Learning nonlinearly separable mod k addition problem using a single multi-valued neuron with a periodic activation function

In this paper, we further develop a complex-valued neuron paradigm. It is shown how a single multi-valued neuron with a periodic activation function may learn multiple-valued nonlinearly separable problems. One of the classical nonlinearly separable problems - mod k addition of n variables is considered in detail. It is shown that to be able to learn this problem using a single multi-valued neuron, it is necessary to use a periodic activation function and a learning algorithm based on the error-correction learning rule and adapted to this activation function.