# AdaMamba: Adaptive Frequency-Gated Mamba for Long-Term Time Series Forecasting

arXiv: https://arxiv.org/abs/2604.23239 · HTML: https://mlsanity.com/paper/2604.23239/

## Key facts

- No citing papers in the map yet (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 18 of its 42 references that are in the map.
- First posted on arXiv 25 Apr 2026.

## 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, 18 of 18)

- [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)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)
- [A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction](https://mlsanity.com/paper/1704.02971/) (2017)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [Conditional Time Series Forecasting with Convolutional Neural Networks](https://mlsanity.com/paper/1703.04691/) (2017)
- [FreDF: Learning to Forecast in the Frequency Domain](https://mlsanity.com/paper/2402.02399/) (2024)
- [TimeMachine: A Time Series is Worth 4 Mambas for Long-term Forecasting](https://mlsanity.com/paper/2403.09898/) (2024)
- [A Survey on Deep Learning based Time Series Analysis with Frequency Transformation](https://mlsanity.com/paper/2302.02173/) (2023)
- [Towards Long-Term Time-Series Forecasting: Feature, Pattern, and Distribution](https://mlsanity.com/paper/2301.02068/) (2023)
- [CSformer: Combining Channel Independence and Mixing for Robust Multivariate Time Series Forecasting](https://mlsanity.com/paper/2312.06220/) (2023)
- [Spatial-Temporal Data Mining for Ocean Science: Data, Methodologies, and Opportunities](https://mlsanity.com/paper/2307.10803/) (2023)
- [Defining Fundamental Frequency for Almost Harmonic Signals](https://mlsanity.com/paper/2003.10767/) (2020)
- [OKG-LLM: Aligning Ocean Knowledge Graph with Observation Data via LLMs for Global Sea Surface Temperature Prediction](https://mlsanity.com/paper/2508.00933/) (2025)

## Abstract (arXiv)

Accurate long-term time series forecasting (LTSF) requires the capture of complex long-range dependencies and dynamic periodic patterns. Recent advances in frequency-domain analysis offer a global perspective for uncovering temporal characteristics. However, real-world time series often exhibit pronounced cross-domain heterogeneity where variables that appear synchronized in the time domain can differ substantially in the frequency domain. Existing frequency-based LTSF methods often rely on implicit assumptions of cross-domain homogeneity, which limits their ability to adapt to such intricate variability. To effectively integrate frequency-domain analysis with temporal dependency learning, we propose AdaMamba, a novel framework that endogenizes adaptive and context-aware frequency analysis within the Mamba state-space update process. Specifically, AdaMamba introduces an interactive patch encoding module to capture inter-variable interaction dynamics. Then, we develop an adaptive frequency-gated state-space module that generates input-dependent frequency bases, and generalizes the conventional temporal forgetting gate into a unified time-frequency forgetting gate. This allows dynamic calibration of state transitions based on learned frequency-domain importance, while preserving Mamba's capability in modeling long-range dependencies. Extensive experiments on seven public LTSF benchmarks and two domain-specific datasets demonstrate that AdaMamba consistently outperforms state-of-the-art methods in forecasting accu racy while maintaining competitive computational efficiency. The code of AdaMamba is available at https://github.com/XDjiang25/AdaMamba.