mlsanityData to 7 Oct 2026

Time-SSM: Simplifying and Unifying State Space Models for Time Series Forecasting

arXiv 2405.16312 ↗First posted 25 May 2024cs.LG cs.AIcited by 9

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Abstract (arXiv)

State Space Models (SSMs) have emerged as a potent tool in sequence modeling tasks in recent years. These models approximate continuous systems using a set of basis functions and discretize them to handle input data, making them well-suited for modeling time series data collected at specific frequencies from continuous systems. Despite its potential, the application of SSMs in time series forecasting remains underexplored, with most existing models treating SSMs as a black box for capturing temporal or channel dependencies. To address this gap, this paper proposes a novel theoretical framework termed Dynamic Spectral Operator, offering more intuitive and general guidance on applying SSMs to time series data. Building upon our theory, we introduce Time-SSM, a novel SSM-based foundation model with only one-seventh of the parameters compared to Mamba. Various experiments validate both our theoretical framework and the superior performance of Time-SSM.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 39 of its 44 references that are in the map. First posted on arXiv 25 May 2024.

Builds on

39 of 44 references.

References · 39

  1. 2023Mamba: Linear-Time Sequence Modeling with Selective State Spacescited by 4,616
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  3. 2021Efficiently Modeling Long Sequences with Structured State Spacescited by 2,424
  4. 2020Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecastingcited by 2,141
  5. 2022A Time Series is Worth 64 Words: Long-term Forecasting with Transformerscited by 1,981
  6. 2021Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecastingcited by 1,654
  7. 2022Are Transformers Effective for Time Series Forecasting?cited by 1,400
  8. 2022FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecastingcited by 1,200
  9. 2022TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysiscited by 1,030
  10. 2023iTransformer: Inverted Transformers Are Effective for Time Series Forecastingcited by 906
  11. 2022Simplified State Space Layers for Sequence Modelingcited by 776
  12. 2020Long Range Arena: A Benchmark for Efficient Transformerscited by 696
27 more
  1. 2023Time-LLM: Time Series Forecasting by Reprogramming Large Language Modelscited by 680
  2. 2023One Fits All:Power General Time Series Analysis by Pretrained LMcited by 615
  3. 2021Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layerscited by 607
  4. 2020HiPPO: Recurrent Memory with Optimal Polynomial Projectionscited by 600
  5. 2024Unified Training of Universal Time Series Forecasting Transformerscited by 588
  6. 2022On the Parameterization and Initialization of Diagonal State Space Modelscited by 418
  7. 2022Non-stationary Transformers: Exploring the Stationarity in Time Series Forecastingcited by 385
  8. 2022Diagonal State Spaces are as Effective as Structured State Spacescited by 350
  9. 2023Long-term Forecasting with TiDE: Time-series Dense Encodercited by 327
  10. 2024Foundation Models for Time Series Analysis: A Tutorial and Surveycited by 234
  11. 2021Multiwavelet-based Operator Learning for Differential Equationscited by 229
  12. 2023UniTime: A Language-Empowered Unified Model for Cross-Domain Time Series Forecastingcited by 139
  13. 2019Cheap Orthogonal Constraints in Neural Networks: A Simple Parametrization of the Orthogonal and Unitary Groupcited by 133
  14. 2022How to Train Your HiPPO: State Space Models with Generalized Orthogonal Basis Projectionscited by 121
  15. 2023Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictorscited by 110
  16. 2024Is Mamba Effective for Time Series Forecasting?cited by 110
  17. 2023Large Models for Time Series and Spatio-Temporal Data: A Survey and Outlookcited by 109
  18. 2024Pathformer: Multi-scale Transformers with Adaptive Pathways for Time Series Forecastingcited by 102
  19. 2024SiMBA: Simplified Mamba-Based Architecture for Vision and Multivariate Time seriescited by 81
  20. 2024TimeMachine: A Time Series is Worth 4 Mambas for Long-term Forecastingcited by 63
  21. 2022Scaleformer: Iterative Multi-scale Refining Transformers for Time Series Forecastingcited by 54
  22. 2023Effectively Modeling Time Series with Simple Discrete State Spacescited by 54
  23. 2023LNO: Laplace Neural Operator for Solving Differential Equationscited by 47
  24. 2024MambaMixer: Efficient Selective State Space Models with Dual Token and Channel Selectioncited by 40
  25. 2023StableSSM: Alleviating the Curse of Memory in State-space Models through Stable Reparameterizationcited by 29
  26. 2024RWKV-TS: Beyond Traditional Recurrent Neural Network for Time Series Taskscited by 22
  27. 2024Attractor Memory for Long-Term Time Series Forecasting: A Chaos Perspectivecited by 17

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 4; 2025: 4; 2026: 1.

9 papers.

  1. 2025Comba: Improving Bilinear RNNs with Closed-loop Controlcited by 12
  2. 2024CMamba: Channel Correlation Enhanced State Space Models for Multivariate Time Series Forecastingcited by 8
  3. 2025Multi-Order Wavelet Derivative Transform for Deep Time Series Forecastingcited by 4
  4. 2024Toward Physics-guided Time Series Embeddingcited by 3
  5. 2025Automatic selection of the best neural architecture for time series forecastingcited by 2
  6. 2024TwinS: Revisiting Non-Stationarity in Multivariate Time Series Forecastingcited by 1
  7. 2024A SSM is Polymerized from Multivariate Time Seriescited by 0
  8. 2025Fourier-KAN-Mamba: A Novel State-Space Equation Approach for Time-Series Anomaly Detectioncited by 0
  9. 2026Correct then Forecast: Observer State-Space Models for Time Series Forecastingcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024From Generalization Analysis to Optimization Designs for State Space Models
  2. 2024Deep Learning-based Approaches for State Space Models: A Selective Review
  3. 2026DMamba: Decomposition-enhanced Mamba for Time Series Forecasting
  4. 2026A Simple State Space Model Excels at Multivariate Time Series Classification
  5. 2026SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting
  6. 2024SST: Multi-Scale Hybrid Mamba-Transformer Experts for Time Series Forecasting
  7. 2025A Generalizable Physics-Enhanced State Space Model for Long-Term Dynamics Forecasting in Complex Environments
  8. 2024Autocorrelation Matters: Understanding the Role of Initialization Schemes for State Space Models