SineKAN: Kolmogorov-Arnold Networks Using Sinusoidal Activation Functions **Authors:** Eric A. F. Reinhardt, P.R. Dinesh, S. Gleyzer **Abstract:** This paper introduces SineKAN, a variant of Kolmogorov-Arnold Networks (KANs) that uses sinusoidal activation functions instead of B-Spline functions. KANs are an alternative to traditional multi-layer perceptrons (MLPs) based on the Kolmogorov-Arnold Representation Theorem, which allows for the approximation of any multivariate function using a sum of continuous univariate functions. The original implementation of KANs uses learnable B-Spline activation functions, which are effective but slower than MLPs. SineKAN aims to improve performance and speed while maintaining numerical accuracy. **Key Contributions:** 1. **Model Architecture:** SineKAN uses a grid of learnable frequencies and amplitudes over fixed phase shifts, reducing the number of learnable parameters. 2. **Weight Initialization:** A novel initialization strategy is proposed to stabilize model performance across different grid sizes and depths. 3. **Universal Approximation:** The combination of learnable amplitudes and sinusoidal activation functions is shown to satisfy universal approximation properties. 4. **Performance and Speed:** SineKAN outperforms B-SplineKAN in terms of accuracy and inference speed, achieving up to 8 times faster performance on large batch sizes. **Results:** - **MNIST Benchmark:** SineKAN achieves better accuracy than B-SplineKAN across various hidden layer sizes and depths. - **Inference Speed:** SineKAN is significantly faster than B-SplineKAN, with better scaling for deep models and large batch sizes. **Discussion:** SineKAN shows promise as a scalable and efficient alternative to B-SplineKAN, particularly for high-depth and large batch models. Further exploration is needed to compare performance across a broader range of tasks and activation functions. **Conclusion:** SineKAN is a promising model that combines the benefits of sinusoidal activation functions with the Kolmogorov-Arnold framework, offering improved numerical performance and speed.SineKAN: Kolmogorov-Arnold Networks Using Sinusoidal Activation Functions **Authors:** Eric A. F. Reinhardt, P.R. Dinesh, S. Gleyzer **Abstract:** This paper introduces SineKAN, a variant of Kolmogorov-Arnold Networks (KANs) that uses sinusoidal activation functions instead of B-Spline functions. KANs are an alternative to traditional multi-layer perceptrons (MLPs) based on the Kolmogorov-Arnold Representation Theorem, which allows for the approximation of any multivariate function using a sum of continuous univariate functions. The original implementation of KANs uses learnable B-Spline activation functions, which are effective but slower than MLPs. SineKAN aims to improve performance and speed while maintaining numerical accuracy. **Key Contributions:** 1. **Model Architecture:** SineKAN uses a grid of learnable frequencies and amplitudes over fixed phase shifts, reducing the number of learnable parameters. 2. **Weight Initialization:** A novel initialization strategy is proposed to stabilize model performance across different grid sizes and depths. 3. **Universal Approximation:** The combination of learnable amplitudes and sinusoidal activation functions is shown to satisfy universal approximation properties. 4. **Performance and Speed:** SineKAN outperforms B-SplineKAN in terms of accuracy and inference speed, achieving up to 8 times faster performance on large batch sizes. **Results:** - **MNIST Benchmark:** SineKAN achieves better accuracy than B-SplineKAN across various hidden layer sizes and depths. - **Inference Speed:** SineKAN is significantly faster than B-SplineKAN, with better scaling for deep models and large batch sizes. **Discussion:** SineKAN shows promise as a scalable and efficient alternative to B-SplineKAN, particularly for high-depth and large batch models. Further exploration is needed to compare performance across a broader range of tasks and activation functions. **Conclusion:** SineKAN is a promising model that combines the benefits of sinusoidal activation functions with the Kolmogorov-Arnold framework, offering improved numerical performance and speed.