Construction of Logical Bases on Fast Neurons with Parabolic Activation Functions and Their Combinations with Linear Elements

The problem of constructing complete logical bases based on activation functions using parabolic functions and their combinations with linear elements is considered. To implement the basis based on the set 'AND', 'OR', 'NOT' neurons with one and two inputs are used. An alternative realization of the complete logical basis based on the 'AND-NOT' and 'OR-NOT' functions has been performed. It is known that the disadvantage of a widespread sigmoid is computational complexity, especially in multilayer neural networks. Based on experimental studies, it has been shown that the new activation functions provide advantages in terms of speed compared to the sigmoid, and are slightly inferior to it in terms of accuracy in approaching threshold values. It is supposed to use new activation functions and neurons based on them in the construction of computer technology elements, for example, triggers and adders. © 2025 Elsevier B.V., All rights reserved.