# Joint Selective State Space Model and Detrending for Robust Time Series Anomaly Detection

arXiv: https://arxiv.org/abs/2405.19823 · HTML: https://mlsanity.com/paper/2405.19823/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 46 references that are in the map.
- First posted on arXiv 30 May 2024.

## Builds on (most cited first, 21 of 21)

- [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)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding](https://mlsanity.com/paper/1802.04431/) (2018)
- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [PyOD: A Python Toolbox for Scalable Outlier Detection](https://mlsanity.com/paper/1901.01588/) (2019)
- [TranAD: Deep Transformer Networks for Anomaly Detection in Multivariate Time Series Data](https://mlsanity.com/paper/2201.07284/) (2022)
- [ECOD: Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions](https://mlsanity.com/paper/2201.00382/) (2022)
- [Current Time Series Anomaly Detection Benchmarks are Flawed and are Creating the Illusion of Progress](https://mlsanity.com/paper/2009.13807/) (2020)
- [Deep Learning for Time Series Anomaly Detection: A Survey](https://mlsanity.com/paper/2211.05244/) (2022)
- [DCdetector: Dual Attention Contrastive Representation Learning for Time Series Anomaly Detection](https://mlsanity.com/paper/2306.10347/) (2023)
- [Towards a Rigorous Evaluation of Time-series Anomaly Detection](https://mlsanity.com/paper/2109.05257/) (2021)
- [Local Evaluation of Time Series Anomaly Detection Algorithms](https://mlsanity.com/paper/2206.13167/) (2022)
- [Dual-path Mamba: Short and Long-term Bidirectional Selective Structured State Space Models for Speech Separation](https://mlsanity.com/paper/2403.18257/) (2024)
- [Master-Auxiliary: an efficient aggregation strategy for video anomaly detection](https://mlsanity.com/paper/2005.11645/) (2020)
- [Unravel Anomalies: An End-to-end Seasonal-Trend Decomposition Approach for Time Series Anomaly Detection](https://mlsanity.com/paper/2310.00268/) (2023)

## Built on by (most cited first, 2 of 2)

- [Fourier-KAN-Mamba: A Novel State-Space Equation Approach for Time-Series Anomaly Detection](https://mlsanity.com/paper/2511.15083/) (2025)
- [Multivariate Time Series Anomaly Detection via Dual-Branch Reconstruction and Autoregressive Flow-based Residual Density Estimation](https://mlsanity.com/paper/2604.08582/) (2026)

## Abstract (arXiv)

Deep learning-based sequence models are extensively employed in Time Series Anomaly Detection (TSAD) tasks due to their effective sequential modeling capabilities. However, the ability of TSAD is limited by two key challenges: (i) the ability to model long-range dependency and (ii) the generalization issue in the presence of non-stationary data. To tackle these challenges, an anomaly detector that leverages the selective state space model known for its proficiency in capturing long-term dependencies across various domains is proposed. Additionally, a multi-stage detrending mechanism is introduced to mitigate the prominent trend component in non-stationary data to address the generalization issue. Extensive experiments conducted on realworld public datasets demonstrate that the proposed methods surpass all 12 compared baseline methods.