A novel family of generalized stochastic neural network operators with illustrations of their various capabilities

Abstract

This study introduces a novel family of generalized stochastic neural network (GSNN) operators with enhanced modeling and approximation capabilities. Point-wise and uniform approximation results are established, along with estimations of the rate of convergence. By utilizing vector functions and vector inputs, the proposed operators achieve improved convergence rates and effectiveness in handling complex data. Their applicability in optimization and modeling real-world phenomena is demonstrated through the approximation of the Rosenbrock function. A detailed comparative analysis confirms that the GSNN operators outperform several existing operators in terms of convergence speed, approximation order, and accuracy metrics, including the $F_1$-score. Furthermore, the operators' modeling capabilities are validated using real-world cardiovascular disease data, where they exhibit superior predictive performance. The incorporation of stochastic processes enables the proposed operators to effectively capture and model the inherent uncertainties present in real-world scenarios.