TKAN: Temporal Kolmogorov-Arnold Networks

TKAN: Temporal Kolmogorov-Arnold Networks

5 Jun 2024 | Rémi Genet¹ and Hugo Inzirillo²
The paper introduces Temporal Kolmogorov-Arnold Networks (TKANs), a novel neural network architecture that combines the strengths of Kolmogorov-Arnold Networks (KANs) and Long Short-Term Memory (LSTM) networks. TKANs are designed to handle multi-step time series forecasting with improved accuracy and efficiency. The architecture incorporates Recurring Kolmogorov-Arnold Networks (RKANs) that manage memory and temporal dependencies, enabling the network to learn and utilize past information effectively. TKANs address the limitations of traditional models in capturing complex sequential patterns, offering significant potential for advancements in time series analysis. KANs are a type of neural network inspired by the Kolmogorov-Arnold representation theorem, which allows for the representation of multivariate functions as compositions of univariate functions. This structure enables KANs to learn complex patterns with improved interpretability. TKANs extend this concept by integrating temporal dynamics through the use of memory mechanisms, allowing the network to maintain and utilize information over time. The TKAN architecture combines RKANs with a modified LSTM cell. This hybrid approach enables the network to capture complex nonlinearities and maintain long-term memory, making it suitable for tasks involving complex sequential data. The key components of TKANs include RKAN layers for short-term memory management and gating mechanisms for controlling information flow. The paper also presents a detailed description of the TKAN architecture, including its training process, preprocessing steps, and loss function. The model is evaluated on real market data, demonstrating its effectiveness in multi-step forecasting. The results show that TKANs outperform traditional models like LSTM and GRU, particularly in longer-term predictions, with higher R-squared values and better stability. The study highlights the potential of TKANs in time series forecasting, showing that they can handle complex sequential data more effectively than traditional models. The paper concludes that TKANs offer a promising approach for improving the accuracy and stability of time series models, particularly in real-world applications.The paper introduces Temporal Kolmogorov-Arnold Networks (TKANs), a novel neural network architecture that combines the strengths of Kolmogorov-Arnold Networks (KANs) and Long Short-Term Memory (LSTM) networks. TKANs are designed to handle multi-step time series forecasting with improved accuracy and efficiency. The architecture incorporates Recurring Kolmogorov-Arnold Networks (RKANs) that manage memory and temporal dependencies, enabling the network to learn and utilize past information effectively. TKANs address the limitations of traditional models in capturing complex sequential patterns, offering significant potential for advancements in time series analysis. KANs are a type of neural network inspired by the Kolmogorov-Arnold representation theorem, which allows for the representation of multivariate functions as compositions of univariate functions. This structure enables KANs to learn complex patterns with improved interpretability. TKANs extend this concept by integrating temporal dynamics through the use of memory mechanisms, allowing the network to maintain and utilize information over time. The TKAN architecture combines RKANs with a modified LSTM cell. This hybrid approach enables the network to capture complex nonlinearities and maintain long-term memory, making it suitable for tasks involving complex sequential data. The key components of TKANs include RKAN layers for short-term memory management and gating mechanisms for controlling information flow. The paper also presents a detailed description of the TKAN architecture, including its training process, preprocessing steps, and loss function. The model is evaluated on real market data, demonstrating its effectiveness in multi-step forecasting. The results show that TKANs outperform traditional models like LSTM and GRU, particularly in longer-term predictions, with higher R-squared values and better stability. The study highlights the potential of TKANs in time series forecasting, showing that they can handle complex sequential data more effectively than traditional models. The paper concludes that TKANs offer a promising approach for improving the accuracy and stability of time series models, particularly in real-world applications.
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[slides and audio] TKAN%3A Temporal Kolmogorov-Arnold Networks