Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Properties

TL;DR

This paper evaluates the impact of angular features in rotationally equivariant neural networks for molecular property prediction, showing that including angular dependencies significantly improves accuracy and parameter efficiency.

Contribution

It provides an ablation study demonstrating the practical benefits of angular features in ENNs using the e3nn library on the QM9 dataset.

Findings

Adding angular features reduces test error by 23% on average.

Increasing network depth reduces test error by only 4%.

Angular features notably improve dipole moment prediction.

Abstract

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 directly via an ablation study with \texttt{e3nn} and the QM9 data set. We find that, for fixed network depth and parameter count, adding angular features decreased test error by an average of 23%. Meanwhile, increasing network depth decreased test error by only 4% on average, implying that rotationally equivariant layers are comparatively parameter efficient. We present an explanation of the accuracy improvement on the dipole moment, the target which benefited most from the introduction of angular features.