Research map / Time series / Long-term forecasting
Spectral-Aware Reservoir Computing for Fast and Accurate Time Series Classification
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Proposes SARC, a training-free reservoir computing framework that extracts multi-scale prominent frequencies (HP-filter, wavelet decomposition, FFT) and uses FreqRes reservoirs with cycle connections plus ridge-regression readouts as dynamic features for time series classification.
Problem
Standard reservoir computing relies on recursive updates from adjacent states and struggles to capture long-term and cyclical dependencies in time series classification, while gradient-based deep models are costly.
Approach
Detrend and wavelet-decompose the series, pick dominant FFT frequencies and their sub-harmonics, then for each frequency run a reservoir with an added cycle connection (state at n-p) whose ridge-regression readout weights serve as dynamic features, fed to a Ridge classifier.
Key results
- SARC achieves the highest average accuracy of 0.8508 and average F1 of 0.8449 across 128 UCR datasets, versus 0.8484 for COTE and 0.8450 for Rocket.
- SARC improves average accuracy by 8.19% over rmESN and 4.00% over ConvMESN.
- SARC beats single BiESN on 119 of 128 datasets (3 ties, 6 losses) and is tens to hundreds of times faster than ConvMESN and InceptionTime in training.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add spectral awareness and multi-scale FreqRes modules to BiESN (ablation) | BiESN · UCR Archive (128 datasets) | accuracy: Win: 119; Tie: 3; Loose: 6 | Helped |
| Replace BiESN with LSTM-based FreqRes (ablation) | SARC · UCR Archive (128 datasets) | accuracy | Hurt |
| Replace BiESN with GRU-based FreqRes (ablation) | SARC · UCR Archive (128 datasets) | accuracy | Hurt |
| Use ESN, LeakyESN, or DeepESN instead of BiESN (ablation) | SARC · UCR Archive (128 datasets) | accuracy: 1.55% | No clear effect |
| Remove derived dynamic features and use only max-pooled hidden states (ablation) | SARC · UCR Archive (128 datasets) | accuracy | Hurt |
| Replace derived dynamic features with average-pooled hidden states (ablation) | SARC · UCR Archive (128 datasets) | accuracy: 5.97% | Hurt |
| Replace derived dynamic features with the final hidden state (ablation) | SARC · UCR Archive (128 datasets) | accuracy: 10.81% | Hurt |
| Use Ridge instead of LR or KNN as the classifier (ablation) | SARC · UCR Archive (128 datasets) | accuracy | Helped |
| Increase threshold κ (ablation) | SARC · UCR Archive (128 datasets) | accuracy | Helped |
| Increase reservoir size (ablation) | SARC · UCR Archive (128 datasets) | accuracy | No clear effect |
| Increase leaky rate above 0.2 (ablation) | SARC · UCR Archive (128 datasets) | accuracy | Hurt |
| Tune spectral radii toward 0.8 for Ws and 0.6 for Wc (ablation) | SARC · UCR Archive (128 datasets) | accuracy: 0.8 for Ws and 0.6 for Wc | Helped |
Surprising findings
- Directly applying gated RNNs (LSTM, GRU) as the reservoir yields notably worse accuracy than plain ESN variants.
- Reservoir size has minimal impact on accuracy but substantially increases runtime.
Limitations
- Accuracy gap over COTE is not statistically significant (p=0.403), so gains over top ensembles are modest.
- Runtime is only slightly exceeded by rmESN; runtime grows with threshold kappa and reservoir size.
Experimental setup
Datasets: UCR Time Series Archive (128 datasets)
Benchmarks: UCR Time Series Archive (128 datasets)
Metrics: accuracy F1-score average rank Wilcoxon signed-rank p-value wins/ties/losses runtime
Baselines: rmESN ConvMESN TimesNet InceptionTime COTE Hydra Rocket MiniRocket
Builds on: Echo State Network Hodrick-Prescott filter Bidirectional ESN rmESN ConvMESN
Closest papers by meaning
- Universality of Real Minimal Complexity Reservoir (AAAI 2025 · similarity 0.87)
- Frequency Domain Reservoir Computing (NeurIPS 2026 · similarity 0.85)
- Rethinking Fourier Transform from A Basis Functions Perspective for Long-term Time Series Forecasting (NeurIPS 2024 · similarity 0.83)
- Learning Robust Spectral Dynamics for Temporal Domain Generalization (NeurIPS 2025 · similarity 0.82)
- MPTSNet: Integrating Multiscale Periodic Local Patterns and Global Dependencies for Multivariate Time Series Classification (AAAI 2025 · similarity 0.82)
- TimeKAN: KAN-based Frequency Decomposition Learning Architecture for Long-term Time Series Forecasting (ICLR 2025 · similarity 0.82)
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