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.
Deep Time-Delay Reservoir Computing: Dynamics and Memory Capacity
Institute of Theoretical Physics, Technische Universität Berlin（柏林工业大学理论物理研究所）；Department of Mathematics, Humboldt-Universität zu Berlin（柏林洪堡大学数学系）；Institute of Mathematics, Technische Universität Berlin（柏林工业大学数学研究所）
Embedding Theory of Reservoir Computing and Reducing Reservoir Network Using Time Delays
Soochow University（苏州大学）；Fudan University（复旦大学）；Potsdam Institute for Climate Impact Research (PIK)（波茨坦气候影响研究所（PIK））；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）
Performance boost of time-delay reservoir computing by non-resonant clock cycle
Technische Universität Berlin（柏林工业大学）；Humboldt-Universität zu Berlin（柏林洪堡大学）；Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB)（跨学科物理与复杂系统研究所（IFISC，西班牙国家研究委员会-巴利阿里群岛大学））
Techniques for Enhancing Memory Capacity of Reservoir Computing
Graduate School of Life Science and Systems Engineering, Kyushu Institute of Technology（九州工业大学生命科学与系统工程学院）；Research Center for Neuromorphic AI Hardware, Kyushu Institute of Technology（九州工业大学神经形态人工智能硬件研究中心）；Faculty of Informatics, The University of Fukuchiyama（福知山公立大学信息学部）
Harnessing Synthetic Active Particles for Physical Reservoir Computing
Peter Debye Institute for Soft Matter Physics, Leipzig University（莱比锡大学彼得·德拜软物质物理研究所）；Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI) Dresden/Leipzig（德累斯顿/莱比锡可扩展数据分析与人工智能中心（ScaDS.AI））
Next-Generation Reservoir Computing for Dynamical Inference
Centre for Mathematical Science, Lund University（数学科学中心，隆德大学）；IMFUFA, Department of Science and Environment, Roskilde University（IMFUFA，科学与环境系，罗斯基尔德大学）
Optimizing the Network Topology of a Linear Reservoir Computer
K. N. Toosi University of Technology, Tehran, Iran（德黑兰技术大学）；Catholic University of America, Washington, D.C., United States（美国天主教大学）；University of New Mexico, Albuquerque, NM 87131, United States（新墨西哥大学）；Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany（复杂系统物理研究所）
Identifying Systems with Symmetries using Equivariant Autoregressive Reservoir Computers
Department of Statistics and Research, CNBS（统计与研究系，CNBS）；Department of Applied Mathematics, UNAH（应用数学系，UNAH）；Department of Chemical Engineering, Norwegian University of Science and Technology（化学工程系，挪威科学技术大学）
