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

ICML 2025 · Time series › Anomaly detection · approach: Time series anomaly detection evaluation · 3 citations (OpenAlex)

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Proposes KAN-AD, a sub-1,000-parameter time series anomaly detector that replaces KAN's B-spline univariate functions with truncated Fourier expansions, adds constant-term elimination via differencing, and a 1D-CNN coefficient learner, evaluated on KPI, TODS, WSD, UCR and five multivariate benchmarks.

Problem

Forecasting-based time series anomaly detection overfits to local disturbances (peaks and drops) in training data, and vanilla KAN with B-spline basis is also sensitive to them, especially when training data contains anomalies.

Approach

Reformulate normal-pattern modeling as approximating the series with smooth univariate functions using truncated Fourier series (instead of B-splines) with learned coefficients from a 1D CNN, combined with first-order differencing to remove trend/constant-term effects and extra periodic univariate terms.

Key results

• On four UTS benchmarks KAN-AD reports average Event F1 of 0.7798 versus 0.6835 for the best prior baseline (KAN), roughly 15% improvement.
• KAN-AD uses 274 trainable parameters on UCR, versus 1,360 for KAN, and runs with 42s GPU time versus KAN's 66s.
• On five multivariate benchmarks KAN-AD achieves average Best F1 of 0.9076 with 4,491 parameters (measured on MSL), beating UniTS (0.8921).

Measured effects reported in the paper

Surprising findings

• Fourier-based KAN-AD using only the raw series X already outperforms vanilla KAN, indicating the Fourier basis itself helps over B-splines.
• Chebyshev polynomial variants underperform, which the authors attribute to minimax vs mean-squared-error objectives.

Limitations

• Trains a separate model per time series for univariate benchmarks, which limits scalability.
• Relies on a first-order differencing heuristic for trend removal and hand-tuned window size and number of Fourier terms.
• Inference efficiency comparisons are limited to a single dataset (UCR) and some baselines are excluded from timing comparisons.

Experimental setup

Datasets: KPI TODS WSD UCR SMD MSL SMAP SWaT PSM

Benchmarks: KPI TODS WSD UCR SMD MSL SMAP SWaT PSM

Metrics: Event F1 Best F1 Delay F1 AUPRC parameter count inference time

Baselines: SRCNN SAND Anomaly Transformer TranAD SubLOF TimesNet FITS OFA FCVAE LSTMAD KAN Informer

Builds on: Kolmogorov-Arnold Networks FITS FCVAE

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