MARKOV NETWORK MODEL

Abstract

Markov networks synthesized from the N-scheme of the Markov algorithm, developed to replace his well-known y-scheme, are studied theoretically from the standpoint of theories of algorithms and categories. The provisions of the theory of Markov algorithms are developed in the direction of synthesizing methods for the joint processing of words and morphism values that are occurrences in these words. In Markov networks, morphisms are weighted according to the method adopted in artificial neural networks. The material for the synthesis of Markov networks are diagrams of Markov occurrences of words into each other, obtained from input data samples, by classifying occurrences in the alphabet M = λιτφпо1…оx/αβδγχκμ. The Markov network model and the activation function of its morphemes are synthesized and subjected to scientific analysis. The idea of joint consideration of category theory and the theory of Markov algorithms is developed for the control channel, so this control channel is understood as an n-category associator introduced into the N-scheme of the Markov algorithm. In Markov networks, chain termination mechanisms are studied, using the control channel command, using combined methods of classifying words and morphisms, previously studied for the N-scheme of his algorithm, the evolution of categories formed by words is considered due to their occurrences in each other. For the method of synthesizing training samples from diagrams of Markov occurrences, a scientific substantiation of prescriptions for processing samples is carried out. For activation functions, examples of their implementation are considered. The categorical representation of the activation function is synthesized for Markov networks and subjected to a separate scientific analysis. For single-layer and multi-layer Markov networks of direct distribution, a block diagram has been developed. In Markov networks, the concept of zero-nets is introduced. As a promising direction for further theoretical research in Markov networks, multilayer Markov networks of indirect propagation are singled out, which have a conclusion that cannot be considered normal according to Markov. In the conclusions to the study, it is noted that Markov networks have a category-theoretic representation and can be synthesized from Markov zero-nets.