# Comparison of Reservoir Computing topologies using the Recurrent Kernel approach

arXiv: https://arxiv.org/abs/2401.14557 · HTML: https://mlsanity.com/paper/2401.14557/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 21 references that are in the map.
- First posted on arXiv 25 Jan 2024.

## Builds on (most cited first, 6 of 6)

- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Orthogonal Random Features](https://mlsanity.com/paper/1610.09072/) (2016)
- [Random vector functional link network: recent developments, applications, and future directions](https://mlsanity.com/paper/2203.11316/) (2022)
- [Reservoir Computing meets Recurrent Kernels and Structured Transforms](https://mlsanity.com/paper/2006.07310/) (2020)
- [Sparsity in Reservoir Computing Neural Networks](https://mlsanity.com/paper/2006.02957/) (2020)
- [Asymptotic Stability in Reservoir Computing](https://mlsanity.com/paper/2206.03854/) (2022)

## Built on by (most cited first, 3 of 3)

- [Revisiting Deep Information Propagation: Fractal Frontier and Finite-size Effects](https://mlsanity.com/paper/2508.03222/) (2025)
- [ParalESN: Enabling parallel information processing in Reservoir Computing](https://mlsanity.com/paper/2601.22296/) (2026)
- [Free-Probability Kernels for Zero-Rollout Hyperparameter Selection in Reservoir Computing](https://mlsanity.com/paper/2608.20998/) (2026)

## Abstract (arXiv)

Reservoir Computing (RC) has become popular in recent years thanks to its fast and efficient computational capabilities. Standard RC has been shown to be equivalent in the asymptotic limit to Recurrent Kernels, which helps in analyzing its expressive power. However, many well-established RC paradigms, such as Leaky RC, Sparse RC, and Deep RC, are yet to be systematically analyzed in such a way. We define the Recurrent Kernel limit of all these RC topologies and conduct a convergence study for a wide range of activation functions and hyperparameters. Our findings provide new insights into various aspects of Reservoir Computing. First, we demonstrate that there is an optimal sparsity level which grows with the reservoir size. Furthermore, our analysis suggests that Deep RC should use reservoir layers of decreasing sizes. Finally, we perform a benchmark demonstrating the efficiency of Structured Reservoir Computing compared to vanilla and Sparse Reservoir Computing.