KAN-AD: Time Series Anomaly Detection with Kolmogorov-Arnold Networks

TL;DR

KAN-AD introduces a novel time series anomaly detection method that models normal behavior with smooth functions, using Fourier expansions for robustness and efficiency, outperforming existing methods on benchmark datasets.

Contribution

This paper proposes KAN-AD, a new TSAD approach that replaces B-splines with Fourier expansions and a lightweight learning mechanism, enhancing robustness and efficiency.

Findings

Achieves 15% average accuracy improvement over baselines

Requires fewer than 1,000 parameters, enabling faster inference

Outperforms state-of-the-art methods on four benchmarks

Abstract

Time series anomaly detection (TSAD) underpins real-time monitoring in cloud services and web systems, allowing rapid identification of anomalies to prevent costly failures. Most TSAD methods driven by forecasting models tend to overfit by emphasizing minor fluctuations. Our analysis reveals that effective TSAD should focus on modeling "normal" behavior through smooth local patterns. To achieve this, we reformulate time series modeling as approximating the series with smooth univariate functions. The local smoothness of each univariate function ensures that the fitted time series remains resilient against local disturbances. However, a direct KAN implementation proves susceptible to these disturbances due to the inherently localized characteristics of B-spline functions. We thus propose KAN-AD, replacing B-splines with truncated Fourier expansions and introducing a novel lightweight learning mechanism that emphasizes global patterns while staying robust to local disturbances. On four popular TSAD benchmarks, KAN-AD achieves an average 15% improvement in detection accuracy (with peaks exceeding 27%) over state-of-the-art baselines. Remarkably, it requires fewer than 1,000 trainable parameters, resulting in a 50% faster inference speed compared to the original KAN, demonstrating the approach's efficiency and practical viability.