Appendix Table of contents

A Empirical measurement of SCN's equivariance to rotations B OC20 IS2RE Direct Results C Implementation details D Note on spherical harmonics properties E Overfitting on the training dataset F Impact of model size The SCN is not strictly equivariant to rotations, but depending on the design choices approximate equivarance may be achieved. We begin by empirically measuring the network's invariance and equivariance to rotation for energy and forces respectively. Mean Absolute Difference (MAD) results for various model choices are shown in Table 3 for models with 12 layers and L = 6. Differences are averaged over a model's outputs for a random 1,000 atomic structures. There are four sources that may lead the network to predict different values for rotated versions of the input: 1) the use of m 0 coefficients during message passing, 2) non-linear message aggregation, Equation (3), 3) the energy and force output blocks, Equations (4,5), and 4) limits to numerical precision especially when using Automatic Mixed Precision (AMP).