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In this study, we explore the potential of orthogonal polynomial functions as activation functions within the SWAG neural network architecture. By employing Chebyshev, Legendre, Hermite polynomials and and sinusoidal functions, we conduct a rigorous comparative analysis to evaluate the performance enhancements across a range of benchmark datasets. Furthermore, this paper investigates the influence of factorial coefficients on the performance of these models, providing a nuanced understanding of how these mathematical modifications affect learning dynamics and model efficacy. Our results offer insights into optimizing neural network architectures through advanced mathematical functions.

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Orthogonal Activation Functions in Neural Networks: Utilizing Chebyshev, Legendre, and Hermite Polynomials

  • 会议论文

  • 发表日期：

    2025年

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  • Saeid Safaei,
  • Khaled Rasheed,
  • Thiab Taha,
  • Vahid Safaei,
  • Budak Arpinar,
  • Juan B. Gutiérrez,
  • Hamid R. Arabnia

摘要

In this study, we explore the potential of orthogonal polynomial functions as activation functions within the SWAG neural network architecture. By employing Chebyshev, Legendre, Hermite polynomials and and sinusoidal functions, we conduct a rigorous comparative analysis to evaluate the performance enhancements across a range of benchmark datasets. Furthermore, this paper investigates the influence of factorial coefficients on the performance of these models, providing a nuanced understanding of how these mathematical modifications affect learning dynamics and model efficacy. Our results offer insights into optimizing neural network architectures through advanced mathematical functions.