Relationship between phase and amplitude generalization errors in complex- and real-valued feedforward neural networks

We compare the generalization characteristics of complex-valued and real-valued feedforward neural networks. We assume a task of function approximation with phase shift and/or amplitude change in signals having various coherence. Experiments demonstrate that complex-valued neural networks show smaller generalization error than real-valued networks having doubled input and output neurons in particular when the signals have high coherence, that is, high degree of wave nature. We also investigate the relationship between amplitude and phase errors. It is found in real-valued networks that abrupt change in amplitude is often accompanied by steep change in phase, which is a consequence of local minima in real-valued supervised learning.