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Deep generative models have achieved remarkable success in various datadomains, including images, time series, and natural languages. There remain,however, substantial challenges for combinatorial structures, including graphs.One of the key challenges lies in the difficulty of ensuring semantic validityin context. For examples, in molecular graphs, the number of bonding-electronpairs must not exceed the valence of an atom; whereas in protein interactionnetworks, two proteins may be connected only when they belong to the same orcorrelated gene ontology terms. These constraints are not easy to beincorporated into a generative model. In this work, we propose a regularizationframework for variational autoencoders as a step toward semantic validity. Wefocus on the matrix representation of graphs and formulate penalty terms thatregularize the output distribution of the decoder to encourage the satisfactionof validity constraints. Experimental results confirm a much higher likelihoodof sampling valid graphs in our approach, compared with others reported in theliterature.

Constrained Generation of Semantically Valid Graphs via Regularizing Variational Autoencoders