Uniqueness of feedforward complex-valued neural network with a given complex-valued function

In this paper, we will prove the uniqueness theorem for complex-valued neural networks: the 3-layered complex-valued neural network is uniquely determined by its corresponding complex-valued function, up to a finite group, provided that the complex-valued neural network is irreducible. Moreover, we will investigate the order of the finite group, and make clear that the redundancy of the learning parameters of the complex-valued neural network is the same as the one of the real-valued neural network. We will also derive a sufficient condition for a given 3-layered complex-valued neural network to he minimal.