Reproduce “rKAN: Rational Kolmogorov-Arnold Networks” on OpenResearch
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About this paper
Alireza Afzal Aghaei
Rational Kolmogorov-Arnold Networks (rKANs) introduce rational functions as trainable basis functions on network edges, enhancing the approximation of functions with asymptotic behavior, singularities, or rapid changes. This architecture achieves high accuracy in synthetic regression tasks and competitive performance in MNIST classification, demonstrating particular efficacy in physics-informed deep learning for solving differential equations.
Key insights
- Rational functions are inherently better suited than polynomials or splines for approximating functions with asymptotic behavior, singularities, or rapid changes, which are common in scientific and engineering problems.
- Integrating trainable rational basis functions into KANs provides a powerful mechanism to achieve higher approximation accuracy with potentially simpler network structures and fewer terms.
- The rKAN framework can generalize and encompass other KAN variants, such as fractional KANs (fKANs), offering a more unified approach to KAN architecture design.
Summary by alphaXiv.
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