# Stochastic Reservoir Computers

arXiv: https://arxiv.org/abs/2405.12382 · HTML: https://mlsanity.com/paper/2405.12382/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 46 references that are in the map.
- First posted on arXiv 20 May 2024.

## Builds on (most cited first, 16 of 16)

- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Echo state networks are universal](https://mlsanity.com/paper/1806.00797/) (2018)
- [Failures of Gradient-Based Deep Learning](https://mlsanity.com/paper/1703.07950/) (2017)
- [Reservoir Computing Universality With Stochastic Inputs](https://mlsanity.com/paper/1807.02621/) (2018)
- [Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems](https://mlsanity.com/paper/1712.00754/) (2017)
- [Reservoir computing approaches for representation and classification of multivariate time series](https://mlsanity.com/paper/1803.07870/) (2018)
- [Using a reservoir computer to learn chaotic attractors, with applications to chaos synchronisation and cryptography](https://mlsanity.com/paper/1802.02844/) (2018)
- [Rapid Time Series Prediction with a Hardware-Based Reservoir Computer](https://mlsanity.com/paper/1807.07627/) (2018)
- [Learning Nonlinear Input-Output Maps with Dissipative Quantum Systems](https://mlsanity.com/paper/1901.01653/) (2019)
- [A full-stack view of probabilistic computing with p-bits: devices, architectures and algorithms](https://mlsanity.com/paper/2302.06457/) (2023)
- [Quantum-limited stochastic optical neural networks operating at a few quanta per activation](https://mlsanity.com/paper/2307.15712/) (2023)
- [Simple Cycle Reservoirs are Universal](https://mlsanity.com/paper/2308.10793/) (2023)
- [Large-scale spatiotemporal photonic reservoir computer for image classification](https://mlsanity.com/paper/2004.02542/) (2020)
- [Universality and approximation bounds for echo state networks with random weights](https://mlsanity.com/paper/2206.05669/) (2022)
- [Nonlinear Autoregression with Convergent Dynamics on Novel Computational Platforms](https://mlsanity.com/paper/2108.08001/) (2021)
- [Universal Time-Uniform Trajectory Approximation for Random Dynamical Systems with Recurrent Neural Networks](https://mlsanity.com/paper/2211.08018/) (2022)

## Built on by (most cited first, 4 of 4)

- [Optical Echo State Network Reservoir Computing](https://mlsanity.com/paper/2504.08224/) (2025)
- [Reservoir-enhanced Segment Anything Model for Subsurface Diagnosis](https://mlsanity.com/paper/2504.18802/) (2025)
- [A Solvable Molecular Switch Model for Stable Temporal Information Processing](https://mlsanity.com/paper/2508.15451/) (2025)
- [Self-induced stochastic resonance: A physics-informed machine learning approach](https://mlsanity.com/paper/2510.22848/) (2025)

## Abstract (arXiv)

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.