Alexander Yu. Dorogov

St. Petersburg State Electrotechnical University, PJSC “Information Telecommunication Technologies” (“Inteltech”)

The plasticity of multilayer modular neural networks with the characteristic property of self-similarity is investigated in the paper. The concept of degrees of freedom, known from mechanics, is used to assess plasticity. The number of degrees of freedom of the network is estimated by the maximum dimension of the operator manifold of the neural network formed by variation of the parameters of neural modules and the presence of intermodule connections. To obtain plasticity estimates, neural modules are considered as linear operators of fixed rank. Calculation formulas for calculating the dimension of the operator manifold of a neural module outside and within the network are obtained. A neural network is considered as a dual operator of a complex structure, the input and output of which are vector spaces. At the level of the structural model, the concept of modal network states is introduced, characterizing the dimensions of vector subspaces at the input and output of neural modules in the network. The dimensionality of the network manifold is estimated through its modal states. It is noted that selfsimilar networks belong to a class of weakly coupled networks for which the calculation of modal states does not cause difficulties. Exact formulas for calculating the degree of plasticity of weakly coupled neural networks are obtained, the results of the analysis are used to assess the plasticity of fast neural networks (BNS), and their subsets - pyramidal BNS of direct and reverse orientation

Neural network, structural model, self-similarity, modal states, plasticity, degrees of freedom