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Biomolecular graph analysis has recently gained much attention in theemerging field of geometric deep learning. Here we focus on organizingbiomolecular graphs in ways that expose meaningful relations and variationsbetween them. We propose a geometric scattering autoencoder (GSAE) network forlearning such graph embeddings. Our embedding network first extracts rich graphfeatures using the recently proposed geometric scattering transform. Then, itleverages a semi-supervised variational autoencoder to extract alow-dimensional embedding that retains the information in these features thatenable prediction of molecular properties as well as characterize graphs. Weshow that GSAE organizes RNA graphs both by structure and energy, accuratelyreflecting bistable RNA structures. Also, the model is generative and cansample new folding trajectories.

Uncovering the Folding Landscape of RNA Secondary Structure with Deep Graph Embeddings