  It has been observed that even a small amount of noise introduced into the
dataset can significantly degrade the performance of KAN. In this brief note,
we aim to quantitatively evaluate the performance when noise is added to the
dataset. We propose an oversampling technique combined with denoising to
alleviate the impact of noise. Specifically, we employ kernel filtering based
on diffusion maps for pre-filtering the noisy data for training KAN network.
Our experiments show that while adding i.i.d. noise with any fixed SNR, when we
increase the amount of training data by a factor of $r$, the test-loss (RMSE)
of KANs will exhibit a performance trend like $\text{test-loss} \sim
\mathcal{O}(r^{-\frac{1}{2}})$ as $r\to +\infty$. We conclude that applying
both oversampling and filtering strategies can reduce the detrimental effects
of noise. Nevertheless, determining the optimal variance for the kernel
filtering process is challenging, and enhancing the volume of training data
substantially increases the associated costs, because the training dataset
needs to be expanded multiple times in comparison to the initial clean data. As
a result, the noise present in the data ultimately diminishes the effectiveness
of Kolmogorov-Arnold networks.
