This paper addresses several pressing concerns in artificial intelligence ( i.e., explainability, interpretability, and transparency) that primarily stem from the black-box nature of artificial intelligence models such as artificial neural networks (ANNs). The possibility of formulating an ANN training problem as a linear regression problem, solvable in a closed form, is explored. The formulation is based on the differential and autoregressive relationships at the training data points. With two Gaussian-activated ANNs, the network parameters are shown to be explicitly related to the moments of the training data. Several scenarios that demonstrate the effectiveness and weaknesses of this formulation approach, including sensitivity to both data noise and the sampling rate, are also discussed. A comparison is made between the differential formulation and autoregressive formulation, leading to the observation that the former is more sensitive to noise than the latter.