用统计方法解析单层神经网络，提升可解释性与准确性

Neural networks are often regarded as "black boxes" due to their complex functions and numerous parameters, which poses significant challenges for interpretability. This study addresses these challenges by introducing methods to enhance the understanding of neural networks, focusing specifically on models with a single hidden layer. We establish a theoretical framework by demonstrating that the neural network estimator can be interpreted as a nonparametric regression model. Building on this foundation, we propose statistical tests to assess the significance of input neurons and introduce algorithms for dimensionality reduction, including clustering and (PCA), to simplify the network and improve its interpretability and accuracy. The key contributions of this study include the development of a bootstrapping technique for evaluating artificial neural network (ANN) performance, applying statistical tests and logistic regression to analyze hidden neurons, and assessing neuron efficiency. We also investigate the behavior of individual hidden neurons in relation to out-put neurons and apply these methodologies to the IDC and Iris datasets to validate their practical utility. This research advances the field of Explainable Artificial Intelligence by presenting robust statistical frameworks for interpreting neural networks, thereby facilitating a clearer understanding of the relationships between inputs, outputs, and individual network components.