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.

我们提出了一种新颖的方法，利用可学习的路径签名和科尔莫哥洛夫 - 阿诺德网络（KANs）来增强多变量函数逼近能力。通过利用可学习的路径签名对 KANs 获得的值加权，我们增强了这些网络的学习能力，从而更全面、灵活地表示顺序和时间数据。通过研究，我们证明了我们的 SigKANs 能够在各种函数逼近挑战中优于传统方法。通过在神经网络中利用路径签名，这种方法为时间序列分析和时间序列预测等领域提供了有趣的性能提升机会。