ИСТИНА

The report will focus on some problems of the modern theory of artificial neural networks and their connection with integrable structures in statistical physics. The main example of a nonlinear dynamical neural network in this talk is the Hopfield’s multiattractor network [1,2]. I will describe the main problems stated in the mathematical context of this model and describe the relationship of these problems with the methods of exactly solved models of statistical mechanics, including the Ising model. The exposition is based on works [3,4]. The authors were supported by the Russian Foundation for Basic Research (project no. 17-01-00366). REFERENCES 1. W. A. Little. The Existence of Persistent States in the Brain, Math. Biosciences 19,101-120 (1974) 101 2. J. J. Hopfield. Neural networks and physical systems with emergent collective com- putational abilities. in Pk. Nat. Academy Sci., USA, vol. 19, 1982, pp. 2554-2558. 3. Dmitry V. Talalaev. Towards integrable structure in 3d Ising model, arXiv:1805.04138 4. Dmitry V. Talalaev. Asymmetric Hopfield neural network and Twisted tetrahedron equation, arXiv:1806.06680