The paper "Reduced Effectiveness of Kolmogorov-Arnold Networks on Functions with Noise" by Haoran Shen, Chen Zeng, Jiahui Wang, and Qiao Wang explores the impact of noise on the performance of Kolmogorov-Arnold Networks (KANs). The authors observe that even a small amount of noise can significantly degrade the performance of KANs. They propose two strategies to mitigate this issue: kernel filtering and oversampling. 1. **Kernel Filtering**: The authors use kernel filtering based on diffusion maps to pre-filter noisy data before training KANs. They find that while kernel filtering can reduce noise, determining the optimal variance parameter $\sigma$ is challenging and nonlinearly dependent on the Signal-to-Noise Ratio (SNR). The effectiveness of kernel filtering diminishes as the SNR increases. 2. **Oversampling**: The authors also explore increasing the volume of training data to reduce the impact of noise. They discover that increasing the training data by a factor of $r$ results in a test-loss (RMSE) that asymptotically follows a trend of $\sim \mathcal{O}(r^{-\frac{1}{2}})$ as $r \to +\infty$. This suggests that while oversampling is effective, it requires a substantial increase in data, which can be costly. 3. **Combining Techniques**: The authors combine both oversampling and kernel filtering to see if they can achieve better results. However, they find that the combined approach does not yield significantly improved outcomes and often results in higher test losses compared to using oversampling alone. The paper concludes that while both techniques can help mitigate the effects of noise, they have limitations. Kernel filtering is effective in low SNR scenarios but becomes less effective as SNR increases, while oversampling is more effective in general but requires a large amount of data. The authors suggest that KANs need to overcome the challenges posed by noise interference to achieve better performance.The paper "Reduced Effectiveness of Kolmogorov-Arnold Networks on Functions with Noise" by Haoran Shen, Chen Zeng, Jiahui Wang, and Qiao Wang explores the impact of noise on the performance of Kolmogorov-Arnold Networks (KANs). The authors observe that even a small amount of noise can significantly degrade the performance of KANs. They propose two strategies to mitigate this issue: kernel filtering and oversampling. 1. **Kernel Filtering**: The authors use kernel filtering based on diffusion maps to pre-filter noisy data before training KANs. They find that while kernel filtering can reduce noise, determining the optimal variance parameter $\sigma$ is challenging and nonlinearly dependent on the Signal-to-Noise Ratio (SNR). The effectiveness of kernel filtering diminishes as the SNR increases. 2. **Oversampling**: The authors also explore increasing the volume of training data to reduce the impact of noise. They discover that increasing the training data by a factor of $r$ results in a test-loss (RMSE) that asymptotically follows a trend of $\sim \mathcal{O}(r^{-\frac{1}{2}})$ as $r \to +\infty$. This suggests that while oversampling is effective, it requires a substantial increase in data, which can be costly. 3. **Combining Techniques**: The authors combine both oversampling and kernel filtering to see if they can achieve better results. However, they find that the combined approach does not yield significantly improved outcomes and often results in higher test losses compared to using oversampling alone. The paper concludes that while both techniques can help mitigate the effects of noise, they have limitations. Kernel filtering is effective in low SNR scenarios but becomes less effective as SNR increases, while oversampling is more effective in general but requires a large amount of data. The authors suggest that KANs need to overcome the challenges posed by noise interference to achieve better performance.