# Expressivity and Generalization: Fragment-Biases for Molecular GNNs

arXiv: https://arxiv.org/abs/2406.08210 · HTML: https://mlsanity.com/paper/2406.08210/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 48 references that are in the map.
- First posted on arXiv 12 Jun 2024.

## Builds on (most cited first, 30 of 32)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [Residual Gated Graph ConvNets](https://mlsanity.com/paper/1711.07553/) (2017)
- [Do Transformers Really Perform Bad for Graph Representation?](https://mlsanity.com/paper/2106.05234/) (2021)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [Can Graph Neural Networks Count Substructures?](https://mlsanity.com/paper/2002.04025/) (2020)
- [Hierarchical Generation of Molecular Graphs using Structural Motifs](https://mlsanity.com/paper/2002.03230/) (2020)
- [On the equivalence between graph isomorphism testing and function approximation with GNNs](https://mlsanity.com/paper/1905.12560/) (2019)
- [Motif-based Graph Self-Supervised Learning for Molecular Property Prediction](https://mlsanity.com/paper/2110.00987/) (2021)
- [A Generalization of ViT/MLP-Mixer to Graphs](https://mlsanity.com/paper/2212.13350/) (2022)
- [Learning to Extend Molecular Scaffolds with Structural Motifs](https://mlsanity.com/paper/2103.03864/) (2021)
- [MolGenSurvey: A Systematic Survey in Machine Learning Models for Molecule Design](https://mlsanity.com/paper/2203.14500/) (2022)
- [Hierarchical Inter-Message Passing for Learning on Molecular Graphs](https://mlsanity.com/paper/2006.12179/) (2020)
- [Boosting the Cycle Counting Power of Graph Neural Networks with I2-GNNs](https://mlsanity.com/paper/2210.13978/) (2022)
- [A Short Tutorial on The Weisfeiler-Lehman Test And Its Variants](https://mlsanity.com/paper/2201.07083/) (2022)
- [De Novo Molecular Generation via Connection-aware Motif Mining](https://mlsanity.com/paper/2302.01129/) (2023)
- [Autobahn: Automorphism-based Graph Neural Nets](https://mlsanity.com/paper/2103.01710/) (2021)
- [The Expressive Power of Graph Neural Networks: A Survey](https://mlsanity.com/paper/2308.08235/) (2023)
- [Motif-aware Attribute Masking for Molecular Graph Pre-training](https://mlsanity.com/paper/2309.04589/) (2023)
- [Deep Learning Methods for Small Molecule Drug Discovery: A Survey](https://mlsanity.com/paper/2303.00313/) (2023)
- [MAGNet: Motif-Agnostic Generation of Molecules from Shapes](https://mlsanity.com/paper/2305.19303/) (2023)

## Built on by (most cited first, 9 of 9)

- [Graph-structured Small Molecule Drug Discovery Through Deep Learning: Progress, Challenges, and Opportunities](https://mlsanity.com/paper/2502.08975/) (2025)
- [What Expressivity Theory Misses: Message Passing Complexity for GNNs](https://mlsanity.com/paper/2509.01254/) (2025)
- [XIMP: Cross Graph Inter-Message Passing for Molecular Property Prediction](https://mlsanity.com/paper/2601.19037/) (2026)
- [Hierarchical Molecular Representation Learning via Fragment-Based Self-Supervised Embedding Prediction](https://mlsanity.com/paper/2602.20344/) (2026)
- [The Role of Node Features in Graph Pooling](https://mlsanity.com/paper/2605.06250/) (2026)
- [MIPS: a Multimodal Infinite Polymer Sequence Pre-training Framework for Polymer Property Prediction](https://mlsanity.com/paper/2507.20326/) (2025)
- [Learning the Neighborhood: Contrast-Free Multimodal Self-Supervised Molecular Graph Pretraining](https://mlsanity.com/paper/2509.22468/) (2025)
- [Multi-scale Graph Autoregressive Modeling: Molecular Property Prediction via Next Token Prediction](https://mlsanity.com/paper/2601.02530/) (2026)
- [Random Probing for Structural Self-Interactions in Graph Neural Networks](https://mlsanity.com/paper/2610.18164/) (2026)

## Abstract (arXiv)

Although recent advances in higher-order Graph Neural Networks (GNNs) improve the theoretical expressiveness and molecular property predictive performance, they often fall short of the empirical performance of models that explicitly use fragment information as inductive bias. However, for these approaches, there exists no theoretic expressivity study. In this work, we propose the Fragment-WL test, an extension to the well-known Weisfeiler & Leman (WL) test, which enables the theoretic analysis of these fragment-biased GNNs. Building on the insights gained from the Fragment-WL test, we develop a new GNN architecture and a fragmentation with infinite vocabulary that significantly boosts expressiveness. We show the effectiveness of our model on synthetic and real-world data where we outperform all GNNs on Peptides and have 12% lower error than all GNNs on ZINC and 34% lower error than other fragment-biased models. Furthermore, we show that our model exhibits superior generalization capabilities compared to the latest transformer-based architectures, positioning it as a robust solution for a range of molecular modeling tasks.