Training Echo State Networks with Regularization through Dimensionality Reduction

TL;DR

This paper presents a novel regularization framework for training Echo State Networks by projecting internal states onto lower-dimensional spaces, improving generalization and predictive performance on chaotic time-series.

Contribution

Introduces a dimensionality reduction-based regularization method for Echo State Networks, enhancing their ability to model complex dynamical systems.

Findings

Superior predictive performance on benchmark tests.

Lower-dimensional embeddings better preserve system dynamics.

Regularization improves generalization to unseen data.

Abstract

In this paper we introduce a new framework to train an Echo State Network to predict real valued time-series. The method consists in projecting the output of the internal layer of the network on a space with lower dimensionality, before training the output layer to learn the target task. Notably, we enforce a regularization constraint that leads to better generalization capabilities. We evaluate the performances of our approach on several benchmark tests, using different techniques to train the readout of the network, achieving superior predictive performance when using the proposed framework. Finally, we provide an insight on the effectiveness of the implemented mechanics through a visualization of the trajectory in the phase space and relying on the methodologies of nonlinear time-series analysis. By applying our method on well known chaotic systems, we provide evidence that the lower dimensional embedding retains the dynamical properties of the underlying system better than the full-dimensional internal states of the network.