We study the problem of offline learning discrete functions on polynomial threshold units over specified set of polynomial. Our approach is based on the generalization of the classical “Relaxation” method of solving linear inequalities. We give theoretical reason justifying heuristic modification improving the performance of spectral learning algorithm. We demonstrate that if the normalizing factor satisfies sufficient conditions, then the learning procedure is finite and stops after some steps, producing the weight vector of the polynomial threshold unit realizing the given threshold function. Our approach can be applied in hybrid systems of computational intelligence.

The fully connected 2-layer feedforward network architecture with the hidden layer consisting of bithreshold neurons is considered in the paper. We design the neural network multicategory classifier based on such an architecture. We also give the upper bound on the size of the bithreshold network, which is capable to recognize an arbitrary partition of the given finite set of patterns into a predefined number of classes. The learning algorithm is proposed for such neural networks. We give simulation results of the classifier performance on the real data set and discuss the influence of algorithm parameters on the quality of learning and the representational capacity of classifier.

The paper deals with the problems of Boolean functions realization on neural-like units with complex weight coefficients. The relation between classes of realizable function is considered for half-plane-like activation function. We also introduce the concept of sets separability, corresponding to our notion of neuron. The iterative online learning algorithm is proposed and sufficient conditions of its convergence are given. We also consider complex neurons with angle-type activation functions.