Kolmogorov-Arnold Networks with Variable Function Basis

Di Wen, Yue WU, Xiao Han, Zhaocheng He, Zhe Wu, Yiling Wu, Shuhui Wang

Keywords: Kolmogorov Arnold Networks; variety function basis; interpretability; Weierstrass Approximation Theorem; Bernstein polynomial; multivarious time series forecasting; image for classification; learn the correct univariate functions.

Abstract:

\begin{abstract}
Neural networks exhibit exceptional performance in processing complex data, yet their internal structures remain largely unexplored. The emergence of Kolmogorov-Arnold Networks (KANs) represents a significant departure from traditional Multi-Layer Perceptrons (MLPs). In contrast to MLPs, KANs replace fixed activation functions at nodes (``neurons") with learnable activation functions on edges (``weights"), enhancing both accuracy and interpretability.
As data evolves, the demand for models that are both flexible and robust minimizing the influence of input data variability continues to grow. Addressing this need, we propose a general framework for KANs utilizing a \underline{\textbf{V}}ariety \underline{\textbf{B}}ernstei\underline{\textbf{n}} Polynomial Function Basis for \underline{\textbf{K}}olmogorov-\underline{\textbf{A}}rnold \underline{\textbf{N}}etworks (VBn-KAN). This framework leverages the Weierstrass approximation theorem to extend function basis within KANs in theory, specifically selecting Bernstein polynomials ($B_n$) for their robustness, assured by the uniform convergence proposition. Additionally, to enhance flexibility, we implement techniques to vary the function basis $B_n$ when handling diverse datasets. Comprehensive experiments across three fields: multivariate time series forecasting, computer vision, and function approximation—demonstrate that our method outperforms conventional approaches and other variants of KANs.
\end{abstract}

Primary Area: other topics in machine learning (i.e., none of the above)

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Submission Number: 1260