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The paper concludes an overview of the most promising methods of pattern recognition (deep learning, convolutional, evolutionary, progressive, shallow, "wide", hybrid artificial neural networks etc.) in regard to the possibility of their use to build highly reliable biometric cryptosystems on the basis of dynamic features. The authors propose a new approach - the development and training of flexible neural networks. For its implementation, the mathematical apparatus is developed that uses elements of various types of artificial neural networks, the probability theory, and mathematical statistics. The paper presents the results of these studies and formulates the range of the problems to be solved for creating a perspective fundamentals for building highly reliable biometric cryptosystems