  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.
