Research Directions on Kolmogorov–Arnold Networks: A Comprehensive Review

Utilizing the Kolmogorov–Arnold representation theorem, KANs have emerged as a mathematically rigorous and easily interpretable alternative to traditional neural networks. These networks decompose high-dimensional functions into sums of univariate continuous functions using adaptive activation functions. Compared to MLPs, KANs exhibit superior or comparable performance in accuracy, parameter efficiency, and interpretability. Applications highlight the advantages of KANs in solving complex partial differential equations with enhanced convergence and uncertainty quantification, modeling dynamic systems in a meaningful manner, and making reliable forecasts in the areas of power systems, environmental monitoring, and demand prediction. Based on current research on KANs, they demonstrate a promising frontier in interpretable deep learning, with increasing influence across numerous interdisciplinary scientific and engineering fields.