Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Properties

Equivariant neural networks (ENNs) are graph neural networks embedded in $\mathbb{R}^3$ and are well suited for predicting molecular properties. The ENN library e3nn has customizable convolutions, which can be designed to depend only on distances between points, or also on angular features, making them rotationally invariant, or equivariant, respectively. This paper studies the practical value of including angular dependencies for molecular property prediction using the QM9 data set. We find that for fixed network depth, adding angular features improves the accuracy on most targets. For most, but not all, molecular properties, distance-only e3nns (L0Nets) can compensate by increasing convolutional layer depth. Our angular-feature e3nn (L1Net) architecture beats previous state-of-the-art results on the global electronic properties dipole moment, isotropic polarizability, and electronic spatial extent.