Research map / Time series / Long-term forecasting
Chimera: Effectively Modeling Multivariate Time Series with 2-Dimensional State Space Models
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Chimera is a three-headed, input-dependent 2D state space model for multivariate time series that captures time and variate dependencies with a 2D parallel selective scan, evaluated on classification, forecasting, and anomaly detection.
Problem
Multivariate time series modeling needs expressive capture of long-term and seasonal temporal dependencies, input-adaptive inter-variate dependencies, and efficient training on long sequences; existing SSMs are linear, univariate, static, or slow.
Approach
A 2D SSM whose hidden states carry both time and variate information, with two discretization step sizes (one for trend, one learnable for seasonality), input-dependent B, C and Delta, and a 2D associative scan operator enabling parallel training; 2D Mamba and Mamba-2 are presented as special cases.
Key results
- Achieves best or second-best average results on all eight long-term forecasting datasets, best on 5 of 8 (e.g., ETTm1 MSE 0.345, ECL MSE 0.154).
- Reaches 98.40% accuracy on speech classification versus 98.32% for S4, and 0.941 on PTB-XL all-statement classification.
- Brain-activity BVFC (9K) image classification accuracy 69.41% vs 41.20% for SpaceTime; parallel 2D scan gives about 4x faster training than the recurrent form.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use Chimera instead of the strongest listed baseline | long-term forecasting · ETTm1, ETTm2, ETTh2, ECL, Weather | MSE: 0.345 vs 0.351; 0.250 vs 0.253; 0.318 vs 0.322; 0.154 vs 0.156; 0.219 vs 0.224 | Helped |
| use Chimera instead of the strongest listed baseline | long-term forecasting · ETTh1, Exchange, Traffic | MSE: 0.405 vs 0.403; 0.311 vs 0.302; 0.403 vs 0.398 | Hurt |
| use Chimera instead of S4 | PTB-XL ECG classification · PTB-XL All | accuracy: 0.938 -> 0.941 | Helped |
| use Chimera instead of S4 | speech classification · Speech classification | accuracy (%): 98.32 -> 98.40 | Helped |
| use Chimera instead of ModernTCN | M4 forecasting · M4 weighted average | SMAPE: 11.698 -> 11.618 | Helped |
| use unidirectional recurrence along the variate dimension (ablation) | Chimera · ETTh1 | MSE: 0.405 -> 0.409 | Hurt |
| remove the gating mechanism (ablation) | Chimera · ETTh1 | MSE: 0.405 -> 0.418 | Hurt |
| use input-independent parameters (ablation) | Chimera · ETTh1 | MSE: 0.405 -> 0.471 | Hurt |
| remove the seasonal-pattern module (ablation) | Chimera · ETTh1 | MSE: 0.405 -> 0.426 | Hurt |
Surprising findings
- The input-independent (convolution-form) variant performs much worse on brain activity and ETT benchmarks, indicating input-dependent parameters are critical.
Limitations
- The naive 2D parallel scan is not yet hardware-aware, leaving efficiency headroom.
- 2D Mamba and Mamba-2 special cases are not experimentally evaluated.
- Variate generalization results show performance comparable to Transformers, not uniformly better.
Experimental setup
Datasets: ETTh1 ETTh2 ETTm1 ETTm2 Electricity Traffic Weather Exchange ILI M4 PTB-XL UEA archive
Benchmarks: ETTh1 ETTh2 ETTm1 ETTm2 ECL Traffic Weather Exchange M4 PTB-XL UEA classification SMD
Metrics: MSE MAE SMAPE MASE OWA accuracy F1
Baselines: TSM2 Simba TCN iTransformer RLinear PatchTST Crossformer TiDE TimesNet DLinear SpaceTime S4
Builds on: Mamba Mamba-2 S4 SpaceTime 2DSSM
Closest papers by meaning
- S4M: S4 for multivariate time series forecasting with Missing values (ICLR 2025 · similarity 0.87)
- UP2ME: Univariate Pre-training to Multivariate Fine-tuning as a General-purpose Framework for Multivariate Time Series Analysis (ICML 2024 · similarity 0.86)
- A Closer Look at Transformers for Time Series Forecasting: Understanding Why They Work and Where They Struggle (ICML 2025 · similarity 0.86)
- Multivariate Probabilistic Time Series Forecasting with Correlated Errors (NeurIPS 2024 · similarity 0.86)
- LogSig-SSM: Time-Series Modelling with Multi-Scale Log-Signature Compression for State-Space Models (NeurIPS 2026 · similarity 0.86)
- Revitalizing Multivariate Time Series Forecasting: Learnable Decomposition with Inter-Series Dependencies and Intra-Series Variations Modeling (ICML 2024 · similarity 0.86)
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