Neural networks, often viewed as black boxes due to their complex composition of functions and parameters, pose significant challenges for interpretability. This study addresses these challenges by exploring various methods for interpreting neural networks, focusing on both theoretical and practical aspects. Firstly, we demonstrate that the neural network estimator \ f_n \ can be interpreted as a nonparametric regression model constructed as a sieved M-estimator. This approach ensures the weak convergence of \ f_n \ within the metric space \ (\Theta, d) \, providing a solid theoretical foundation for understanding neural networks. Building on these theoretical insights, the study introduces statistical tests designed to assess the importance of input variables, offering a clearer understanding of their contributions to the model. Dimensionality reduction algorithms are also explored, highlighting their role in simplifying the model, enhancing both interpretability and accuracy. Furthermore, we show that statistical confidence intervals enhance model reliability by providing more robust estimates. Statistical tests are also employed to evaluate and interpret the performance of individual neurons, identifying their contribution to classification tasks and providing insights into the network's functioning. To validate these theoretical findings, simulations were conducted and applied to the IDC and Iris datasets. These experiments illustrate the practical utility of the proposed methods and affirm the effectiveness of the neural network estimator in real-world applications. This study contributes to the emerging field of Explainable Artificial Intelligence by presenting methodologies for interpreting traditional deep artificial neural networks through statistical frameworks, thereby facilitating a better understanding of the relationship between inputs and outputs and the performance of individual network components.
