VIRTUAL ENHANCEMENT OF THE EFFECT OF PARALLELIZATION OF CALCULATIONS IN THE TRANSITION FROM BINARY NEURONS TO THE USE OF Q-ARY ARTIFICIAL NEURONS 

Aleksandr I. Ivanov, Doctor of technical sciences, associate professor, senior researcher, Penza Research Electrotechnical Institute (9 Sovetskaya street, Penza, Russia), E-mail: ivan@pniei.penza.ru
Aleksey P. Ivanov, Candidate of technical sciences, associate professor, head of the sub-department of technical means of information security, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: ap_ivanov@pnzgu.ru
Konstantin N. Savinov, Senior lecturer of the sub-department of wired telecommunications and automated systems, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: tsib@pnzgu.ru
Roman V. Eremenko, Senior lecturer of the sub-department of radio and satellite communications, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: tsib@pnzgu.ru 

Background. The problem of parallelization of neural network calculations in an implicit form is considered. The problem occurs mainly when trying to speed up calculations on multi-core processors. A similar situation arises when a neural network combines several classical statistical criteria. Materials and methods. Summarization of five classical statistical criteria for testing the hypothesis of normal distribution of small samples in 16 experiments is considered. Classical tests of Anderson-Darling, normalized range, Vasicek, Frotsini and the test of the fourth statistical moment are considered. Unfortunately, their neural network counterparts have a low decision confidence of – 0.75. Five binary neurons are not enough. In this regard, the simulation of the result of combining up to 1000 binary neurons was performed. Results. Binary neurons cannot provide a confidence level greater than 0.93. A thousand ternary neurons can provide a confidence level of 0.98. The transition to 5-art artificial neurons should allow reaching a confidence level of 0.997 when combining 40 neurons. Conclusions. We observe a significant increase in the quality of decisions made by neural networks with an increase in the number of levels in their output quantizes. Natural neurons of living beings exchange bursts of impulses, which indirectly indicates that they have multilevel quantizes. There is no need to synthesize new statistical criteria; it is enough to switch to the use of q-ary artificial neurons, which are analogues of already known statistical criteria. 

statistical criteria, artificial neurons equivalent to statistical criteria, error correction of the neural network output code 

Ivanov A.I., Ivanov A.P., Savinov K.N., Eremenko R.V. Virtual enhancement of the effect of parallelization of calculations in the transition from binary neurons to the use of q-ary artificial neurons. Nadezhnost' i kachestvo slozhnykh sistem = Reliability and quality of complex systems. 2022;(4):89–97. (In Russ.). doi:10.21685/2307-4205-2022-4-10