensional real-valued neural networks. The complex-valued neural networks are used in many fields, including: **Signal Processing:**Complex-valued neural networks are used for signal processing like Fourier analysis and image processing with complex values.- Complex-valued neural networks are also implemented in
**Computer Vision**, involving reconstruction of images, deblurring of images, etc. - Complex-valued neural networks can also be used in
**electromagnetics**in**designing antennas**and representing electromagnetic waves. - Complex-valued neural networks are also implemented in
**machine learning**to design algorithms and process huge amounts of data.
## Complex-valued Neural Network in PythonPython provides different libraries like ## Challenges of Complex-valued Neural NetworksThough complex-valued neural networks have many advantages and are used to improve the efficiency of the neural networks, they face various challenges: - The complex-valued neural networks' activation functions
**cannot be complex-differentiable**and**bounded simultaneously**. - The complex-valued neural network
**needs specific deep-learning libraries**that can be optimised for the complex value computations. - The complex-valued neural networks
**need more expertise**to interpret results from the complex-value computations. - Though implementing complex values in the neural networks helps to improve their efficiency and accuracy, there has been
**less research till now**.
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