An Analytical Approach to Single Node Delay-Coupled Reservoir Computing

Schumacher, Johannes; Toutounji, Hazem; Pipa, Gordon

Abstract

Reservoir computing has been successfully applied in difficult time series prediction tasks by injecting an input signal into a spatially extended reservoir of nonlinear subunits to perform history-dependent nonlinear computation. Recently, the network was replaced by a single nonlinear node, delay-coupled to itself. Instead of a spatial topology, subunits are arrayed in time along one delay span of the system. As a result, the reservoir exists only implicitly in a single delay differential equation, numerical solving of which is costly. We derive here approximate analytical equations for the reservoir by solving the underlying system explicitly. The analytical approximation represents the system accurately and yields comparable performance in reservoir benchmark tasks, while reducing computational costs by several orders of magnitude. This has important implications with respect to electronic realizations of the reservoir and opens up new possibilities for optimization and theoretical investigation.

• Conference Name: 23rd International Conference on Artificial Neural Networks (ICANN)
• Start Date: Sep 10, 2013
• End Date: Sep 13, 2013
• Publication Date: 2013
• Deposit Date: Jul 6, 2020
• Pages: 26-33
• Series Title: Lecture Notes in Computer Science
• Series Number: 8131
• Book Title: Artificial Neural Networks and Machine Learning – ICANN 2013 23rd International Conference on Artificial Neural Networks Sofia, Bulgaria, September 10-13, 2013. Proceedings
• ISBN: 9783642407277
• DOI: https://doi.org/10.1007/978-3-642-40728-4_4
• Public URL: https://nottingham-repository.worktribe.com/output/4754335
• Publisher URL: https://link.springer.com/chapter/10.1007%2F978-3-642-40728-4_4