# Auto-encoding Molecules: Graph-Matching Capabilities Matter

arXiv: https://arxiv.org/abs/2503.00426 · HTML: https://mlsanity.com/paper/2503.00426/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 31 references that are in the map.
- First posted on arXiv 1 Mar 2025.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Hierarchical Generation of Molecular Graphs using Structural Motifs](https://mlsanity.com/paper/2002.03230/) (2020)
- [Graph Matching Networks for Learning the Similarity of Graph Structured Objects](https://mlsanity.com/paper/1904.12787/) (2019)
- [Pure Transformers are Powerful Graph Learners](https://mlsanity.com/paper/2207.02505/) (2022)
- [MoFlow: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/2006.10137/) (2020)
- [GraphNVP: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/1905.11600/) (2019)
- [Multi-Objective De Novo Drug Design with Conditional Graph Generative Model](https://mlsanity.com/paper/1801.07299/) (2018)
- [SimGNN: A Neural Network Approach to Fast Graph Similarity Computation](https://mlsanity.com/paper/1808.05689/) (2018)
- [Learning to Extend Molecular Scaffolds with Structural Motifs](https://mlsanity.com/paper/2103.03864/) (2021)
- [NeVAE: A Deep Generative Model for Molecular Graphs](https://mlsanity.com/paper/1802.05283/) (2018)
- [Does equivariance matter at scale?](https://mlsanity.com/paper/2410.23179/) (2024)
- [Graph Auto-Encoder Via Neighborhood Wasserstein Reconstruction](https://mlsanity.com/paper/2202.09025/) (2022)
- [A Two-Step Graph Convolutional Decoder for Molecule Generation](https://mlsanity.com/paper/1906.03412/) (2019)
- [Graph Deconvolutional Generation](https://mlsanity.com/paper/2002.07087/) (2020)
- [Scalable Optimal Transport in High Dimensions for Graph Distances, Embedding Alignment, and More](https://mlsanity.com/paper/2107.06876/) (2021)
- [Decoding Molecular Graph Embeddings with Reinforcement Learning](https://mlsanity.com/paper/1904.08915/) (2019)
- [Are VAEs Bad at Reconstructing Molecular Graphs?](https://mlsanity.com/paper/2305.03041/) (2023)

## Abstract (arXiv)

Autoencoders are effective deep learning models that can function as generative models and learn latent representations for downstream tasks. The use of graph autoencoders - with both encoder and decoder implemented as message passing networks - is intriguing due to their ability to generate permutation-invariant graph representations. However, this approach faces difficulties because decoding a graph structure from a single vector is challenging, and comparing input and output graphs requires an effective permutation-invariant similarity measure. As a result, many studies rely on approximate methods. In this work, we explore the effect of graph matching precision on the training behavior and generation capabilities of a Variational Autoencoder (VAE). Our contribution is two-fold: (1) we propose a transformer-based message passing graph decoder as an alternative to a graph neural network decoder, that is more robust and expressive by leveraging global attention mechanisms. (2) We show that the precision of graph matching has significant impact on training behavior and is essential for effective de novo (molecular) graph generation. Code is available at https://github.com/mcunow/graph-matching