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

TL;DR

SigKAN introduces a novel neural network architecture that combines learnable path signatures with Kolmogorov-Arnold networks to improve multivariate function approximation and time series analysis.

Contribution

The paper presents a new method integrating learnable path signatures with KANs, enhancing their ability to model complex sequential data.

Findings

Outperforms conventional methods in function approximation tasks

Improves time series forecasting accuracy

Provides a flexible representation of temporal data

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.