# Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems

arXiv: https://arxiv.org/abs/1712.00754 · HTML: https://mlsanity.com/paper/1712.00754/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2017.

## Built on by (most cited first, 30 of 39)

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- [ResCP: Reservoir Conformal Prediction for Time Series Forecasting](https://mlsanity.com/paper/2510.05060/) (2025)
- [Stochastic Reservoir Computers](https://mlsanity.com/paper/2405.12382/) (2024)
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- [Fading memory and the convolution theorem](https://mlsanity.com/paper/2408.07386/) (2024)
- [Quantum Reservoir Computing and Risk Bounds](https://mlsanity.com/paper/2501.08640/) (2025)
- [ParalESN: Enabling parallel information processing in Reservoir Computing](https://mlsanity.com/paper/2601.22296/) (2026)
- [Interpretable Design of Reservoir Computing Networks using Realization Theory](https://mlsanity.com/paper/2112.06891/) (2021)
- [Universal Time-Uniform Trajectory Approximation for Random Dynamical Systems with Recurrent Neural Networks](https://mlsanity.com/paper/2211.08018/) (2022)
- [Refined Kolmogorov Complexity of Analog, Evolving and Stochastic Recurrent Neural Networks](https://mlsanity.com/paper/2309.17032/) (2023)
- [Universality of reservoir systems with recurrent neural networks](https://mlsanity.com/paper/2403.01900/) (2024)
- [Separation capacity of linear reservoirs with random connectivity matrix](https://mlsanity.com/paper/2404.17429/) (2024)
- [Upper Approximation Bounds for Neural Oscillators](https://mlsanity.com/paper/2512.01015/) (2025)

## Abstract (arXiv)

A new class of non-homogeneous state-affine systems is introduced for use in reservoir computing. Sufficient conditions are identified that guarantee first, that the associated reservoir computers with linear readouts are causal, time-invariant, and satisfy the fading memory property and second, that a subset of this class is universal in the category of fading memory filters with stochastic almost surely uniformly bounded inputs. This means that any discrete-time filter that satisfies the fading memory property with random inputs of that type can be uniformly approximated by elements in the non-homogeneous state-affine family.