Evaluating Kolmogorov–Arnold Networks for Scientific Discovery: A Simple Yet Effective Approach

KolmogorovArnold Network (KAN) is an emerging interpretable neural network compared to fully black-box MLPs. Recently, emerging works focus on comprehensive and fair comparisons between KAN and MLP in various tasks. However, these works didn't focus on the strongest advantage of KAN: generating symbolic outputs. The ability of KAN to provide scientific insights or even discover new science is under-examined. In this work, we propose several novel metrics to measure how well a KAN performs on symbolic function fitting: R²-Mean, weighted R²-complexity loss, and ranking metrics. We also propose a metric to determine mathematical complexity of a target function and evaluate KAN with several functions of different mathematical complexity. Additionally, we also tried inputs with different ranges to find the effect of normalization.