  We present Symphony, an $E(3)$-equivariant autoregressive generative model
for 3D molecular geometries that iteratively builds a molecule from molecular
fragments. Existing autoregressive models such as G-SchNet and G-SphereNet for
molecules utilize rotationally invariant features to respect the 3D symmetries
of molecules. In contrast, Symphony uses message-passing with higher-degree
$E(3)$-equivariant features. This allows a novel representation of probability
distributions via spherical harmonic signals to efficiently model the 3D
geometry of molecules. We show that Symphony is able to accurately generate
small molecules from the QM9 dataset, outperforming existing autoregressive
models and approaching the performance of diffusion models.

Machine Learning;Biomolecules