Kolmogorov-Arnold Networks (KAN) for Time Series Classification and Robust Analysis

TL;DR

A fair comparison among KAN, MLP, and mixed structures indicates that KAN can achieve performance comparable to, or even slightly better than, MLP across 128 time series datasets, and assesses the robustness of these models.

Abstract

Kolmogorov-Arnold Networks (KAN) has recently attracted significant attention as a promising alternative to traditional Multi-Layer Perceptrons (MLP). Despite their theoretical appeal, KAN require validation on large-scale benchmark datasets. Time series data, which has become increasingly prevalent in recent years, especially univariate time series are naturally suited for validating KAN. Therefore, we conducted a fair comparison among KAN, MLP, and mixed structures. The results indicate that KAN can achieve performance comparable to, or even slightly better than, MLP across 128 time series datasets. We also performed an ablation study on KAN, revealing that the output is primarily determined by the base component instead of b-spline function. Furthermore, we assessed the robustness of these models and found that KAN and the hybrid structure MLP\_KAN exhibit significant robustness advantages, attributed to their lower Lipschitz constants. This suggests that KAN and KAN layers hold strong potential to be robust models or to improve the adversarial robustness of other models.

Figures (8)

• Figure 1: A three-layer KAN structure with the architecture [3-5-3-1].
• Figure 2: Performance comparison of five models across 128 datasets
• Figure 3: Critical diagram of accuracy for five models across 128 datasets (higher rank is better)
• Figure 4: Distribution of the flattened Train/Test output values of the last layer of the model under different configurations on the CBF dataset. (a) Train: Grid size of 1, (b)Train: Grid size of 50, (c) Test: Grid size of 1, and (d)Test: Grid size of 50.
• Figure 5: ASR distribution across 128 datasets for five models in different perturbation eps.