In this paper we present an algorithm for training two-layer sigmoidal artificial neural networks (ANN) in the presence of significant interference and low-informative variables. Mixed smooth and non- smooth regularizing functionals are used to suppress the low –informative variables and to control interference. A computational experiment was organized comparing the quality of approximation by ANN models and logistic models with various types of regularization. The proposed algorithm for ANN learning in combination with non-smooth regularization allows us to obtain efficient ANN models for classification problems.