Interpretable Design of Reservoir Computing Networks Using Realization Theory
Interpretable Design of Reservoir Computing Networks Using Realization Theory
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DOI：
10.1109/tnnls.2021.3136495
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发表时间：
2021-12
影响因子：
10.4
通讯作者：
Wei Miao;Vignesh Narayanan;Jr-Shin Li
中科院分区：
文献类型：
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作者：
Wei Miao;Vignesh Narayanan;Jr-Shin Li
油藏计算网络（RCN）已成功用作学习和复杂决策任务的工具。尽管 RCN 效率高且训练成本低，但其实际应用在很大程度上依赖于经验设计。在本文中，我们开发了一种使用线性动力系统的实现理论来设计 RCN 的算法。特别是，我们引入了 $\alpha $ 稳定实现的概念，并提供了一种有效的方法来修剪线性 RCN 的大小，而不会降低训练精度。此外，我们基于系统论中可控性和可观性的概念，推导了线性RCN中隐藏节点数量不可约性的充要条件。利用线性 RCN 设计，我们提供了一种易于处理的程序来实现具有非线性激活函数的 RCN。我们提出了预测时滞系统和混沌系统的数值实验，以验证所提出的 RCN 设计方法并证明其有效性。
The reservoir computing networks (RCNs) have been successfully employed as a tool in learning and complex decision-making tasks. Despite their efficiency and low training cost, practical applications of RCNs rely heavily on empirical design. In this article, we develop an algorithm to design RCNs using the realization theory of linear dynamical systems. In particular, we introduce the notion of $\alpha $ -stable realization and provide an efficient approach to prune the size of a linear RCN without deteriorating the training accuracy. Furthermore, we derive a necessary and sufficient condition on the irreducibility of the number of hidden nodes in linear RCNs based on the concepts of controllability and observability from systems theory. Leveraging the linear RCN design, we provide a tractable procedure to realize RCNs with nonlinear activation functions. We present numerical experiments on forecasting time-delay systems and chaotic systems to validate the proposed RCN design methods and demonstrate their efficacy.