Algebraic properties of abstract neural network

I. I. Slepovichev

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 1, pp. 96-103

Résumé

The modern level of neuroinformatics allows to use artificial neural networks for the solution of various applied problems. However many neural network methods put into practice have no strict formal mathematical substantiation, being heuristic algorithms. It imposes certain restrictions on development of neural network methods of the solution of problems. At the same time there is a wide class of mathematical models which are well studied within such disciplines as theory of abstract algebras, graph theory, automata theory. Opportunity to use results received within these disciplines in relation to neural network models can be a good help in studying of artificial neural networks, their properties and functionality. In this work formulations and definitions of neural network models from the point of view of universal algebra and the theory of graphs are given. The main theorems of universal algebra are provided in neural network treatment. In article is also offered the way of the formal description of a neuronet by graph-schemes which allows to use results of graph theory for the analysis of neural network structures.