SigKAN: Signature-Weighted Kolmogorov-Arnold Networks for Time Series

TL;DR

SigKAN advances multivariate time-series modeling by weighting Kolmogorov-Arnold networks with learnable path-signature features, capturing the geometry of sequential data. The architecture combines gated residual KANs with a learnable path-signature pathway, producing a sequence-weighted output that preserves temporal structure. Across two Binance crypto prediction tasks, SigKAN achieves higher stability and competitive accuracy, notably excelling in 1-step ahead forecasts and offering robust performance without relying on recurrent calculus. The approach holds promise for time-series analysis and financial forecasting, with potential extensions to broader sequential domains and further efficiency improvements.

Abstract

We propose a novel approach that enhances multivariate function approximation using learnable path signatures and Kolmogorov-Arnold networks (KANs). We enhance the learning capabilities of these networks by weighting the values obtained by KANs using learnable path signatures, which capture important geometric features of paths. This combination allows for a more comprehensive and flexible representation of sequential and temporal data. We demonstrate through studies that our SigKANs with learnable path signatures perform better than conventional methods across a range of function approximation challenges. By leveraging path signatures in neural networks, this method offers intriguing opportunities to enhance performance in time series analysis and time series forecasting, among other fields.

Figures (4)

• Figure 1: KAN: Kolmogorov Arnold Networks
• Figure 2: SigKAN
• Figure 3: Gated Residual KAN (GRKAN)
• Figure 4: Model and errors based on number of steps forward