用傅里叶函数改进KAN，实现高效高精度时序异常检测
KAN-AD: Time Series Anomaly Detection with Kolmogorov-Arnold Networks
- 用截断傅里叶展开替代B样条，增强模型对局部扰动的鲁棒性
- 在4个基准上平均提升15%检测准确率，峰值超27%
- 参数少于1000个，推理速度比原KAN快50%，适合实时系统
时序异常检测（TSAD）是云服务与网络系统实时监控的核心，能快速识别异常以避免重大故障。现有基于预测模型的TSAD方法常因过度拟合微小波动而表现不佳。我们分析发现，有效的TSAD应聚焦于通过平滑局部模式建模“正常”行为。为此，我们将时序建模重新定义为用平滑的单变量函数逼近时序数据，局部平滑性确保拟合结果对局部扰动具有韧性。然而，直接使用KAN会因B样条的局部特性而易受扰动影响。因此我们提出KAN-AD，将B样条替换为截断傅里叶展开，并引入一种轻量级学习机制，强调全局模式同时保持对局部扰动的鲁棒性。在四个主流TSAD基准上，KAN-AD相比最先进基线平均提升15%检测准确率（峰值超过27%）。尤为突出的是，其可训练参数少于1000个，推理速度比原KAN快50%，展现出优异的效率与实用性。
原文摘要 · Abstract (English)
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.
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