In this paper we give a profound insight into the computation capability of delay based reservoir computing via an eigenvalue analysis. We concentrate on the task-independent memory capacity to quantify the reservoir performance and compare these with the eigenvalue spectrum of the dynamical system. We show that these two quantities are deeply connected, and thus the reservoir computing performance is predictable by analysing the small signal response of the reservoir. Our results suggest that any dynamical system used as a reservoir can be analysed in this way. We apply our method exemplarily to a photonic laser system with feedback and compare the numerically computed recall capabilities with the eigenvalue spectrum. Optimal performance is found for a system with the eigenvalues having real parts close to zero and off-resonant imaginary parts.

在本文中，我们通过特征值分析深入了解基于延迟的储层计算的计算能力。我们专注于与任务无关的内存容量来量化储层性能，并将其与动力系统的特征值谱进行比较。我们表明这两个量是紧密相连的，因此通过分析储层的小信号响应可以预测储层计算性能。我们的结果表明，任何用作储层的动力系统都可以通过这种方式进行分析。我们将我们的方法示例性地应用于具有反馈的光子激光系统，并将数值计算的召回能力与特征值谱进行比较。对于特征值具有接近于零的实部和非共振虚部的系统，可以找到最佳性能。