Hebbian and error-correction learning for complex-valued neurons

In this paper, we observe some important aspects of Hebbian and error-correction learning rules for complex-valued neurons. These learning rules, which were previously considered for the multi-valued neuron whose inputs and output are located on the unit circle, are generalized for a complex-valued neuron whose inputs and output are arbitrary complex numbers. The Hebbian learning rule is also considered for the multi-valued neuron with a periodic activation function. It is experimentally shown that Hebbian weights, even if they still cannot implement an input/output mapping to be learned, are better starting weights for the error-correction learning, which converges faster starting from the Hebbian weights rather than from the random ones.