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，因其训练成本低、速度快、计算能力强，RC将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才刚刚起步。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关键。基于这一重要成果，本文揭示了RC神经网络中输入权重矩阵和循环权重矩阵的隐藏结构，并证明此类结构能够实现对AR型时间序列数据的完美预测。