2025/01/17 by Rômulo Damasclin Chaves dos Santos, Santos, Rômulo Damasclin Chaves dos, Jorge Henrique de Oliveira Sales +1
Computer Science · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications
paper · pdf · doi:10.48550/arxiv.2501.10496
openalex publication_date 2025/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a novel extension to symmetrized neural network operators by incorporating fractional and mixed activation functions. This study addresses the limitations of existing models in approximating higher-order smooth functions, particularly in complex and high-dimensional spaces. Our framework introduces a fractional exponent in the activation functions, allowing adaptive non-linear approximations with improved accuracy. We define new density functions based on q-deformed and θ-parametrized logistic models and derive advanced Jackson-type inequalities that establish uniform convergence rates. Additionally, we provide a rigorous mathematical foundation for the proposed operators, supported by numerical validations demonstrating their efficiency in handling oscillatory and fractional components. The results extend the applicability of neural network approximation theory to broader functional spaces, paving the way for applications in solving partial differential equations and modeling complex systems.