Harnessing Interpretability and Efficiency with Kolmogorov–Arnold Networks in Machine Learning

Kolmogorov–Arnold Networks (KANs) are a class of machine learning models that offer a unique blend of interpretability and flexibility by representing complex functions as compositions of simpler, univariate functions. This framework is inspired by the Kolmogorov-Arnold representation theorem, which asserts that any continuous multivariate function can be approximated as a sum of univariate functions. KANs have gained attention for their ability to provide transparent and efficient models, particularly in domains where understanding the decision-making process is crucial. This paper surveys the foundational concepts of KANs, explores their various architectural extensions (such as convolutional, probabilistic, and deep KANs), and examines their applications across diverse fields, including symbolic regression, time-series forecasting, scientific computing, healthcare, and reinforcement learning. We also discuss the challenges that remain in scaling KANs to larger datasets and integrating prior knowledge. Finally, we highlight the promising future directions for research, including hybrid models and the extension of KANs to unsupervised learning tasks. KANs present a compelling approach for building interpretable and efficient machine learning models, and their continued development is expected to drive advancements in both theory and practical applications.