Нейромережа Хопфілда як відкрита динамічна система

Abstract

The paper provides an analysis of a Hopfield neural network model from the standpoint of the concept of open dynamic systems (ODS) offered earlier. According to it, the evolution of the universe can be represented as a sequence of stages of the ODS development, during which more and more complex ODSs were formed. Living cells were later formed from them and their further development led to the appearance of humans and their intelligence, the formation of civilization, and the emergence of artificial intelligence. An overview of the provisions of the ODS concept is presented and the stage of the emergence of life as a collective development of ODS in the form of populations of the offspring of the mother cell, that led to the emergence of complex organisms, the nervous system, human, and intelligence as an intangible form of the ODS development, is analyzed in detail. It has been suggested that transforming an inanimate macromolecule of ODS into a living cell is connected with the appearance in its composition of a multistable component like a Hopfield network, whose prototype – spin glass – is a quantum object that existed even before the emergence of life on Earth. To verify it, there has been car-ried out a detailed analysis of the Hopfield network model as a linear manifold stretched over a set of memorized data vectors. New evidence of the network convergence process coinciding is presented, and the source of energy that a living cell requires for reproduction is revealed. In the paper, a structure of a living ODS that is similar to the Hopfield network and supplemented with a reproduction module similar to a DNA molecule is offered. It fully corresponds to the struc-ture of the first bacteria on Earth detected by archaeologists. The results of the study confirm the efficiency of the methods of the ODS concept when studying the dynamics of the develop-ment of systems of different natures, including the latest artificial intelligence systems whose behavior may not be controlled.