Stochastic reservoir computers

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. Recent advancements in reservoir computing, in particular quantum reservoir computing, use reservoirs that are inherently stochastic. In this paper, we investigate the universality of stochastic reservoir computers which use the probabilities of each stochastic reservoir state as the readout instead of the states themselves. This allows the number of readouts to 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 form universal approximating classes. We also investigate the performance of two practical examples in classification and chaotic time series prediction. While shot noise is a limiting factor, we show significantly improved performance compared to a deterministic reservoir computer with similar hardware when noise effects are small. Many recent advances in reservoir computing utilize inherently stochastic dynamics and can be designed so that the number of readouts scales exponentially with device size. Here, authors prove the universality of stochastic echo state networks and test the performance of two practical examples.