Reservoir Computing (RC) is a type of recursive neural network (RNN), and there can be no doubt that the RC will be more and more widely used for building future prediction models for time-series data, with low training cost, high speed and high computational power. However, research into the mathematical structure of RC neural networks has only recently begun. Bollt (2021) clarified the necessity of the autoregressive (AR) model for gaining the insight into the mathematical structure of RC neural networks, and indicated that the Wold decomposition theorem is the milestone for understanding of these. Keeping this celebrated result in mind, in this paper, we clarify hidden structures of input and recurrent weight matrices in RC neural networks, and show that such structures attain perfect prediction for the AR type of time series data.

翻译：储层计算（RC）是一种递归神经网络（RNN），毫无疑问，RC 将因其低训练成本、高速和高计算能力而越来越广泛地用于构建时间序列数据的未来预测模型。然而，关于 RC 神经网络数学结构的研究最近才刚开始。Bollt（2021）阐明了自回归（AR）模型对于理解 RC 神经网络数学结构的必要性，并指出 Wold 分解定理是理解这些结构的重要里程碑。基于这一杰出成果，本文阐明了 RC 神经网络中输入权重矩阵和循环权重矩阵的隐藏结构，并证明了这些结构能够对 AR 类型的时间序列数据实现完美预测。