# Reservoir Computing meets Recurrent Kernels and Structured Transforms

arXiv: https://arxiv.org/abs/2006.07310 · HTML: https://mlsanity.com/paper/2006.07310/

## Key facts

- Cited by 15 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 12 Jun 2020.

## Built on by (most cited first, 15 of 15)

- [A Framework for Machine Learning of Model Error in Dynamical Systems](https://mlsanity.com/paper/2107.06658/) (2021)
- [Neural signature kernels as infinite-width-depth-limits of controlled ResNets](https://mlsanity.com/paper/2303.17671/) (2023)
- [Unsupervised Reservoir Computing for Solving Ordinary Differential Equations](https://mlsanity.com/paper/2108.11417/) (2021)
- [Asymptotic Stability in Reservoir Computing](https://mlsanity.com/paper/2206.03854/) (2022)
- [Is the Number of Trainable Parameters All That Actually Matters?](https://mlsanity.com/paper/2109.11928/) (2021)
- [Beyond accuracy: generalization properties of bio-plausible temporal credit assignment rules](https://mlsanity.com/paper/2206.00823/) (2022)
- [Comparison of Reservoir Computing topologies using the Recurrent Kernel approach](https://mlsanity.com/paper/2401.14557/) (2024)
- [Revisiting Deep Information Propagation: Fractal Frontier and Finite-size Effects](https://mlsanity.com/paper/2508.03222/) (2025)
- [Kernel-based optimization of measurement operators for quantum reservoir computers](https://mlsanity.com/paper/2602.14677/) (2026)
- [Restrictions on Physical Stochastic Reservoir Computers](https://mlsanity.com/paper/2307.14474/) (2023)
- [Thermodynamic limit in learning period three](https://mlsanity.com/paper/2405.08825/) (2024)
- [Inertial Confinement Fusion Forecasting via Large Language Models](https://mlsanity.com/paper/2407.11098/) (2024)
- [ParalESN: Enabling parallel information processing in Reservoir Computing](https://mlsanity.com/paper/2601.22296/) (2026)
- [Reservoir Subspace Injection for Online ICA under Top-n Whitening](https://mlsanity.com/paper/2603.02178/) (2026)
- [Free-Probability Kernels for Zero-Rollout Hyperparameter Selection in Reservoir Computing](https://mlsanity.com/paper/2608.20998/) (2026)

## Abstract (arXiv)

Reservoir Computing is a class of simple yet efficient Recurrent Neural Networks where internal weights are fixed at random and only a linear output layer is trained. In the large size limit, such random neural networks have a deep connection with kernel methods. Our contributions are threefold: a) We rigorously establish the recurrent kernel limit of Reservoir Computing and prove its convergence. b) We test our models on chaotic time series prediction, a classic but challenging benchmark in Reservoir Computing, and show how the Recurrent Kernel is competitive and computationally efficient when the number of data points remains moderate. c) When the number of samples is too large, we leverage the success of structured Random Features for kernel approximation by introducing Structured Reservoir Computing. The two proposed methods, Recurrent Kernel and Structured Reservoir Computing, turn out to be much faster and more memory-efficient than conventional Reservoir Computing.