In this paper, we propose to use Sinc interpolation in the context of Kolmogorov-Arnold Networks, neural networks with learnable activation functions, which recently gained attention as alternatives to Multilayer Perceptron. Many different function representations have already been tried, but we show that Sinc interpolation proposes a viable alternative, since it is known in numerical analysis to effectively represent both smooth functions and functions with singularities. This is important not only for function approximation but also for solving the partial differential equations with physics-informed neural networks. Through a series of experiments, we show that SincKANs provide better results in almost all of the examples we have considered.

翻译：本文提出将Sinc插值应用于Kolmogorov-Arnold网络——一种具有可学习激活函数的神经网络，该网络近期作为多层感知机的替代方案受到关注。尽管已有多种函数表示方法被尝试，但我们论证了Sinc插值是一种可行的替代方案，因为在数值分析中，它已被证明能有效表示光滑函数及含奇点函数。这一特性不仅对函数逼近至关重要，对基于物理信息神经网络求解偏微分方程也同样关键。通过一系列实验，我们展示了所考虑的几乎所有案例中，SincKANs均能提供更优结果。