ParalESN: Enabling parallel information processing in Reservoir Computing

TL;DR

ParalESN introduces a parallel reservoir computing model using diagonal linear recurrence in complex space, significantly improving scalability and efficiency while maintaining predictive accuracy for temporal processing tasks.

Contribution

The paper presents ParalESN, a novel parallel reservoir computing framework that preserves key properties and enhances scalability through structured operators and state space modeling.

Findings

Matches traditional RC accuracy on time series benchmarks

Reduces computational costs and energy consumption by orders of magnitude

Achieves competitive accuracy on pixel-level classification tasks

Abstract

Reservoir Computing (RC) has established itself as an efficient paradigm for temporal processing. However, its scalability remains severely constrained by (i) the necessity of processing temporal data sequentially and (ii) the prohibitive memory footprint of high-dimensional reservoirs. In this work, we revisit RC through the lens of structured operators and state space modeling to address these limitations, introducing Parallel Echo State Network (ParalESN). ParalESN enables the construction of high-dimensional and efficient reservoirs based on diagonal linear recurrence in the complex space, enabling parallel processing of temporal data. We provide a theoretical analysis demonstrating that ParalESN preserves the Echo State Property and the universality guarantees of traditional Echo State Networks while admitting an equivalent representation of arbitrary linear reservoirs in the complex diagonal form. Empirically, ParalESN matches the predictive accuracy of traditional RC on time series benchmarks, while delivering substantial computational savings. On 1-D pixel-level classification tasks, ParalESN achieves competitive accuracy with fully trainable neural networks while reducing computational costs and energy consumption by orders of magnitude. Overall, ParalESN offers a promising, scalable, and principled pathway for integrating RC within the deep learning landscape.