# Channel-Dependent State Space Model for Multivariate Time Series Forecasting

arXiv: https://arxiv.org/abs/2609.36453 · HTML: https://mlsanity.com/paper/2609.36453/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 39 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Gated Delta Networks: Improving Mamba2 with Delta Rule](https://mlsanity.com/paper/2412.06464/) (2024)
- [Parallelizing Linear Transformers with the Delta Rule over Sequence Length](https://mlsanity.com/paper/2406.06484/) (2024)
- [Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019](https://mlsanity.com/paper/1911.13288/) (2019)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [Is Mamba Effective for Time Series Forecasting?](https://mlsanity.com/paper/2403.11144/) (2024)
- [DUET: Dual Clustering Enhanced Multivariate Time Series Forecasting](https://mlsanity.com/paper/2412.10859/) (2024)
- [Chaos as an interpretable benchmark for forecasting and data-driven modelling](https://mlsanity.com/paper/2110.05266/) (2021)
- [SOFTS: Efficient Multivariate Time Series Forecasting with Series-Core Fusion](https://mlsanity.com/paper/2404.14197/) (2024)
- [TimeMachine: A Time Series is Worth 4 Mambas for Long-term Forecasting](https://mlsanity.com/paper/2403.09898/) (2024)
- [TimeFilter: Patch-Specific Spatial-Temporal Graph Filtration for Time Series Forecasting](https://mlsanity.com/paper/2501.13041/) (2025)
- [Revitalizing Multivariate Time Series Forecasting: Learnable Decomposition with Inter-Series Dependencies and Intra-Series Variations Modeling](https://mlsanity.com/paper/2402.12694/) (2024)
- [Channel Dependence, Limited Lookback Windows, and the Simplicity of Datasets: How Biased is Time Series Forecasting?](https://mlsanity.com/paper/2502.09683/) (2025)
- [SDE: A Simplified and Disentangled Dependency Encoding Framework for State Space Models in Time Series Forecasting](https://mlsanity.com/paper/2408.12068/) (2024)
- [Channel Normalization for Time Series Channel Identification](https://mlsanity.com/paper/2506.00432/) (2025)

## Abstract (arXiv)

Multivariate time series forecasting (MTSF) is critical across many real-world domains. Existing deep learning approaches fall into two paradigms with distinct limitations: channel-independent (CI) methods unconditionally ignore cross-variable dependencies and model only temporal dynamics, while channel-dependent (CD) methods consider both but typically rely on architectural compromises to mitigate overfitting and computational overhead. We therefore propose Chameleon, a specialized CD state space model (SSM) that enables data-dependent, fine-grained interactions across variables while scaling linearly with their number. By connecting selective SSMs with the Kalman filter, we leverage the missing measurement update in the former for cross-variable modeling while preserving the SSM backbone for robust temporal modeling. We further identify favorable inductive biases of GatedDeltaNet for time series, adapt it as our backbone, and improve generalization through additional techniques, including a previously unexplored stochastic perturbation of reversible instance normalization. On strongly dependent ODE and PEMS datasets, Chameleon achieves the best MSE and MAE across all settings, while its CI ablation and prior CD methods incur 61-178% higher MSE on average. Across 28 standard benchmark settings, Chameleon also achieves better MSE and MAE than each baseline in at least 27 and 22 cases, respectively. Training-time and peak-memory analyses on Traffic and ETT further demonstrate competitive efficiency and favorable memory scalability across different variable counts.