We introduce Clifford Kolmogorov-Arnold Network (ClKAN), a flexible and efficient architecture for function approximation in arbitrary Clifford algebra spaces. We propose the use of Randomized Quasi Monte Carlo grid generation as a solution to the exponential scaling associated with higher dimensional algebras. Our ClKAN also introduces new batch normalization strategies to deal with variable domain input. ClKAN finds application in scientific discovery and engineering, and is validated in synthetic and physics inspired tasks.

翻译：本文提出克利福德-柯尔莫哥洛夫-阿诺德网络（ClKAN），这是一种适用于任意克利福德代数空间的灵活高效函数逼近架构。针对高维代数伴随的指数级计算复杂度问题，我们提出采用随机拟蒙特卡洛网格生成方法作为解决方案。ClKAN还引入了创新的批归一化策略以处理变定义域输入问题。该网络在科学发现与工程领域具有应用价值，并在合成任务及物理启发的任务中得到了验证。