This article presents an input convex neural network architecture using Kolmogorov-Arnold networks (ICKAN). Two specific networks are presented: the first is based on a low-order, linear-by-part, representation of functions, and a universal approximation theorem is provided. The second is based on cubic splines, for which only numerical results support convergence. We demonstrate on simple tests that these networks perform competitively with classical input convex neural networks (ICNNs). In a second part, we use the networks to solve some optimal transport problems needing a convex approximation of functions and demonstrate their effectiveness. Comparisons with ICNNs show that cubic ICKANs produce results similar to those of classical ICNNs.

翻译：本文提出了一种基于Kolmogorov-Arnold网络的输入凸神经网络架构（ICKAN）。文中介绍了两种具体网络：第一种基于函数的低阶分段线性表示，并给出了相应的通用逼近定理；第二种基于三次样条，其收敛性仅通过数值结果予以支持。我们在简单测试中证明，这些网络的性能可与经典输入凸神经网络（ICNN）相媲美。在第二部分中，我们利用这些网络求解若干需要函数凸近似的最优传输问题，并验证了其有效性。与ICNN的比较表明，三次ICKAN能够产生与经典ICNN相似的结果。