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The architecture of deep neural networks (DNNs), particularly the determination of their width and depth, significantly influences their performance and interpretability. The Kolmogorov-Arnold representation theorem provides a mathematical foundation for approximating multivariate continuous functions using univariate functions and has inspired the development of Kolmogorov-Arnold Networks (KANs). This paper explores how KANs can inform the architectural design of DNNs by guiding decisions on their width and depth. We provide a rigorous mathematical treatment and propose a novel neural network design with implementation using PyTorch. Through theoretical analysis, practical examples, and empirical experiments, we demonstrate that employing KAN principles can lead to more efficient, interpretable, and theoretically grounded neural network designs.

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Determining the Width and Depth of Deep Neural Networks by Leveraging Kolmogorov-Arnold Networks

  • 会议论文

  • 发表日期：

    2025年

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  • Tze-Houng Lee,
  • Xue-Ming Yuan

摘要

The architecture of deep neural networks (DNNs), particularly the determination of their width and depth, significantly influences their performance and interpretability. The Kolmogorov-Arnold representation theorem provides a mathematical foundation for approximating multivariate continuous functions using univariate functions and has inspired the development of Kolmogorov-Arnold Networks (KANs). This paper explores how KANs can inform the architectural design of DNNs by guiding decisions on their width and depth. We provide a rigorous mathematical treatment and propose a novel neural network design with implementation using PyTorch. Through theoretical analysis, practical examples, and empirical experiments, we demonstrate that employing KAN principles can lead to more efficient, interpretable, and theoretically grounded neural network designs.