# FunQG: Molecular Representation Learning Via Quotient Graphs

arXiv: https://arxiv.org/abs/2207.08597 · HTML: https://mlsanity.com/paper/2207.08597/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 72 references that are in the map.
- First posted on arXiv 18 Jul 2022.

## Builds on (most cited first, 24 of 24)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Tune: A Research Platform for Distributed Model Selection and Training](https://mlsanity.com/paper/1807.05118/) (2018)
- [Analyzing Learned Molecular Representations for Property Prediction](https://mlsanity.com/paper/1904.01561/) (2019)
- [Molecular Graph Convolutions: Moving Beyond Fingerprints](https://mlsanity.com/paper/1603.00856/) (2016)
- [ChemRL-GEM: Geometry Enhanced Molecular Representation Learning for Property Prediction](https://mlsanity.com/paper/2106.06130/) (2021)
- [Discriminative Embeddings of Latent Variable Models for Structured Data](https://mlsanity.com/paper/1603.05629/) (2016)
- [Molecular Property Prediction: A Multilevel Quantum Interactions Modeling Perspective](https://mlsanity.com/paper/1906.11081/) (2019)
- [Spectrally approximating large graphs with smaller graphs](https://mlsanity.com/paper/1802.07510/) (2018)
- [Graph Coarsening with Neural Networks](https://mlsanity.com/paper/2102.01350/) (2021)
- [Massively Multitask Networks for Drug Discovery](https://mlsanity.com/paper/1502.02072/) (2015)
- [A Unifying Framework for Spectrum-Preserving Graph Sparsification and Coarsening](https://mlsanity.com/paper/1902.09702/) (2019)
- [Ripple Walk Training: A Subgraph-based training framework for Large and Deep Graph Neural Network](https://mlsanity.com/paper/2002.07206/) (2020)
- [Deep learning long-range information in undirected graphs with wave networks](https://mlsanity.com/paper/1810.12153/) (2018)

## Built on by (most cited first, 2 of 2)

- [SE3Set: Harnessing equivariant hypergraph neural networks for molecular representation learning](https://mlsanity.com/paper/2405.16511/) (2024)
- [GLaRE: A Graph-based Landmark Region Embedding Network for Emotion Recognition](https://mlsanity.com/paper/2508.20579/) (2025)

## Abstract (arXiv)

Learning expressive molecular representations is crucial to facilitate the accurate prediction of molecular properties. Despite the significant advancement of graph neural networks (GNNs) in molecular representation learning, they generally face limitations such as neighbors-explosion, under-reaching, over-smoothing, and over-squashing. Also, GNNs usually have high computational costs because of the large-scale number of parameters. Typically, such limitations emerge or increase when facing relatively large-size graphs or using a deeper GNN model architecture. An idea to overcome these problems is to simplify a molecular graph into a small, rich, and informative one, which is more efficient and less challenging to train GNNs. To this end, we propose a novel molecular graph coarsening framework named FunQG utilizing Functional groups, as influential building blocks of a molecule to determine its properties, based on a graph-theoretic concept called Quotient Graph. By experiments, we show that the resulting informative graphs are much smaller than the molecular graphs and thus are good candidates for training GNNs. We apply the FunQG on popular molecular property prediction benchmarks and then compare the performance of some popular baseline GNNs on the obtained datasets with the performance of several state-of-the-art baselines on the original datasets. By experiments, this method significantly outperforms previous baselines on various datasets, besides its dramatic reduction in the number of parameters and low computational costs. Therefore, the FunQG can be used as a simple, cost-effective, and robust method for solving the molecular representation learning problem.