# SDE: A Simplified and Disentangled Dependency Encoding Framework for State Space Models in Time Series Forecasting

arXiv: https://arxiv.org/abs/2408.12068 · HTML: https://mlsanity.com/paper/2408.12068/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Time series forecasting with SSMs, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 17 of its 32 references that are in the map.
- First posted on arXiv 22 Aug 2024.

## Placed in

- State-space sequence models (S4, Mamba) / [Time series forecasting with SSMs](https://mlsanity.com/ssm/time-series-forecasting-with-ssms/)

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [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)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layers](https://mlsanity.com/paper/2110.13985/) (2021)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Hungry Hungry Hippos: Towards Language Modeling with State Space Models](https://mlsanity.com/paper/2212.14052/) (2022)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Generative Pretrained Hierarchical Transformer for Time Series Forecasting](https://mlsanity.com/paper/2402.16516/) (2024)
- [Polestar: An Intelligent, Efficient and National-Wide Public Transportation Routing Engine](https://mlsanity.com/paper/2007.07195/) (2020)
- [Addressing Prediction Delays in Time Series Forecasting: A Continuous GRU Approach with Derivative Regularization](https://mlsanity.com/paper/2407.01622/) (2024)

## Built on by (most cited first, 5 of 5)

- [Sequential Order-Robust Mamba for Time Series Forecasting](https://mlsanity.com/paper/2410.23356/) (2024)
- [Federated Causal Representation Learning in State-Space Systems for Decentralized Counterfactual Reasoning](https://mlsanity.com/paper/2602.19414/) (2026)
- [Multiple cyclicity and Wavelet Decomposition with Channel Correlation for Long-term Time Series Forecasting](https://mlsanity.com/paper/2606.17996/) (2026)
- [Correct then Forecast: Observer State-Space Models for Time Series Forecasting](https://mlsanity.com/paper/2609.33566/) (2026)
- [Channel-Dependent State Space Model for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2609.36453/) (2026)

## Abstract (arXiv)

In recent years, advancements in deep learning have spurred the development of numerous models for Long-term Time Series Forecasting (LTSF). However, most existing approaches struggle to fully capture the complex and structured dependencies inherent in time series data. In this work, we identify and formally define three critical dependencies that are fundamental to forecasting accuracy: order dependency and semantic dependency along the temporal dimension, as well as cross-variate dependency across the feature dimension. These dependencies are often treated in isolation, and improper handling can introduce noise and degrade forecasting performance. To bridge this gap, we investigate the potential of State Space Models (SSMs) for LTSF and emphasize their inherent advantages in capturing these essential dependencies. Additionally, we empirically observe that excessive nonlinearity in conventional SSMs introduce redundancy when applied to semantically sparse time series data. Motivated by this insight, we propose SDE (Simplified and Disentangled Dependency Encoding), a novel framework designed to enhance the capability of SSMs for LTSF. Specifically, we first eliminate unnecessary nonlinearities in vanilla SSMs, thereby improving the suitability for time series forecasting. Building on this foundation, we introduce a disentangled encoding strategy, which empowers SSMs to efficiently model cross-variate dependencies while mitigating interference between the temporal and feature dimensions. Furthermore, we provide rigorous theoretical justifications to substantiate our design choices. Extensive experiments on nine real-world benchmark datasets demonstrate that SDE-enhanced SSMs consistently outperform state-of-the-art time series forecasting models.Our code is available at https://github.com/YukinoAsuna/SAMBA.