Abstract

Reservoir computing is a machine learning method that solves tasks using the response of a dynamical system to a certain input. As the training scheme only involves optimising the weights of the responses of the dynamical system, this method is particularly suited for hardware implementation. Furthermore, the inherent memory of dynamical systems which are suitable for use as reservoirs mean that this method has the potential to perform well on time series prediction tasks, as well as other tasks with time dependence. However, reservoir computing still requires extensive task-dependent parameter optimisation in order to achieve good performance. We demonstrate that by including a time-delayed version of the input for various time series prediction tasks, good performance can be achieved with an unoptimised reservoir. Furthermore, we show that by including the appropriate time-delayed input, one unaltered reservoir can perform well on six different time series prediction tasks at a very low computational expense. Our approach is of particular relevance to hardware implemented reservoirs, as one does not necessarily have access to pertinent optimisation parameters in physical systems but the inclusion of an additional input is generally possible.

Highlights

  • Reservoir computing (RC) is a machine learning method that is suited to solving dynamical tasks [1]

  • The performance of the reservoir with additional delayed input is tested on six tasks; we first consider Mackey–Glass time series prediction for one, three, and ten steps into the future

  • For each of the three cases, the delayed input leads to a reduction in the normalised root mean squared error (NRMSE), ranging from 20% for s = 1 to over a factor three for s = 10

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Summary

Introduction

Reservoir computing (RC) is a machine learning method that is suited to solving dynamical tasks [1]. The main principle underpinning reservoir computing is that the reservoir projects the inputs into a sufficiently high dimensional phase space such that it suffices to linearly sample the response of the reservoir in order to approximate the desired target for a given task. For this to work, the reservoir must fulfil certain criteria: the response to sufficiently different inputs must be linearly separable, the reservoir must be capable of performing nonlinear transforms, and the reservoir must have the fading memory property [2]. The optimisation of the reservoir is a task-specific problem [1,10,11,12] and a universal reservoir, which performs well in a range of tasks, remains elusive

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