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199070 https://hdl.handle.net/2286/R.2.N.199070 <p>Basina, D., Vishal, J. R., Choudhary, A., &amp; Chakravarthi, B. (2024). <em>KAT to KANs: A Review of Kolmogorov-Arnold Networks and the Neural Leap Forward. </em><a href="https://hdl.handle.net/2286/R.2.N.199070"><em>https://hdl.handle.net/2286/R.2.N.199070</em></a><em> </em>[Preprint]</p><p>Also available in arXiv as:</p><p>Basina, D., Vishal, J. R., Choudhary, A., &amp; Chakravarthi, B. (2024). <em>KAT to KANs: A Review of Kolmogorov-Arnold Networks and the Neural Leap Forward</em> (arXiv:2411.10622; Version 1). arXiv. <a href="https://doi.org/10.48550/arXiv.2411.10622">https://doi.org/10.48550/arXiv.2411.10622</a></p> 10.48550/arXiv.2411.10622 http://rightsstatements.org/vocab/InC/1.0/ http://creativecommons.org/licenses/by/4.0 2024-11-15 13 pages eng Basina, Divesh Vishal, Joseph Raj Choudhary, Aarya Chakravarthi, Bharatesh Text <p>The <em>curse of dimensionality</em> poses a significant challenge to modern multilayer perceptron-based architectures, often causing performance stagnation and scalability issues. Addressing this limitation typically requires vast amounts of data. In contrast, Kolmogorov-Arnold Networks have gained attention in the machine learning community for their bold claim of being unaffected by the curse of dimensionality. This paper explores the Kolmogorov-Arnold representation theorem and the mathematical principles underlying Kolmogorov-Arnold Networks, which enable their scalability and high performance in high-dimensional spaces. We begin with an introduction to foundational concepts necessary to understand Kolmogorov-Arnold Networks, including interpolation methods and Basis-splines, which form their mathematical backbone. This is followed by an overview of perceptron architectures and the Universal approximation theorem, a key principle guiding modern machine learning. This is followed by an overview of the Kolmogorov-Arnold representation theorem, including its mathematical formulation and implications for overcoming dimensionality challenges. Next, we review the architecture and error-scaling properties of Kolmogorov-Arnold Networks, demonstrating how these networks achieve true freedom from the curse of dimensionality. Finally, we discuss the practical viability of Kolmogorov-Arnold Networks, highlighting scenarios where their unique capabilities position them to excel in real-world applications. This review aims to offer insights into Kolmogorov-Arnold Networks' potential to redefine scalability and performance in high-dimensional learning tasks.</p> Neural networks (Computer science) Machine learning Mathematical models KAT to KANs: a review of Kolmogorov-Arnold Networks and the neural leap forward