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HDMixer: Hierarchical Dependency with Extendable Patch for Multivariate Time Series Forecasting
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Proposes HDMixer, a pure-MLP multivariate time series forecaster with a learnable length-extendable patcher (trained with a patch entropy loss) and a hierarchical MLP-Mixer that models short-term, long-term, and cross-variable dependencies.
Problem
Long-term multivariate time series forecasting with fixed-length patches loses temporal boundary information (complete peaks/periods) and existing patch-based models neglect short-term intra-patch and cross-variable interactions.
Approach
Replaces fixed-length patches with learnable length-extendable patches (learned center offset and left/right expansion, sampled via differentiable bilinear interpolation) and uses a stack of three MLP-Mixers that sequentially mix within patches, across patches, and across variables, with a patch entropy loss guiding patch partitioning.
Key results
- HDMixer ranks first in 59 and second in 13 of 72 settings across 9 datasets (Table 1).
- Compared with Transformer-based baselines, HDMixer reduces MSE by an overall 7.27% and MAE by 4.21%; versus MTGNN, MSE drops 59.66%.
- Removing the Length-Extendable Patcher (fixed patch size 16) raises MSE by an average of 5.6% across 3 datasets in ablation.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use HDMixer instead of PatchTST | MTS forecasting · ILI, prediction length 24 | MSE: 1.522 -> 1.305 | Helped |
| Use HDMixer instead of PatchTST | MTS forecasting · Weather, prediction length 96 | MSE: 0.152 -> 0.145 | Helped |
| Use HDMixer instead of PatchTST | MTS forecasting · ETTm1, prediction length 96 | MSE: 0.290 -> 0.291 | Hurt |
| Add long-term dependency capturing MLP (ablation) | HDMixer · ETTm2, prediction length 96 | MSE: 0.165 -> 0.162 | Helped |
| Add variable interaction capturing MLP (ablation) | HDMixer · ETTm2, prediction length 96 | MSE: 0.169 -> 0.162 | Helped |
| Add short-term dependency capturing MLP (ablation) | HDMixer · ETTm2, prediction length 96 | MSE: 0.164 -> 0.162 | Helped |
| Use Length-Extendable Patcher instead of fixed patch size 16 (ablation) | HDMixer · ETTm2, prediction length 96 | MSE: 0.169 -> 0.162 | Helped |
Surprising findings
- Extending patch length beyond 0.5x of the original length gives notable gains, but the authors cap it at 0.5x to limit semantic overlap between patches.
Limitations
- Input length fixed at 336 (ILI: 60), and experiments are limited to standard long-term forecasting benchmarks.
- Patch extension length hyperparameter (0.5x) chosen empirically to avoid patch overlap.
Experimental setup
Datasets: Weather Traffic Exchange Electricity ILI ETTh1 ETTh2 ETTm1 ETTm2
Benchmarks: Weather Traffic Exchange Electricity ILI ETTh1 ETTh2 ETTm1 ETTm2
Metrics: MSE MAE
Baselines: PatchTST Crossformer DLinear MICN Autoformer MTGNN
Builds on: PatchTST MLP-Mixer DLinear
Closest papers by meaning
- Unlocking the Power of Patch: Patch-Based MLP for Long-Term Time Series Forecasting (AAAI 2025 · similarity 0.89)
- WPMixer: Efficient Multi-Resolution Mixing for Long-Term Time Series Forecasting (AAAI 2025 · similarity 0.88)
- WaveletMixer: A Multi-Resolution Wavelets Based MLP-Mixer for Multivariate Long-Term Time Series Forecasting (AAAI 2025 · similarity 0.88)
- TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting (ICLR 2024 · similarity 0.87)
- xLSTM-Mixer: Multivariate Time Series Forecasting by Mixing via Scalar Memories (NeurIPS 2025 · similarity 0.87)
- HDT: Hierarchical Discrete Transformer for Multivariate Time Series Forecasting (AAAI 2025 · similarity 0.87)
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