Orthogonality of decision boundaries in complex-valued neural networks
Neural Computation
Complex-valued Neural Networks: Utilizing High-dimensional Parameters
Complex-valued Neural Networks: Utilizing High-dimensional Parameters
Exceptional reducibility of complex-valued neural networks
IEEE Transactions on Neural Networks
On the complex backpropagation algorithm
IEEE Transactions on Signal Processing
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Most of local minima caused by the hierarchical structure can be resolved by extending the real-valued neural network to complex numbers. It was proved in 2000 that a critical point of the real-valued neural network with H-1 hidden neurons always gives many critical points of the real-valued neural network with H hidden neurons. These critical points consist of many lines in the parameter space which could be local minima or saddle points. Local minima cause plateaus which have a strong negative influence on learning. However, most of the critical points of complex-valued neural network are saddle points unlike those of the real-valued neural network. This is a prominent property of the complex-valued neural network.