Topological Properties of Reservoir Computing Architectures as Probes for Hyperparameter Optimization

Kurzfassung

The efficiency and performance of Reservoir Computing (RC) depend critically on various hyperparameters, which to date have been guided largely by heuristics. A deeper understanding is needed of how RCs learn and of the mathematical relationship linking hyperparameters to learning ability and prediction performance. In this thesis, we develop a novel approach that uses topological statistics such as continuity and differentiability on a specialized minimal RC architecture to optimize the minimal nonlinearity of the readout and the offset parameters in two system and three system multifunctional reservoirs. We provide our own numerical implementation of these topological statistics. We perform this study in the context of dynamical systems as synthetic data and use the minimal RC architecture, and the classical RC architecture as the basis for our conclusions. The methods we propose are useful in understanding the structure of the reservoir and the process of embedding the data within the reservoir. We provide a method that correctly predicts regions in parameter space conducive to multifunctionality.