# Richness of Deep Echo State Network Dynamics

arXiv: https://arxiv.org/abs/1903.05174 · HTML: https://mlsanity.com/paper/1903.05174/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Mar 2019.

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

- [Echo State Speech Recognition](https://mlsanity.com/paper/2102.09114/) (2021)
- [Master memory function for delay-based reservoir computers with single-variable dynamics](https://mlsanity.com/paper/2108.12643/) (2021)
- [On the Post-hoc Explainability of Deep Echo State Networks for Time Series Forecasting, Image and Video Classification](https://mlsanity.com/paper/2102.08634/) (2021)

## Abstract (arXiv)

Reservoir Computing (RC) is a popular methodology for the efficient design of Recurrent Neural Networks (RNNs). Recently, the advantages of the RC approach have been extended to the context of multi-layered RNNs, with the introduction of the Deep Echo State Network (DeepESN) model. In this paper, we study the quality of state dynamics in progressively higher layers of DeepESNs, using tools from the areas of information theory and numerical analysis. Our experimental results on RC benchmark datasets reveal the fundamental role played by the strength of inter-reservoir connections to increasingly enrich the representations developed in higher layers. Our analysis also gives interesting insights into the possibility of effective exploitation of training algorithms based on stochastic gradient descent in the RC field.