The Evolution of Kolmogorov-Arnold Networks: A Bibliometric Study of Theoretical Foundations and Engineering Applications

Abstract The Kolmogorov Arnold Network (KAN) has emerged as one of the most rapidly growing research fronts in computational deep learning since its modern architectural formulation in 2024, yet no prior study has systematically mapped the intellectual structure and conceptual evolution of this field using bibliometric methods. This study addresses that gap by conducting a comprehensive bibliometric analysis of 625 peer reviewed publications retrieved from the Web of Science Core Collection using the search string combining “Kolmogorov Arnold network” and “Kolmogorov Arnold representation.” Two complementary science mapping techniques were employed: bibliographic coupling analysis and co-word analysis, both visualized using VOSviewer. The bibliographic coupling analysis identified four thematic clusters representing the current research front of the field, namely high stakes engineering applications and hybrid architectures, advanced feature extraction and diagnostic classification, theoretical foundations and empirical benchmarking, and specialized architectures for high dimensional and security critical tasks. The co-word analysis of 51 retained keywords further revealed four conceptual clusters spanning architectural foundations and deep learning integration, signal processing and robustness, predictive modeling and time series applications, and geospatial and sensor network applications. Collectively, the findings confirm that hybrid architectural integration and model interpretability constitute the defining design philosophy of contemporary KAN research, and that the field has achieved sufficient academic maturity to warrant strategic investment in its engineering deployment. The study concludes by identifying key theoretical and managerial implications and proposing concrete directions for future research to advance KAN toward computationally efficient and domain diversified engineering implementations.