The weekly Wednesday seminar on 17 December 2014, 10.00 a.m., will feature сhair of the department of “Theory of Functions” c.ph-m.s. Vugar Ismailov who will talk about «Hilbert’s 13-th problem and neural networks».

In this talk, we present a survey on Hilbert’s 13-th problem, its solution by V.I.Arnold and A.N.Kolmogorov, and some important results on the theory of linear superpositions, arisen from the Kolmogorov superposition theorem. Then the mathematical models of one and two hidden layer neural networks and some approximation results concerning such networks will be considered. Using the Kolmogorov superposition theorem, we give the analysis of one new result on the approximation of multivariate functions by two hidden layer neural networks.