mlsanityData to 14 Oct 2026

Fourier-KAN-Mamba: A Novel State-Space Equation Approach for Time-Series Anomaly Detection

arXiv 2511.15083 ↗First posted 19 Nov 2025cs.LG eess.SPcited by 0

On the map: State-space sequence models (S4, Mamba) → Time series forecasting with SSMs

Abstract (arXiv)

Time-series anomaly detection plays a critical role in numerous real-world applications, including industrial monitoring and fault diagnosis. Recently, Mamba-based state-space models have shown remarkable efficiency in long-sequence modeling. However, directly applying Mamba to anomaly detection tasks still faces challenges in capturing complex temporal patterns and nonlinear dynamics. In this paper, we propose Fourier-KAN-Mamba, a novel hybrid architecture that integrates Fourier layer, Kolmogorov-Arnold Networks (KAN), and Mamba selective state-space model. The Fourier layer extracts multi-scale frequency features, KAN enhances nonlinear representation capability, and a temporal gating control mechanism further improves the model's ability to distinguish normal and anomalous patterns. Extensive experiments on MSL, SMAP, and SWaT datasets demonstrate that our method significantly outperforms existing state-of-the-art approaches. Keywords: time-series anomaly detection, state-space model, Mamba, Fourier transform, Kolmogorov-Arnold Network

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 11 of its 26 references that are in the map. First posted on arXiv 19 Nov 2025.

Builds on

11 of 26 references.

Closest ancestors · 1

Same direction, newest first

  1. 2025Mamba Adaptive Anomaly Transformer with association discrepancy for time series11 Feb

Other references · 10

  1. 2022Transformers in Time Series: A Surveycited by 497
  2. 2021Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancycited by 394
  3. 2024TimeSeriesBench: An Industrial-Grade Benchmark for Time Series Anomaly Detection Modelscited by 23
  4. 2024KAN-AD: Time Series Anomaly Detection with Kolmogorov-Arnold Networkscited by 23
  5. 2023A Comprehensive Survey of Deep Transfer Learning for Anomaly Detection in Industrial Time Series: Methods, Applications, and Directionscited by 22
  6. 2024Time-SSM: Simplifying and Unifying State Space Models for Time Series Forecastingcited by 9
  7. 2022Online Time Series Anomaly Detection with State Space Gaussian Processescited by 5
  8. 2025Decomposition-based multi-scale transformer framework for time series anomaly detectioncited by 5
  9. 2024Joint Selective State Space Model and Detrending for Robust Time Series Anomaly Detectioncited by 2
  10. 2025PatchTrAD: A Patch-Based Transformer focusing on Patch-Wise Reconstruction Error for Time Series Anomaly Detectioncited by 2

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  1. 2025Adaptive State-Space Mamba for Real-Time Sensor Data Anomaly Detection
  2. 2025MamNet: A Novel Hybrid Model for Time-Series Forecasting and Frequency Pattern Analysis in Network Traffic
  3. 2024MambaAD: Exploring State Space Models for Multi-class Unsupervised Anomaly Detection
  4. 2026MambaADv2: Evolving Duality-enhanced State Space Model for Unsupervised Anomaly Detection
  5. 2025FLDmamba: Integrating Fourier and Laplace Transform Decomposition with Mamba for Enhanced Time Series Prediction
  6. 2026SMKC: Sketch Based Kernel Correlation Images for Variable Cardinality Time Series Anomaly Detection
  7. 2026MambaSL: Exploring Single-Layer Mamba for Time Series Classification
  8. 2023BSSAD: Towards A Novel Bayesian State-Space Approach for Anomaly Detection in Multivariate Time Series