  Biomolecular graph analysis has recently gained much attention in the
emerging field of geometric deep learning. Here we focus on organizing
biomolecular graphs in ways that expose meaningful relations and variations
between them. We propose a geometric scattering autoencoder (GSAE) network for
learning such graph embeddings. Our embedding network first extracts rich graph
features using the recently proposed geometric scattering transform. Then, it
leverages a semi-supervised variational autoencoder to extract a
low-dimensional embedding that retains the information in these features that
enable prediction of molecular properties as well as characterize graphs. We
show that GSAE organizes RNA graphs both by structure and energy, accurately
reflecting bistable RNA structures. Also, the model is generative and can
sample new folding trajectories.
