# Composite FORCE learning of chaotic echo state networks for time-series prediction

arXiv: https://arxiv.org/abs/2207.02420 · HTML: https://mlsanity.com/paper/2207.02420/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 38 references that are in the map.
- First posted on arXiv 6 Jul 2022.

## Builds on (most cited first, 5 of 5)

- [full-FORCE: A Target-Based Method for Training Recurrent Networks](https://mlsanity.com/paper/1710.03070/) (2017)
- [Supervised Learning in Spiking Neural Networks with FORCE Training](https://mlsanity.com/paper/1609.02545/) (2016)
- [Designing spontaneous behavioral switching via chaotic itinerancy](https://mlsanity.com/paper/2002.08332/) (2020)
- [One step back, two steps forward: interference and learning in recurrent neural networks](https://mlsanity.com/paper/1805.09603/) (2018)
- [Populations of Spiking Neurons for Reservoir Computing: Closed Loop Control of a Compliant Quadruped](https://mlsanity.com/paper/2004.04560/) (2020)

## Built on by (most cited first, 1 of 1)

- [Improving the Performance of Echo State Networks Through State Feedback](https://mlsanity.com/paper/2312.15141/) (2023)

## Abstract (arXiv)

Echo state network (ESN), a kind of recurrent neural networks, consists of a fixed reservoir in which neurons are connected randomly and recursively and obtains the desired output only by training output connection weights. First-order reduced and controlled error (FORCE) learning is an online supervised training approach that can change the chaotic activity of ESNs into specified activity patterns. This paper proposes a composite FORCE learning method based on recursive least squares to train ESNs whose initial activity is spontaneously chaotic, where a composite learning technique featured by dynamic regressor extension and memory data exploitation is applied to enhance parameter convergence. The proposed method is applied to a benchmark problem about predicting chaotic time series generated by the Mackey-Glass system, and numerical results have shown that it significantly improves learning and prediction performances compared with existing methods.