On the concept of influence in the concept of cognitive modeling when using the activation function of the ReLU type

The algorithmic principles of introducing nonlinear activation functions into the cognitive model of a complex weakly formalized system are considered. From the point of view of the transparency of theoretical consideration, a function of the ReLU type is used as such a nonlinear function. A complex system is represented as a directed graph, the vertices and edges of which are assigned certain values. The paper defines a nonlinear procedure for calculating the values of system elements (internal vertices) on a graph depending on external factors (input vertices) and, accordingly, calculating the coefficients of influence. It is shown that, in contrast to the linear case considered earlier, in the nonlinear case, the coefficients of influence significantly depend on the values of the vertices – elements of the system. Using the example of two simple models describing the main trends in global energy and the impact of some viral infection on the production process, the emergence of a richer set of scenarios for the development of the situation compared to the linear case is shown.