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Frequency Domain Reservoir Computing

NeurIPS 2026 · Architectures and efficiency › RNNs and normalization · approach: Brain-inspired recurrent architectures · 0 citations (OpenAlex)

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Introduces FRESCO, an echo state network that runs entirely in the frequency domain using dimensional zero-padding, circulant-style Hadamard recurrence, and a packed real-valued readout to get O(N) per-step cost with ridge-regression training.

Problem

Dense echo state networks have O(N^2) per-step state updates, and naive frequency-domain versions incur costly FFT/IFFT domain transitions, limiting ESN scalability to large reservoirs.

Approach

Lift the 1D circular convolution to 2D so a low-dimensional input is embedded via an N_x-point FFT (dimensional zero-padding), run the recurrence as element-wise complex Hadamard products on frequency-domain weights, apply a native frequency-domain invabs nonlinearity with optional circular-shift mixing, and read out from a packed, non-redundant real vector so no inverse FFT is needed.

Key results

• On long-horizon forecasting, FRESCO matches or exceeds deep sequence baselines while consuming up to three orders of magnitude less energy.
• FRESCO runs up to two orders of magnitude faster than dense ESNs at the largest reservoir sizes on Mackey-Glass and NARMA10.
• On ten UCR/UEA classification datasets, FRESCO reaches inference speedups up to 26x over standard ESNs with accuracy statistically in a single clique under Wilcoxon testing.

Surprising findings

• FRESCO (mix) and FRESCO (plain) performance is task-dependent; the optimal variant varies across classification datasets.
• On Libras, hyperparameter search selected a small ESN paired with a much larger FRESCO configuration, the sole case where FRESCO was not competitive.

Limitations

• Linear O(N) scaling requires constraining recurrent connectivity to circulant (circular convolution) structure, a structural prior.
• The optimal choice between isolated-frequency and cross-frequency mixing variants is task-dependent.
• Forecasting comparison uses a generic hyperparameter search and fixed recurrent dynamics, and results are taken from literature for some baselines.

Experimental setup

Datasets: NARMA10 Mackey-Glass UCR/UEA archive (ten datasets) ETT Solar Weather

Benchmarks: NARMA10 Mackey-Glass UCR/UEA ten-dataset classification ETT Solar Weather

Metrics: NRMSE accuracy MSE MAE inference time energy (kWh)

Baselines: standard ESN LSTM Mamba Transformer iTransformer PatchTST TimesNet FEDformer Autoformer

Builds on: Echo State Networks circular convolution theorem Mamba S4

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