# Evolutionary Echo State Network: evolving reservoirs in the Fourier space

arXiv: https://arxiv.org/abs/2206.04951 · HTML: https://mlsanity.com/paper/2206.04951/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 53 references that are in the map.
- First posted on arXiv 10 Jun 2022.

## Builds on (most cited first, 10 of 10)

- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Deep Echo State Network (DeepESN): A Brief Survey](https://mlsanity.com/paper/1712.04323/) (2017)
- [Controlling Recurrent Neural Networks by Conceptors](https://mlsanity.com/paper/1403.3369/) (2014)
- [Safe Mutations for Deep and Recurrent Neural Networks through Output Gradients](https://mlsanity.com/paper/1712.06563/) (2017)
- [Efficient Optimization of Echo State Networks for Time Series Datasets](https://mlsanity.com/paper/1903.05071/) (2019)
- [TE-ESN: Time Encoding Echo State Network for Prediction Based on Irregularly Sampled Time Series Data](https://mlsanity.com/paper/2105.00412/) (2021)
- [Reservoir Topology in Deep Echo State Networks](https://mlsanity.com/paper/1909.11022/) (2019)
- [An Experimental Analysis of the Echo State Network Initialization Using the Particle Swarm Optimization](https://mlsanity.com/paper/1501.00436/) (2015)
- [Empirical Analysis of the Necessary and Sufficient Conditions of the Echo State Property](https://mlsanity.com/paper/1703.06664/) (2017)
- [Neuroevolution on the Edge of Chaos](https://mlsanity.com/paper/1706.01330/) (2017)

## Built on by (most cited first, 2 of 2)

- [Re-visiting Reservoir Computing architectures optimized by Evolutionary Algorithms](https://mlsanity.com/paper/2211.06254/) (2022)
- [Evolutionary Algorithm for Reservoir Learning and Yielding](https://mlsanity.com/paper/2605.30372/) (2026)

## Abstract (arXiv)

The Echo State Network (ESN) is a class of Recurrent Neural Network with a large number of hidden-hidden weights (in the so-called reservoir). Canonical ESN and its variations have recently received significant attention due to their remarkable success in the modeling of non-linear dynamical systems. The reservoir is randomly connected with fixed weights that don't change in the learning process. Only the weights from reservoir to output are trained. Since the reservoir is fixed during the training procedure, we may wonder if the computational power of the recurrent structure is fully harnessed. In this article, we propose a new computational model of the ESN type, that represents the reservoir weights in the Fourier space and performs a fine-tuning of these weights applying genetic algorithms in the frequency domain. The main interest is that this procedure will work in a much smaller space compared to the classical ESN, thus providing a dimensionality reduction transformation of the initial method. The proposed technique allows us to exploit the benefits of the large recurrent structure avoiding the training problems of gradient-based method. We provide a detailed experimental study that demonstrates the good performances of our approach with well-known chaotic systems and real-world data.