  The point cloud is a flexible representation for a wide variety of data
types, and is a particularly natural fit for the 3D conformations of molecules.
Extant molecule embedding/representation schemes typically focus on internal
degrees of freedom, ignoring the global 3D orientation. For tasks that depend
on knowledge of both molecular conformation and 3D orientation, such as the
generation of molecular dimers, clusters, or condensed phases, we require a
representation which is provably complete in the types and positions of atomic
nuclei and roto-inversion equivariant with respect to the input point cloud. We
develop, train, and evaluate a new type of autoencoder, molecular O(3) encoding
net (Mo3ENet), for multi-type point clouds, for which we propose a new
reconstruction loss, capitalizing on a Gaussian mixture representation of the
input and output point clouds. Mo3ENet is end-to-end equivariant, meaning the
learned representation can be manipulated on O(3), a practical bonus for
downstream learning tasks. An appropriately trained Mo3ENet latent space
comprises a universal embedding for scalar and vector molecule property
prediction tasks, as well as other downstream tasks incorporating the 3D
molecular pose.
