On the Sufficiency of a Single Hidden Layer in Feed-Forward Neural Networks Used for Machine Learning of Materials Properties

Abstract

Feed-forward neural networks (NNs) are widely used for the machine learning of properties of materials and molecules from descriptors of their composition and structure (materials informatics) as well as in other physics and chemistry applications. Often, multilayer (so-called “deep”) NNs are used. Considering that universal approximator properties hold for single-hidden-layer NNs, we compare here the performance of single-hidden-layer NNs (SLNN) with that of multilayer NNs (MLNN), including those previously reported in different applications. We consider three representative cases: the prediction of the band gaps of two-dimensional materials, prediction of the reorganization energies of oligomers, and prediction of the formation energies of polyaromatic hydrocarbons. In all cases, results as good as or better than those obtained with an MLNN could be obtained with an SLNN, and with a much smaller number of neurons. As SLNNs offer a number of advantages (including ease of construction and use, more favorable scaling of the number of nonlinear parameters, and ease of the modulation of properties of the NN model by the choice of the neuron activation function), we hope that this work will entice researchers to have a closer look at when an MLNN is genuinely needed and when an SLNN could be sufficient.