Complex numbers neural networks

Are complex numbers used in AI?
Computer engineers at Duke University have demonstrated that using complex numbers—numbers with both real and imaginary components—can play an integral part in securing artificial intelligence algorithms against malicious attacks that try to fool object-identifying software by subtly altering the images..
Can neural networks handle complex numbers?
Complex-valued neural networks (CVNN) are ANNs that process information using complex-valued parameters and variables [4].
The main reason for their advocacy lies in the difference between the representation of the arithmetic of complex numbers, especially the multiplication operation._{Jan 28, 2021}.
What do the numbers in the neural network refer to?
The number suffix in the name of network means the number of layers that have learnable parameters, such as convolution layer, fully conneted layer, in the network.
Hence number suffix does not counts the non-learnable layers, such pooling layer and activation layer, do not have any learnable parameters..
What is the application of complex number in machine learning?
Complex numbers (which have imaginary part) are used in all speech recognition systems.
Particularly in the first step: Fast Fourier Transform.
It transforms sound wave into array where every frequency is a complex number (which describes both amplitude and phase).
Machine learning algo learns on the amplitudes..
The Neural Network is constructed from 3 type of layers:
Input layer — initial data for the neural network.Hidden layers — intermediate layer between input and output layer and place where all the computation is done.Output layer — produce the result for given inputs.
ConvNet is a particular type of neural network which is used for automatic feature extraction.
The ConvNet feature extractor is composed of stacks of the convolution layer and the pooling layer.
A CNN consists of a feature extraction network and a classifier network.
The information complexity k(ϵ), is the minimal number of examples ( x → i ,f( x → i )) from which it is possible to approximate f within ϵ, assuming an unlimited number of neurons available.
Information complexity dominates neural complexity, i.e.
We need to match the neural network's complexity with our data complexity.
If the neural network is too complex, it will start memorizing the training data instead of having a general understanding of the data, hence causing overfitting.

Complex-valued neural networks (CVNN) are ANNs that process information using complex-valued parameters and variables [4]. The main reason for their advocacy lies in the difference between the representation of the arithmetic of complex numbers, especially the multiplication operation.

Neural Network Quantum States is a general class of variational quantum states parameterized in terms of an artificial neural network.
It was first introduced in 2017 by the physicists Giuseppe Carleo and Matthias Troyer to approximate wave functions of many-body quantum systems.

Complex numbers neural networks

Are complex numbers used in AI?

Can neural networks handle complex numbers?

What do the numbers in the neural network refer to?

What is the application of complex number in machine learning?

The Neural Network is constructed from 3 type of layers: