Scalable and Interpretable Function-Based Architectures: A Survey of Kolmogorov–Arnold Networks

Kolmogorov–Arnold Networks (KANs) are an emerging class of neural architectures that replace traditional linear transformations and activation functions with learnable univariate function compositions, inspired by the Kolmogorov–Arnold representation theorem. By leveraging this foundational result in multivariate function decomposition, KANs offer a highly expressive yet interpretable alternative to standard multilayer perceptrons (MLPs) and convolutional or attention-based architectures. Recent advancements have shown that KANs can match or exceed the performance of conventional models across a range of tasks—particularly those characterized by smoothness, structure, or low-dimensional manifolds—while providing inherent advantages in data efficiency, robustness, and variable-level interpretability. In this survey, we provide an extensive overview of the KAN framework, tracing its theoretical underpinnings, architectural variants, and practical implementations. We examine the scalability of KANs in terms of model capacity, optimization efficiency, and hardware feasibility, and we benchmark their performance on synthetic, tabular, visual, and scientific datasets. We also analyze the unique trade-offs involved in deploying KANs at scale, including computational overhead and training dynamics. Finally, we identify key open research directions—including generalization theory, hybrid model integration, compiler support, and domain-specific applications—that will shape the future of KAN research. This survey aims to serve both as a comprehensive introduction and a roadmap for researchers and practitioners interested in functional architectures and the next generation of interpretable machine learning systems.