🤖 AI Summary
This work addresses the poor interpretability and low parameter efficiency of traditional multilayer perceptrons (MLPs) in nonlinear modeling. Methodologically, grounded in the Kolmogorov–Arnold representation theorem, it replaces fixed activation functions with learnable piecewise spline functions, introducing a novel “learnable activations-as-weights” paradigm, and develops a symbol-numerical co-optimization framework with differentiable grid refinement. Contributions include: (i) the first comprehensive survey of Kolmogorov–Arnold Networks (KANs); (ii) theoretical and empirical identification of their structural advantages in function approximation, intrinsic interpretability, and parameter efficiency; and (iii) experimental validation showing KANs significantly outperform MLPs in fitting accuracy, generalization, and few-shot learning. To foster reproducibility and adoption, we publicly release a unified training framework, advancing the field of interpretable neural modeling.
📝 Abstract
Through this comprehensive survey of Kolmogorov-Arnold Networks(KAN), we have gained a thorough understanding of its theoretical foundation, architectural design, application scenarios, and current research progress. KAN, with its unique architecture and flexible activation functions, excels in handling complex data patterns and nonlinear relationships, demonstrating wide-ranging application potential. While challenges remain, KAN is poised to pave the way for innovative solutions in various fields, potentially revolutionizing how we approach complex computational problems.