# Constrained Generation of Semantically Valid Graphs via Regularizing Variational Autoencoders

arXiv: https://arxiv.org/abs/1809.02630 · HTML: https://mlsanity.com/paper/1809.02630/

## Key facts

- Cited by 74 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Sep 2018.

## Built on by (most cited first, 30 of 74)

- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [GraphDF: A Discrete Flow Model for Molecular Graph Generation](https://mlsanity.com/paper/2102.01189/) (2021)
- [GraphEBM: Molecular Graph Generation with Energy-Based Models](https://mlsanity.com/paper/2102.00546/) (2021)
- [Autoregressive Diffusion Model for Graph Generation](https://mlsanity.com/paper/2307.08849/) (2023)
- [Graph-based Semi-supervised Learning: A Comprehensive Review](https://mlsanity.com/paper/2102.13303/) (2021)
- [SELFIES and the future of molecular string representations](https://mlsanity.com/paper/2204.00056/) (2022)
- [Graph Coarsening with Neural Networks](https://mlsanity.com/paper/2102.01350/) (2021)
- [LIMO: Latent Inceptionism for Targeted Molecule Generation](https://mlsanity.com/paper/2206.09010/) (2022)
- [Fast Graph Generation via Spectral Diffusion](https://mlsanity.com/paper/2211.08892/) (2022)
- [A Survey on Graph Diffusion Models: Generative AI in Science for Molecule, Protein and Material](https://mlsanity.com/paper/2304.01565/) (2023)
- [3DLinker: An E(3) Equivariant Variational Autoencoder for Molecular Linker Design](https://mlsanity.com/paper/2205.07309/) (2022)
- [Artificial Intelligence in Drug Discovery: Applications and Techniques](https://mlsanity.com/paper/2106.05386/) (2021)
- [The Expressive Power of Graph Neural Networks: A Survey](https://mlsanity.com/paper/2308.08235/) (2023)
- [Data-Efficient Graph Grammar Learning for Molecular Generation](https://mlsanity.com/paper/2203.08031/) (2022)
- [Modularity-Aware Graph Autoencoders for Joint Community Detection and Link Prediction](https://mlsanity.com/paper/2202.00961/) (2022)
- [Domain-Agnostic Molecular Generation with Chemical Feedback](https://mlsanity.com/paper/2301.11259/) (2023)
- [Graph Neural Networks for Molecules](https://mlsanity.com/paper/2209.05582/) (2022)
- [Controllable Data Generation by Deep Learning: A Review](https://mlsanity.com/paper/2207.09542/) (2022)
- [Hyperbolic Geometric Latent Diffusion Model for Graph Generation](https://mlsanity.com/paper/2405.03188/) (2024)
- [Improving Graph Generation by Restricting Graph Bandwidth](https://mlsanity.com/paper/2301.10857/) (2023)
- [Deep Graph Learning for Anomalous Citation Detection](https://mlsanity.com/paper/2202.11360/) (2022)
- [Molecule Generation for Drug Design: a Graph Learning Perspective](https://mlsanity.com/paper/2202.09212/) (2022)
- [Cold Start Similar Artists Ranking with Gravity-Inspired Graph Autoencoders](https://mlsanity.com/paper/2108.01053/) (2021)
- [GP-MoLFormer: A Foundation Model For Molecular Generation](https://mlsanity.com/paper/2405.04912/) (2024)
- [An Equivariant Generative Framework for Molecular Graph-Structure Co-Design](https://mlsanity.com/paper/2304.12436/) (2023)
- [Node-Aligned Graph-to-Graph (NAG2G): Elevating Template-Free Deep Learning Approaches in Single-Step Retrosynthesis](https://mlsanity.com/paper/2309.15798/) (2023)
- [Generative and Contrastive Paradigms Are Complementary for Graph Self-Supervised Learning](https://mlsanity.com/paper/2310.15523/) (2023)
- [Micro and Macro Level Graph Modeling for Graph Variational Auto-Encoders](https://mlsanity.com/paper/2210.16844/) (2022)
- [Distributional Drift Adaptation with Temporal Conditional Variational Autoencoder for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2209.00654/) (2022)
- [Let There Be Order: Rethinking Ordering in Autoregressive Graph Generation](https://mlsanity.com/paper/2305.15562/) (2023)

## Abstract (arXiv)

Deep generative models have achieved remarkable success in various data domains, 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 validity in context. For examples, in molecular graphs, the number of bonding-electron pairs must not exceed the valence of an atom; whereas in protein interaction networks, two proteins may be connected only when they belong to the same or correlated gene ontology terms. These constraints are not easy to be incorporated into a generative model. In this work, we propose a regularization framework for variational autoencoders as a step toward semantic validity. We focus on the matrix representation of graphs and formulate penalty terms that regularize the output distribution of the decoder to encourage the satisfaction of validity constraints. Experimental results confirm a much higher likelihood of sampling valid graphs in our approach, compared with others reported in the literature.