  This paper introduces a tensor neural network (TNN) to address nonparametric
regression problems. Characterized by its distinct sub-network structure, the
TNN effectively facilitates variable separation, thereby enhancing the
approximation of complex, unknown functions. Our comparative analysis reveals
that the TNN outperforms conventional Feed-Forward Networks (FFN) and Radial
Basis Function Networks (RBN) in terms of both approximation accuracy and
generalization potential, despite a similar scale of parameters. A key
innovation of our approach is the integration of statistical regression and
numerical integration within the TNN framework. This integration allows for the
efficient computation of high-dimensional integrals associated with the
regression function. The implications of this advancement extend to a broader
range of applications, particularly in scenarios demanding precise
high-dimensional data analysis and prediction.
