# Augmenting Molecular Deep Generative Models with Topological Data Analysis Representations

arXiv: https://arxiv.org/abs/2106.04464 · HTML: https://mlsanity.com/paper/2106.04464/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 65 references that are in the map.
- First posted on arXiv 8 Jun 2021.

## Builds on (most cited first, 30 of 34)

- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [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)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (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)
- [Molecular Sets (MOSES): A Benchmarking Platform for Molecular Generation Models](https://mlsanity.com/paper/1811.12823/) (2018)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [Constrained Graph Variational Autoencoders for Molecule Design](https://mlsanity.com/paper/1805.09076/) (2018)
- [Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules](https://mlsanity.com/paper/1906.00957/) (2019)
- [Deep Reinforcement Learning for De-Novo Drug Design](https://mlsanity.com/paper/1711.10907/) (2017)
- [Syntax-Directed Variational Autoencoder for Structured Data](https://mlsanity.com/paper/1802.08786/) (2018)
- [Multi-Objective De Novo Drug Design with Conditional Graph Generative Model](https://mlsanity.com/paper/1801.07299/) (2018)
- [A Topology Layer for Machine Learning](https://mlsanity.com/paper/1905.12200/) (2019)
- [Sliced Wasserstein Kernel for Persistence Diagrams](https://mlsanity.com/paper/1706.03358/) (2017)
- [A Stable Multi-Scale Kernel for Topological Machine Learning](https://mlsanity.com/paper/1412.6821/) (2014)
- [Molecular generative model based on conditional variational autoencoder for de novo molecular design](https://mlsanity.com/paper/1806.05805/) (2018)
- [NeVAE: A Deep Generative Model for Molecular Graphs](https://mlsanity.com/paper/1802.05283/) (2018)
- [An End-to-End Framework for Molecular Conformation Generation via Bilevel Programming](https://mlsanity.com/paper/2105.07246/) (2021)
- [Symmetry-Aware Actor-Critic for 3D Molecular Design](https://mlsanity.com/paper/2011.12747/) (2020)
- [Reinforcement Learning for Molecular Design Guided by Quantum Mechanics](https://mlsanity.com/paper/2002.07717/) (2020)
- [Conditional molecular design with deep generative models](https://mlsanity.com/paper/1805.00108/) (2018)
- [Persistence Fisher Kernel: A Riemannian Manifold Kernel for Persistence Diagrams](https://mlsanity.com/paper/1802.03569/) (2018)
- [Application of generative autoencoder in de novo molecular design](https://mlsanity.com/paper/1711.07839/) (2017)
- [Interactive Visualization of 2-D Persistence Modules](https://mlsanity.com/paper/1512.00180/) (2015)
- [Generating valid Euclidean distance matrices](https://mlsanity.com/paper/1910.03131/) (2019)
- [3DMolNet: A Generative Network for Molecular Structures](https://mlsanity.com/paper/2010.06477/) (2020)

## Built on by (most cited first, 6 of 6)

- [Data-Efficient Graph Grammar Learning for Molecular Generation](https://mlsanity.com/paper/2203.08031/) (2022)
- [GP-MoLFormer: A Foundation Model For Molecular Generation](https://mlsanity.com/paper/2405.04912/) (2024)
- [Deep Learning Methods for Small Molecule Drug Discovery: A Survey](https://mlsanity.com/paper/2303.00313/) (2023)
- [Accelerating Inhibitor Discovery With A Deep Generative Foundation Model: Validation for SARS-CoV-2 Drug Targets](https://mlsanity.com/paper/2204.09042/) (2022)
- [LightGBM robust optimization algorithm based on topological data analysis](https://mlsanity.com/paper/2406.13300/) (2024)
- [MacroGuide: Topological Guidance for Macrocycle Generation](https://mlsanity.com/paper/2602.14977/) (2026)

## Abstract (arXiv)

Deep generative models have emerged as a powerful tool for learning useful molecular representations and designing novel molecules with desired properties, with applications in drug discovery and material design. However, most existing deep generative models are restricted due to lack of spatial information. Here we propose augmentation of deep generative models with topological data analysis (TDA) representations, known as persistence images, for robust encoding of 3D molecular geometry. We show that the TDA augmentation of a character-based Variational Auto-Encoder (VAE) outperforms state-of-the-art generative neural nets in accurately modeling the structural composition of the QM9 benchmark. Generated molecules are valid, novel, and diverse, while exhibiting distinct electronic property distribution, namely higher sample population with small HOMO-LUMO gap. These results demonstrate that TDA features indeed provide crucial geometric signal for learning abstract structures, which is non-trivial for existing generative models operating on string, graph, or 3D point sets to capture.