Radial Basis Function Neural Networks (RBFNNs) represent a powerful and flexible class of artificial neural networks, widely utilized in various domains such as function approximation, classification, and system modeling. This paper presents a comprehensive study on multiple RBFNN models trained using different loss functions, including Mean Squared Error (MSE), Hinge Loss, Smoothed Hinge Loss, Huber Loss, and Poisson Loss. We investigate how these loss functions influence the learning dynamics, convergence behavior, and generalization capability of RBFNNs, particularly in the context of classification problems such as the XNOR problem. Furthermore, we explore the impact of varying key parameters, such as the centers, weights, and standard deviations on the overall performance of the models. A comparative evaluation is conducted across the models to identify strengths and limitations associated with each loss function. The findings from this analysis provide valuable insights and practical guidelines for selecting appropriate loss functions and designing optimal RBFNN architectures for classification tasks.