What is complex-valued neural networks?
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.
Why do we need complex-valued neural networks?
It is shown that a single complex-valued neuron can learn non-linearly separable input/output mappings and is much more functional than a single real-valued neuron. Historical observation of complex-valued neural networks and the state of the art in this area are also presented.
What are the elements of neural network?
Neural Network: Components
- Input Layers, Neurons, and Weights –
- Hidden Layers and Output Layer –
- One-dimensional optimization.
- Golden Section Method.
- Brent’s Method.
- Multidimensional optimization.
- Gradient descent.
- Newton’s method.
Why are neural networks suited to complex valued inputs?
The analysis there is that problems suited to complex-valued neural networks are ones where interesting input has phase-coherent structure, however they did only show one specific problem where the type of network worked well. Thanks for contributing an answer to Signal Processing Stack Exchange!
Can you train a neural network with complex numbers?
As the question states. I am aiming to train a neural network where the weights are complex numbers.
What are the ingredients of complex valued signal processing?
There are two key ingredients in the statistical signal processing of complex-valued data: 1) utilizing the complete statistical characterization of complex-valued random signals; and 2) the optimization of real-valued cost functions with respect to complex parameters.
How are neural networks used in deep learning?
As for neural networks, and of course deep learning, the recent theory of scattering networks, and subsequent works, have provided a solid ground for understanding how deep learning works, from a solid mathematical point of view, based on complex wavelet frames and non-linear operators. Another interesting paper for your question is: