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.

翻译：我们提出了一种新方法，通过使用可学习路径签名和Kolmogorov-Arnold网络（KANs）来增强多元函数逼近能力。我们利用可学习路径签名对KANs的输出值进行加权，从而增强这些网络的学习能力；路径签名能够捕捉路径的重要几何特征。这种结合使得对序列数据和时间数据的表示更加全面和灵活。我们通过实验证明，在多种函数逼近任务中，我们提出的带有可学习路径签名的SigKANs优于传统方法。通过在神经网络中利用路径签名，该方法为时间序列分析和时间序列预测等领域的性能提升提供了引人注目的新途径。