Designing molecules with specific properties is a long-lasting research problem and is central to advancing crucial domains such as drug discovery and material science. Recent advances in deep graph generative models treat molecule design as graph generation problems which provide new opportunities toward the breakthrough of this long-lasting problem. Existing models, however, have many shortcomings, including poor interpretability and controllability toward desired molecular properties. This paper focuses on new methodologies for molecule generation with interpretable and controllable deep generative models, by proposing new monotonically-regularized graph variational autoencoders. The proposed models learn to represent the molecules with latent variables and then learn the correspondence between them and molecule properties parameterized by polynomial functions. To further improve the intepretability and controllability of molecule generation towards desired properties, we derive new objectives which further enforce monotonicity of the relation between some latent variables and target molecule properties such as toxicity and clogP. Extensive experimental evaluation demonstrates the superiority of the proposed framework on accuracy, novelty, disentanglement, and control towards desired molecular properties. The code is open-source at https://anonymous.4open.science/r/MDVAE-FD2C.
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