Album of artificial neurons with piecewise linear excitation
functions tuned to predict the probabilities of their own errors 

Vladimir I. Volchikhin, Doctor of engineering sciences, professor, president of Penza State University (40 Krasnaya street, Penza, Russia), E-mail: cnit@pnzgu.ru
Aleksandr I. Ivanov, Doctor of engineering sciences, professor, scientific adviser, Penza Scientific Research Electrotechnical Institute (9 Sovetskaya street, Penza, Russia), E-mail: ivan@pniei.penza.ru
Aleksandr V. Bezyaev, Candidate of engineering sciences, doctor’s degree student, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: tsib@pnzgu.ru
Ivan A. Filipov, Lecturer of the Military Training Center,, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: re.wo1f@mail.ru

Background. Currently, single-layer networks of artificial neurons are used, which are equivalent to classical statistical criteria. The purpose of the work is to move to more complex algorithms for using multilayer networks of artificial neurons. Materials and methods. Replacing classical statistical criteria with their equivalent binary neurons provides significant redundancy of the output code of the neural network, which isconvolved with error elimination. The mechanism of convolution of code redundancy can be improved if the most informative part of the neuron response is not quantized. For this purpose, it is proposed to use artificial neurons with piecewise linear excitation functions. Results. It is shown that the linear part of the excitation function is easily adjusted so as to predict the probability of errors of each of the used neurocriteria. This ultimately allows moving from single-layer networks of binary artificial neurons to two-layer networks. Examples of adjusting the functions of piecewise linear excitation for 7 artificial neurons are given

statistical criteria for testing the hypothesis of normality and uniformity, binary neurons equivalent to the criteria, piecewise linear excitation functions, prediction of the probability of neuron errors, small samples of 16 experiments

Volchikhin V.I., Ivanov A.I., Bezyaev A.V., Filipov I.A. Album of artificial neurons with piecewise linear excitation functions tuned to predict the probabilities of their own errors. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Tekhnicheskie nauki = University proceedings. Volga region. Engineering sciences. 2024 (4):39–49. (In Russ.). doi: 10.21685/2072-3059-2024-4-4