ParalESN: Enabling parallel information processing in Reservoir Computing
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.
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Matteo Pinna
claimed_verified
2026-02-03T14:01:31.176Z
6898c8c3e9e1c6671e64a8ff
https://cdn-avatars.huggingface.co/v1/production/uploads/6898c8c3e9e1c6671e64a8ff/NLRxGoqH036cq5x55wvk6.jpeg
Matteo Pinna
nennomp
user
nennomp
6981fccb47987be58cdb7d26
Giacomo Lagomarsini
6981fccb47987be58cdb7d27
Andrea Ceni
6981fccb47987be58cdb7d28
Claudio Gallicchio
ParalESN: Enabling parallel information processing in Reservoir Computing
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.
Parallel Echo State Network (ParalESN) addresses reservoir computing limitations by enabling parallel temporal processing through diagonal linear recurrence, maintaining theoretical guarantees while achieving significant computational efficiency gains.
reservoir computing echo state property temporal processing parallel processing diagonal linear recurrence complex space state space modeling structured operators echo state networks temporal data