# Interpretable Molecular Graph Generation via Monotonic Constraints

arXiv: https://arxiv.org/abs/2203.00412 · HTML: https://mlsanity.com/paper/2203.00412/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 52 references that are in the map.
- First posted on arXiv 28 Feb 2022.

## Builds on (most cited first, 28 of 28)

- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [Learning Deep Generative Models of Graphs](https://mlsanity.com/paper/1803.03324/) (2018)
- [Constrained Graph Variational Autoencoders for Molecule Design](https://mlsanity.com/paper/1805.09076/) (2018)
- [Isolating Sources of Disentanglement in Variational Autoencoders](https://mlsanity.com/paper/1802.04942/) (2018)
- [NetGAN: Generating Graphs via Random Walks](https://mlsanity.com/paper/1803.00816/) (2018)
- [InfoVAE: Information Maximizing Variational Autoencoders](https://mlsanity.com/paper/1706.02262/) (2017)
- [Objective-Reinforced Generative Adversarial Networks (ORGAN) for Sequence Generation Models](https://mlsanity.com/paper/1705.10843/) (2017)
- [Graphite: Iterative Generative Modeling of Graphs](https://mlsanity.com/paper/1803.10459/) (2018)
- [Syntax-Directed Variational Autoencoder for Structured Data](https://mlsanity.com/paper/1802.08786/) (2018)
- [Learning Deep Disentangled Embeddings with the F-Statistic Loss](https://mlsanity.com/paper/1802.05312/) (2018)
- [MolecularRNN: Generating realistic molecular graphs with optimized properties](https://mlsanity.com/paper/1905.13372/) (2019)
- [Structured Disentangled Representations](https://mlsanity.com/paper/1804.02086/) (2018)
- [Differentiable Scaffolding Tree for Molecular Optimization](https://mlsanity.com/paper/2109.10469/) (2021)
- [MIMOSA: Multi-constraint Molecule Sampling for Molecule Optimization](https://mlsanity.com/paper/2010.02318/) (2020)
- [CORE: Automatic Molecule Optimization Using Copy & Refine Strategy](https://mlsanity.com/paper/1912.05910/) (2019)
- [Towards Interpretable Sparse Graph Representation Learning with Laplacian Pooling](https://mlsanity.com/paper/1905.11577/) (2019)
- [Deep Graph Translation](https://mlsanity.com/paper/1805.09980/) (2018)
- [Actively Learning what makes a Discrete Sequence Valid](https://mlsanity.com/paper/1708.04465/) (2017)

## Built on by (most cited first, 15 of 15)

- [Machine Learning for Synthetic Data Generation: A Review](https://mlsanity.com/paper/2302.04062/) (2023)
- [A Comprehensive Survey on Deep Graph Representation Learning](https://mlsanity.com/paper/2304.05055/) (2023)
- [A Survey on Deep Graph Generation: Methods and Applications](https://mlsanity.com/paper/2203.06714/) (2022)
- [MolGenSurvey: A Systematic Survey in Machine Learning Models for Molecule Design](https://mlsanity.com/paper/2203.14500/) (2022)
- [Controllable Data Generation by Deep Learning: A Review](https://mlsanity.com/paper/2207.09542/) (2022)
- [Exploring the Potential of Large Language Models in Graph Generation](https://mlsanity.com/paper/2403.14358/) (2024)
- [LLM-Based Multi-Agent Systems are Scalable Graph Generative Models](https://mlsanity.com/paper/2410.09824/) (2024)
- [Multi-objective Deep Data Generation with Correlated Property Control](https://mlsanity.com/paper/2210.01796/) (2022)
- [Deep Learning Methods for Small Molecule Drug Discovery: A Survey](https://mlsanity.com/paper/2303.00313/) (2023)
- [Neural Graph Generator: Feature-Conditioned Graph Generation using Latent Diffusion Models](https://mlsanity.com/paper/2403.01535/) (2024)
- [Overcoming Order in Autoregressive Graph Generation](https://mlsanity.com/paper/2402.03387/) (2024)
- [SCGG: A Deep Structure-Conditioned Graph Generative Model](https://mlsanity.com/paper/2209.09681/) (2022)
- [Large Generative Graph Models](https://mlsanity.com/paper/2406.05109/) (2024)
- [De Novo Generation of Hit-like Molecules from Gene Expression Profiles via Deep Learning](https://mlsanity.com/paper/2412.19422/) (2024)
- [NGTM: Substructure-based Neural Graph Topic Model for Interpretable Graph Generation](https://mlsanity.com/paper/2507.13133/) (2025)

## Abstract (arXiv)

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.