Experimental study of Pac-Man conditions for learn-ability of discrete linear dynamical systems
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Date
2019-05-01
Authors
Damiyev, Zhaksybek
Journal Title
Journal ISSN
Volume Title
Publisher
Nazarbayev University School of Science and Technology
Abstract
In 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.
Description
Submitted to the Department of Mathematics on May 1, 2019, in partial fulfillment of the requirements for the degree of Master of Applied Mathematics
Keywords
Research Subject Categories::MATHEMATICS::Applied mathematics, discrete dynamical system