Reservoir computing is a form of machine learning that utilizes nonlinear
dynamical systems to perform complex tasks in a cost-effective manner when
compared to typical neural networks. Many recent advancements in reservoir
computing, in particular quantum reservoir computing, make use of reservoirs
that are inherently stochastic. However, the theoretical justification for
using these systems has not yet been well established. In this paper, we
investigate the universality of stochastic reservoir computers, in which we use
a stochastic system for reservoir computing using the probabilities of each
reservoir state as the readout instead of the states themselves. In stochastic
reservoir computing, the number of distinct states of the entire reservoir
computer can potentially scale exponentially with the size of the reservoir
hardware, offering the advantage of compact device size. We prove that classes
of stochastic echo state networks, and therefore the class of all stochastic
reservoir computers, are universal approximating classes. We also investigate
the performance of two practical examples of stochastic reservoir computers in
classification and chaotic time series prediction. While shot noise is a
limiting factor in the performance of stochastic reservoir computing, we show
significantly improved performance compared to a deterministic reservoir
computer with similar hardware in cases where the effects of noise are small.

该论文研究了随机库容计算机的普适性，证明了具有随机特性的库容计算机是一种普遍的逼近类，并通过两个实际应用示例展示了其在分类和混沌时间序列预测方面相对确定性库容计算机的高性能。