# Universality of reservoir systems with recurrent neural networks

arXiv: https://arxiv.org/abs/2403.01900 · HTML: https://mlsanity.com/paper/2403.01900/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 32 references that are in the map.
- First posted on arXiv 4 Mar 2024.

## Builds on (most cited first, 15 of 15)

- [Echo state networks are universal](https://mlsanity.com/paper/1806.00797/) (2018)
- [Approximation by Combinations of ReLU and Squared ReLU Ridge Functions with  ℓ1  and  ℓ0  Controls](https://mlsanity.com/paper/1607.07819/) (2016)
- [Approximation Bounds for Random Neural Networks and Reservoir Systems](https://mlsanity.com/paper/2002.05933/) (2020)
- [Reservoir Computing Universality With Stochastic Inputs](https://mlsanity.com/paper/1807.02621/) (2018)
- [On Generalization Bounds of a Family of Recurrent Neural Networks](https://mlsanity.com/paper/1910.12947/) (2019)
- [Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems](https://mlsanity.com/paper/1712.00754/) (2017)
- [Fading memory echo state networks are universal](https://mlsanity.com/paper/2010.12047/) (2020)
- [Simultaneous approximation of a smooth function and its derivatives by deep neural networks with piecewise-polynomial activations](https://mlsanity.com/paper/2206.09527/) (2022)
- [Neural network approximation and estimation of classifiers with classification boundary in a Barron class](https://mlsanity.com/paper/2011.09363/) (2020)
- [Neural Estimation of Statistical Divergences](https://mlsanity.com/paper/2110.03652/) (2021)
- [Discrete-time signatures and randomness in reservoir computing](https://mlsanity.com/paper/2010.14615/) (2020)
- [Non-Asymptotic Performance Guarantees for Neural Estimation of mathsff-Divergences](https://mlsanity.com/paper/2103.06923/) (2021)
- [Optimal Approximation of Zonoids and Uniform Approximation by Shallow Neural Networks](https://mlsanity.com/paper/2307.15285/) (2023)
- [Infinite-dimensional reservoir computing](https://mlsanity.com/paper/2304.00490/) (2023)
- [Universality and approximation bounds for echo state networks with random weights](https://mlsanity.com/paper/2206.05669/) (2022)

## Built on by (most cited first, 1 of 1)

- [Upper Generalization Bounds for Neural Oscillators](https://mlsanity.com/paper/2603.09742/) (2026)

## Abstract (arXiv)

Approximation capability of reservoir systems whose reservoir is a recurrent neural network (RNN) is discussed. We show what we call uniform strong universality of RNN reservoir systems for a certain class of dynamical systems. This means that, given an approximation error to be achieved, one can construct an RNN reservoir system that approximates each target dynamical system in the class just via adjusting its linear readout. To show the universality, we construct an RNN reservoir system via parallel concatenation that has an upper bound of approximation error independent of each target in the class.