SigKAN: Signature-Weighted Kolmogorov-Arnold Networks for Time Series This paper introduces SigKAN, a novel approach that enhances multivariate function approximation using learnable path signatures and Kolmogorov-Arnold networks (KANs). SigKAN improves the learning capabilities of KANs by weighting their outputs 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. The method leverages path signatures in neural networks to enhance performance in time series analysis and forecasting. SigKAN integrates learnable path signatures into the KAN framework, using them to compute path signatures for each input path. These signatures capture the underlying geometry of paths through iterated integrals, making them suitable for complex sequential data. The SigKAN architecture includes a Gated Residual KAN (GRKAN) layer that allows for modulating information flow and improving model interpretability. The path signature is used as a weighting mechanism to enhance the output of KAN layers. The paper evaluates SigKAN on two tasks: predicting volumes and predicting absolute returns. Results show that SigKAN outperforms conventional methods like TKAN, GRU, and LSTM in both tasks. SigKAN achieves higher R-squared values and demonstrates greater stability across different runs. The model also has a higher number of parameters due to the flattening of its output, but this does not significantly affect performance. The study demonstrates that SigKAN is effective in handling complex temporal relationships and can be applied to various fields, including financial modeling and time series analysis. The integration of path signatures into KANs offers new opportunities for improving the performance of neural networks in time series tasks. The method is implemented using TensorFlow and is available for use through the provided code.SigKAN: Signature-Weighted Kolmogorov-Arnold Networks for Time Series This paper introduces SigKAN, a novel approach that enhances multivariate function approximation using learnable path signatures and Kolmogorov-Arnold networks (KANs). SigKAN improves the learning capabilities of KANs by weighting their outputs 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. The method leverages path signatures in neural networks to enhance performance in time series analysis and forecasting. SigKAN integrates learnable path signatures into the KAN framework, using them to compute path signatures for each input path. These signatures capture the underlying geometry of paths through iterated integrals, making them suitable for complex sequential data. The SigKAN architecture includes a Gated Residual KAN (GRKAN) layer that allows for modulating information flow and improving model interpretability. The path signature is used as a weighting mechanism to enhance the output of KAN layers. The paper evaluates SigKAN on two tasks: predicting volumes and predicting absolute returns. Results show that SigKAN outperforms conventional methods like TKAN, GRU, and LSTM in both tasks. SigKAN achieves higher R-squared values and demonstrates greater stability across different runs. The model also has a higher number of parameters due to the flattening of its output, but this does not significantly affect performance. The study demonstrates that SigKAN is effective in handling complex temporal relationships and can be applied to various fields, including financial modeling and time series analysis. The integration of path signatures into KANs offers new opportunities for improving the performance of neural networks in time series tasks. The method is implemented using TensorFlow and is available for use through the provided code.