This paper introduces an Interpretable Neural Network (INN) incorporating spatial information to tackle the opaque parameterization process of random weighted neural networks. The INN leverages spatial information to elucidate the connection between parameters and network residuals. Furthermore, it devises a geometric relationship strategy using a pool of candidate nodes and established relationships to select node parameters conducive to network convergence. Additionally, a lightweight version of INN tailored for large-scale data modeling tasks is proposed. The paper also showcases the infinite approximation property of INN. Experimental findings on various benchmark datasets and real-world industrial cases demonstrate INN's superiority over other neural networks of the same type in terms of modeling speed, accuracy, and network structure.