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

Tiered Latent Representations and Latent Spaces for Molecular Graphs