Research map / Time series / Long-term forecasting
SOFTS: Efficient Multivariate Time Series Forecasting with Series-Core Fusion
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Proposes SOFTS, an MLP-based multivariate forecaster with a STAR module that aggregates all channel series into a global core and fuses it back into each channel, achieving SOTA with linear complexity in channels.
Problem
Multivariate time series forecasting must capture channel correlations without the quadratic cost of attention and without losing robustness to distribution drift, especially with many channels.
Approach
A centralized STAR (Star Aggregate-Redistribute) module pools all channel embeddings into a global core representation via stochastic pooling, then concatenates the core back to each channel and fuses with an MLP, replacing pairwise channel attention with linear-cost indirect interaction.
Key results
- SOFTS reports best or second-best average results across the six dataset groups, e.g., Traffic MSE 0.409 vs iTransformer 0.428 (about 4.4% reduction).
- On PEMS07, SOFTS reduces average MSE from 0.101 to 0.087 (about 13.9%) relative to the prior best.
- Plugging STAR into iTransformer lowers Traffic MSE from 0.428 to 0.409 and into PatchTST lowers Traffic MSE from 0.454 to 0.448 (STAR replacing time attention).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add STAR channel interaction to a channel-independent MLP (ablation) | SOFTS · Traffic | MSE: 0.442 -> 0.409 | Helped |
| Replace stochastic pooling with mean pooling (ablation) | SOFTS · Traffic | MSE: 0.409 -> 0.420 | Hurt |
| Replace stochastic pooling with max pooling (ablation) | SOFTS · Traffic | MSE: 0.409 -> 0.406 | No clear effect |
| Replace stochastic pooling with weighted average pooling (ablation) | SOFTS · Traffic | MSE: 0.409 -> 0.440 | Hurt |
| Replace time attention with STAR (ablation) | PatchTST · Traffic | MSE: 0.454 -> 0.448 | Helped |
| Replace time and channel attention with STAR (ablation) | Crossformer · Traffic | MSE: 0.546 -> 0.549 | Hurt |
| Replace channel attention with STAR (ablation) | iTransformer · Traffic | MSE: 0.428 -> 0.409 | Helped |
| Add STAR embedding adaptation (ablation) | SOFTS · Traffic test example | MSE: 0.414 -> 0.376 | Helped |
| Increase lookback window length (ablation) | SOFTS · Forecasting datasets | MSE | Helped |
| Vary core dimension d' (ablation) | SOFTS · Traffic and PEMS | forecasting performance | No clear effect |
| Use larger hidden dimensions and more encoder layers (ablation) | SOFTS · Traffic and PEMS | forecasting performance | Helped |
| Replace permutation-variant core aggregation with permutation-invariant aggregation (ablation) | SOFTS core representation · Time-series forecasting | performance | Helped |
Surprising findings
- Stochastic pooling outperforms mean and max pooling across nearly all datasets.
- Variations in the core dimension d' have minimal influence on overall performance.
Limitations
- Reported gains on some datasets are small or absent (e.g., Crossformer-STAR on Traffic slightly worse; Weather/ETTh1 mixed).
- Complexity analysis ignores model dimension d as constant.
Experimental setup
Datasets: ETT Traffic Electricity Weather Solar-Energy PEMS03 PEMS04 PEMS07 PEMS08
Benchmarks: ETTh1 ETTh2 ETTm1 ETTm2 ECL Traffic Weather Solar-Energy PEMS03 PEMS04 PEMS07 PEMS08
Metrics: MSE MAE
Baselines: iTransformer PatchTST TSMixer Crossformer TiDE TimesNet DLinear SCINet FEDformer Stationary
Builds on: iTransformer PatchTST DeepSets Kolmogorov-Arnold representation theorem
Closest papers by meaning
- Unlocking the Power of Patch: Patch-Based MLP for Long-Term Time Series Forecasting (AAAI 2025 · similarity 0.88)
- CSformer: Combining Channel Independence and Mixing for Robust Multivariate Time Series Forecasting (AAAI 2025 · similarity 0.88)
- From Similarity to Superiority: Channel Clustering for Time Series Forecasting (NeurIPS 2024 · similarity 0.88)
- TimeCHEAT: A Channel Harmony Strategy for Irregularly Sampled Multivariate Time Series Analysis (AAAI 2025 · similarity 0.88)
- Rethinking Channel Dependence for Multivariate Time Series Forecasting: Learning from Leading Indicators (ICLR 2024 · similarity 0.87)
- xLSTM-Mixer: Multivariate Time Series Forecasting by Mixing via Scalar Memories (NeurIPS 2025 · similarity 0.87)
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