Fundamentals of information processing on an analog reservoir computer

Abstract

[eng] Physical dynamical systems are able to process information in a nontrivial manner. The machine learning paradigm of reservoir computing provides valuable insights into how information is memorized and nonlinearly transformed in these analog substrates. Since the computational capabilities of such systems are fundamentally different from those of well-studied digital computers, a theory for the assessment of a dynamical systems computational power is required. The information processing capacity (IPC) proposed by Dambre et al. provides such a quantitative framework. It allows to create a profile of memory and nonlinear transformation carried out by a system at hand. So far it has been used in simulation studies of various systems. In this thesis we evaluate the IPC in an experimental setup to assess information processing in a reservoir computer that consists of an analog Mackey-Glass nonlinearity coupled to itself via a delay line. We link the different dynamical regimes of this system to distinct modes of information processing and assess the influence of various dynamical phenomena, such as fixed point, periodic and chaotic dynamics on computation carried out by the system. We measure nonlinear memory up to seventh order and give its distribution as a function of the system parameters. Further we explore the influence of noise by performing matching numerical simulations. Thereby we find that the presence of noise, which is inevitable in every experimental setup, does not homogeneously degrade a system’s computational power as measured by the IPC, but instead implies a change in the distribution of capacity across the degrees of information processing observed in the system. Finally, we use theoretical considerations from the literature on the IPC to explain our observations and distill suggestions to guide experimental setup.