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Smooth Kolmogorov Arnold networks enabling structural knowledge representation
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Kolmogorov-Arnold Networks (KANs) offer an efficient and interpretable alternative to traditional multi-layer perceptron (MLP) architectures due to their finite network topology. However, according to the results of Kolmogorov and Vitushkin, the representation of generic smooth functions by KAN implementations using analytic functions constrained to a finite number of cutoff points cannot be exact. Hence, the convergence of KAN throughout the training process may be limited. This paper explores the relevance of smoothness in KANs, proposing that smooth, structurally informed KANs can achieve equivalence to MLPs in specific function classes. By leveraging inherent structural knowledge, KANs may reduce the data required for training and mitigate the risk of generating hallucinated predictions, thereby enhancing model reliability and performance in computational biomedicine.
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Cited by 4 Pith papers
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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics
KKANs, a two-block KART-based architecture with MLP inner functions and basis-function outer functions, universally approximate continuous functions and empirically outperform MLP and cKAN baselines in regression, PIN...
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iTFKAN: Interpretable Time Series Forecasting with Kolmogorov-Arnold Network
iTFKAN uses KANs with injected trend and seasonal formulas plus time-frequency learning to forecast time series and expose prediction rationales as symbolic expressions.
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MatrixKAN: Parallelized Kolmogorov-Arnold Network
MatrixKAN replaces KAN's recursive B-spline evaluation with precomputed matrix multiplications, making training time nearly independent of spline degree.
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KAT to KANs: A Review of Kolmogorov-Arnold Networks and the Neural Leap Forward
A review of Kolmogorov-Arnold Networks that restates existing theory and claims, without new experiments or derived results.
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