A new Kolmogorov-Arnold network (KAN) is proposed to approximate potentially irregular functions in high dimensions. We provide error bounds for this approximation, assuming that the Kolmogorov-Arnold expansion functions are sufficiently smooth. When the function is only continuous, we also provide universal approximation theorems. We show that it outperforms multilayer perceptrons in terms of accuracy and convergence speed. We also compare it with several proposed KAN networks: it outperforms all networks for irregular functions and achieves similar accuracy to the original spline-based KAN network for smooth functions. Finally, we compare some of the KAN networks in optimizing a French hydraulic valley.

翻译：提出了一种新的Kolmogorov-Arnold网络（KAN），用于逼近高维中可能不规则的函数。我们给出了该逼近的误差界，假设Kolmogorov-Arnold展开函数具有足够的光滑性。当函数仅为连续时，我们还提供了通用逼近定理。结果表明，该网络在精度和收敛速度上优于多层感知器。此外，我们将其与几种已有的KAN网络进行了比较：在不规则函数上，它优于所有网络；在光滑函数上，其精度与基于样条的原始KAN网络相当。最后，我们比较了部分KAN网络在优化法国某水力峡谷问题上的表现。