WormKAN: Are KAN Effective for Identifying and Tracking Concept Drift in Time Series?

TL;DR

This work tackles concept drift in co-evolving time series by introducing WormKAN, a patch-based, Kolmogorov-Arnold Network (KAN)–driven framework. It combines PatchNorm for robust patch-level inputs, a KAN-based autoencoder with a self-representation layer $\boldsymbol{\Theta}_s$, and a temporal-smoothness constraint to learn cross-patch dependencies and reveal concept transitions. Concept dynamics are identified via the evolution of $\boldsymbol{\Theta}_s \mathbf{R}$, with boundaries detected by peak analysis and drift signaled by proximity to concept prototypes; forecasting leverages autoregressive concept transitions to predict future patches. Empirically, WormKAN demonstrates strong concept identification and drift tracking across MoCap, stock market, and online activity data, while achieving competitive forecasting performance against both standard and concept-aware baselines; the original KAN, while interpretable, benefits from WormKAN’s structured representation and drift-aware objectives. The approach highlights the potential of $k$-block diagonal self-representation in $\boldsymbol{\Theta}_s$ for interpretable segmentation of complex, dynamic time-series systems.

Abstract

Dynamic concepts in time series are crucial for understanding complex systems such as financial markets, healthcare, and online activity logs. These concepts help reveal structures and behaviors in sequential data for better decision-making and forecasting. However, existing models often struggle to detect and track concept drift due to limitations in interpretability and adaptability. To address this challenge, inspired by the flexibility of the recent Kolmogorov-Arnold Network (KAN), we propose WormKAN, a concept-aware KAN-based model to address concept drift in co-evolving time series. WormKAN consists of three key components: Patch Normalization, Temporal Representation Module, and Concept Dynamics. Patch normalization processes co-evolving time series into patches, treating them as fundamental modeling units to capture local dependencies while ensuring consistent scaling. The temporal representation module learns robust latent representations by leveraging a KAN-based autoencoder, complemented by a smoothness constraint, to uncover inter-patch correlations. Concept dynamics identifies and tracks dynamic transitions, revealing structural shifts in the time series through concept identification and drift detection. These transitions, akin to passing through a \textit{wormhole}, are identified by abrupt changes in the latent space. Experiments show that KAN and KAN-based models (WormKAN) effectively segment time series into meaningful concepts, enhancing the identification and tracking of concept drift.

Figures (5)

• Figure 1: The framework of WormKAN. The co-evolving time series first passes through PatchNorm to transform into normalized patches, followed by a KAN-based Temporal Representation module to extract representations enriched with concept information. Finally, the Concept Dynamics module identifies concepts and tracks concept drift.
• Figure 2: Concept transition through wormhole.
• Figure 3: Training original KAN and detecting concept drift.
• Figure 4: WormKAN identifies concepts and transitions on co-evolving motion series.
• Figure 5: Predicted results using WormKAN: true (blue) and forecasted (red) values for the first six stock series.