Frequency Domain Reservoir Computing

2026-06-23

AI Summary

This work addresses the scalability limitations of traditional echo state networks (ESNs), which suffer from an O(N²) state-update bottleneck due to their reliance on large reservoirs. The authors propose a fully frequency-domain reservoir computing architecture that eliminates time–frequency conversion overhead by leveraging zero-padded input embeddings, native frequency-domain nonlinear activation, and a packed frequency-domain readout mechanism, thereby achieving O(N) computational complexity for recurrent state updates. Combined with a closed-form training solution and fast Fourier transforms, the proposed method attains state-of-the-art performance on memory capacity, sequence classification, and multivariate long-term forecasting tasks while substantially reducing computational cost and energy consumption.

Abstract

While the quadratic sequence-length bottleneck of transformers has fueled a resurgence in recurrent models, effectively capturing complex dynamics requires architectures that balance efficient training with highly expressive latent states. Echo State Networks (ESNs) offer a compelling approach by utilizing fixed recurrent weights to circumvent backpropagation through time, enabling a closed-form training solution. However, achieving the expressivity needed for complex tasks demands large reservoirs, exposing an $\mathcal{O}(N^2)$ state-update bottleneck that prevents ESNs from matching the scale of contemporary recurrent models. To address this limitation, we introduce Frequency Domain Reservoir Computing (FRESCO), an ESN architecture operating entirely in the frequency domain while avoiding domain-shift overheads to achieve $\mathcal{O}(N)$ complexity for dense, non-linear recurrent updates. By employing a novel dimensional zero-padding input embedding, a packed \FDh readout, and a natively applied frequency-domain non-linearity, FRESCO drastically reduces computational costs and energy consumption of training and inference. Furthermore, FRESCO matches the state-of-the-art predictive performance on memory benchmarks, sequential classification, and multivariate long-horizon forecasting, offering a scalable path forward for dense recurrent architectures.

Problem

• Echo State Networks
• computational bottleneck
• reservoir computing
• recurrent models
• scalability

Innovation

• Frequency Domain Reservoir Computing
• Echo State Networks
• O(N) complexity
• frequency-domain non-linearity
• recurrent architectures