  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.
