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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.