The convergence results obtained in the paper have significant implications for the generalization performance of neural networks trained with finite samples. As the sample size grows to infinity, the convergence of the optimal parameters and value functions indicates that the neural network model becomes more robust and generalizable. The convergence of the objective functionals and optimal parameters to suitable limit objects defined on the Wasserstein space of Borel probability measures suggests that the neural network can effectively capture the underlying patterns in the data and make accurate predictions even with limited training samples. This convergence ensures that the neural network model can generalize well to unseen data and maintain its performance across different datasets.