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WPMixer: Efficient Multi-Resolution Mixing for Long-Term Time Series Forecasting
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Proposes WPMixer, an MLP-mixer forecaster that combines multi-level wavelet decomposition with per-coefficient resolution branches, patching, and patch/embedding mixing, reporting state-of-the-art long-term forecasting with lower compute than TimeMixer.
Problem
Long-term multivariate time series forecasting, where MLP-mixer models underperform their potential and existing multi-scale decompositions (moving average) miss abrupt spikes/dips and mix information across scales.
Approach
Decompose the normalized series with a multi-level discrete wavelet transform, process each approximation/detail coefficient series in a separate resolution branch with patching, a patch mixer followed by an embedding mixer, and reconstruct the forecast via inverse wavelet transform.
Key results
- Under the optimized look-back setup, WPMixer achieves the best average MSE/MAE on ETTh1 (0.379/0.409), ETTh2 (0.309/0.370), ETTm1 (0.336/0.373), ETTm2 (0.246/0.307), and Weather (0.217/0.252).
- WPMixer uses less than one tenth of TimeMixer's GFLOPs at each prediction length on ETTh1 with embedding dimension d=16 (e.g., 0.210 vs 2.774 GFLOPs at T=96).
- Under the unified TimeMixer setting, WPMixer improves average MSE on ETTh1 by 5.6% over TimeMixer (0.422 vs 0.447), but is not best on Traffic or Electricity, where iTransformer is stronger.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use WPMixer instead of TimeMixer | Multivariate forecasting · ETTh1, ETTh2, ETTm1, ETTm2, Weather, Traffic (averaged prediction lengths) | MSE: 0.411 -> 0.379; 0.316 -> 0.309; 0.348 -> 0.336; .256 -> 0.246; 0.222 -> 0.217; 0.387 -> 0.386 | Helped |
| Use WPMixer instead of TimeMixer | Multivariate forecasting · Electricity (Avg) | MSE: 0.156 -> 0.158 | Hurt |
| Add wavelet decomposition (ablation) | WPMixer · ETT datasets | MSE: 0.388 -> 0.379; 0.311 -> 0.308; 0.339 -> 0.336; 0.247 -> 0.245 | Helped |
| Add patching and embedding (ablation) | WPMixer · ETT datasets | MSE: 0.384 -> 0.379; 0.316 -> 0.308; 0.339 -> 0.336; 0.250 -> 0.245 | Helped |
| Add the embedding module (ablation) | WPMixer · ETT datasets | MSE: 0.378 -> 0.379; 0.314 -> 0.308; 0.339 -> 0.336; 0.247 -> 0.245 | Mixed |
| Add the patch mixer and embedding mixer (ablation) | WPMixer · ETT datasets | MSE: 0.394 -> 0.379; 0.311 -> 0.308; 0.353 -> 0.336; 0.252 -> 0.245 | Helped |
| Add decomposition, patching, embedding, and mixer modules together (ablation) | WPMixer · ETT datasets | MSE: 0.403 -> 0.379; 0.315 -> 0.308; 0.355 -> 0.336; 0.252 -> 0.245 | Helped |
| Add the patch mixer (ablation) | WPMixer · ETT datasets | MSE: 0.377 -> 0.379; 0.314 -> 0.308; 0.339 -> 0.336; 0.247 -> 0.245 | Mixed |
| Vary decomposition level from 1 to 5 (ablation) | WPMixer · ETTh1 and ETTh2, prediction lengths 336 and 720 | MSE | Mixed |
| Use SmoothL1 loss instead of MSE loss (ablation) | WPMixer · ETTm2 and ETTh2 | MSE: 0.165 -> 0.159; 0.219 -> 0.214; 0.271 -> 0.266; 0.349 -> 0.344; 0.251 -> 0.253; 0.308 -> 0.303; 0.306 -> 0.305; 0.374 -> | Helped |
| Increase look-back window length (ablation) | WPMixer · ETTh datasets | MSE | Mixed |
Surprising findings
- Under the unified setting, WPMixer trails TimeMixer on Traffic (0.489 vs 0.484 MSE) and iTransformer is best on Traffic and Electricity MAE in the unified table.
- The best decomposition level m varies with prediction length and dataset, so it is treated as a hyperparameter.
Limitations
- Results under the optimized setup rely on per-dataset tuning of look-back window and many hyperparameters via Optuna, so comparisons are not fully controlled.
- Does not beat the best baselines on all datasets, e.g., Traffic and Electricity under the unified setting.
Experimental setup
Datasets: ETTh1 ETTh2 ETTm1 ETTm2 Weather Electricity Traffic
Benchmarks: ETTh1 ETTh2 ETTm1 ETTm2 Weather Electricity Traffic
Metrics: MSE MAE GFLOPs
Baselines: TimeMixer TSMixer PatchTST TimesNet FiLM DLinear Crossformer iTransformer
Builds on: MLP-Mixer PatchTST TimeMixer RevIN Optuna
Closest papers by meaning
- WaveletMixer: A Multi-Resolution Wavelets Based MLP-Mixer for Multivariate Long-Term Time Series Forecasting (AAAI 2025 · similarity 0.94)
- TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting (ICLR 2024 · similarity 0.90)
- xLSTM-Mixer: Multivariate Time Series Forecasting by Mixing via Scalar Memories (NeurIPS 2025 · similarity 0.89)
- Unlocking the Power of Patch: Patch-Based MLP for Long-Term Time Series Forecasting (AAAI 2025 · similarity 0.89)
- HDMixer: Hierarchical Dependency with Extendable Patch for Multivariate Time Series Forecasting (AAAI 2024 · similarity 0.88)
- Adaptive Multi-Scale Decomposition Framework for Time Series Forecasting (AAAI 2025 · similarity 0.87)
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