Time Shifts to Reduce the Size of Reservoir Computers

TL;DR

This paper introduces a method to reduce the complexity of reservoir computers by using time-shifted output signals, enabling high performance with fewer nonlinear nodes and faster operation.

Contribution

The authors propose a novel time-shifting technique that simplifies reservoir computer design by decreasing the number of nonlinear nodes needed for effective computation.

Findings

High performance achieved with fewer nonlinear nodes

Delay-based reservoir computers operate at higher speeds

Time-shifting increases reservoir memory and rank

Abstract

A reservoir computer is a type of dynamical system arranged to do computation. Typically, a reservoir computer is constructed by connecting a large number of nonlinear nodes in a network that includes recurrent connections. In order to achieve accurate results, the reservoir usually contains hundreds to thousands of nodes. This high dimensionality makes it difficult to analyze the reservoir computer using tools from dynamical systems theory. Additionally, the need to create and connect large numbers of nonlinear nodes makes it difficult to design and build analog reservoir computers that can be faster and consume less power than digital reservoir computers. We demonstrate here that a reservoir computer may be divided into two parts; a small set of nonlinear nodes (the reservoir), and a separate set of time-shifted reservoir output signals. The time-shifted output signals serve to increase the rank and memory of the reservoir computer, and the set of nonlinear nodes may create an embedding of the input dynamical system. We use this time-shifting technique to obtain excellent performance from an opto-electronic delay-based reservoir computer with only a small number of virtual nodes. Because only a few nonlinear nodes are required, construction of a reservoir computer becomes much easier, and delay-based reservoir computers can operate at much higher speeds.