Damiyev, ZhaksybekTakhanov, RustemTourassis, Vassilios D.2019-08-292019-08-292019-05-01http://nur.nu.edu.kz/handle/123456789/4191Submitted to the Department of Mathematics on May 1, 2019, in partial fulfillment of the requirements for the degree of Master of Applied MathematicsIn this work, we are going to reconstruct parameters of a discrete dynamical system with a hidden layer, given by a quadruple of matrices (𝐴,𝐵,𝐶,𝐷), from system’s past behaviour. First, we reproduced experimentally the well-known result of Hardt et al. that the reconstruction can be made under some conditions, called Pac-Man conditions. Then we demonstrated experimentally that the system approaches the global minimum even if an input 𝑥 is a sequence of i.i.d. random variables with a nongaussian distribution. We also formulated hypotheses beyond Pac-Man conditions that Gradient Descent solves the problem if the operator norm (or alternatively, the spectral radius) of transition matrix 𝐴 is bounded by 1 and obtained the negative result, i.e. a counterexample to those conjectures.enAttribution-NonCommercial-ShareAlike 3.0 United StatesResearch Subject Categories::MATHEMATICS::Applied mathematicsdiscrete dynamical systemMaster's thesis