Generalization characteristics of complex-valued feedforward neural networks in relation to signal coherence.

Applications of complex-valued neural networks (CVNNs) have expanded widely in recent years-in particular in radar and coherent imaging systems. In general, the most important merit of neural networks lies in their generalization ability. This paper compares the generalization characteristics of complex-valued and real-valued feedforward neural networks in terms of the coherence of the signals to be dealt with. We assume a task of function approximation such as interpolation of temporal signals. Simulation and real-world experiments demonstrate that CVNNs with amplitude-phase-type activation function show smaller generalization error than real-valued networks, such as bivariate and dual-univariate real-valued neural networks. Based on the results, we discuss how the generalization characteristics are influenced by the coherence of the signals depending on the degree of freedom in the learning and on the circularity in neural dynamics.