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 analyzing the small signal response of the reservoir. Our results suggest that any dynamical system used as a reservoir can be analyzed 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.
翻译:在本文中,我们深刻地洞察了通过电子价值分析计算延迟的储油层的计算能力。我们集中研究独立的任务内存能力,以量化储油层的性能,并将这些内存能力与动态系统的电子价值频谱进行比较。我们表明,这两个数量是紧密相连的,因此储油层的计算性能可以通过分析储油层的小型信号反应而预测。我们的结果表明,任何用作储油层的动态系统都可以以这种方式加以分析。我们采用的方法典型地适用于光学激光系统,提供反馈,并将数字计算的回收能力与电子价值频谱作比较。对真正零和离共的假想部件具有电子价值的系统来说,其最佳性能被找到。