  Molecular graphs generally contain subgraphs (known as groups) that are
identifiable and significant in composition, functionality, geometry, etc. Flat
latent representations (node embeddings or graph embeddings) fail to represent,
and support the use of, groups. Fully hierarchical latent representations, on
the other hand, are difficult to learn and, even if learned, may be too complex
to use or interpret. We propose tiered latent representations and latent spaces
for molecular graphs as a simple way to explicitly represent and utilize
groups, which consist of the atom (node) tier, the group tier and the molecule
(graph) tier. Specifically, we propose an architecture for learning tiered
latent representations and latent spaces using graph autoencoders, graph neural
networks, differentiable group pooling and the membership matrix. We discuss
its various components, major challenges and related work, for both a
deterministic and a probabilistic model. We also briefly discuss the usage and
exploration of tiered latent spaces. The tiered approach is applicable to other
types of structured graphs similar in nature to molecular graphs.
