# Multiparameter Persistent Homology for Molecular Property Prediction

arXiv: https://arxiv.org/abs/2311.10808 · HTML: https://mlsanity.com/paper/2311.10808/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 50 references that are in the map.
- First posted on arXiv 17 Nov 2023.

## Builds on (most cited first, 29 of 29)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (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)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Analyzing Learned Molecular Representations for Property Prediction](https://mlsanity.com/paper/1904.01561/) (2019)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Molecular Graph Convolutions: Moving Beyond Fingerprints](https://mlsanity.com/paper/1603.00856/) (2016)
- [Hierarchical Generation of Molecular Graphs using Structural Motifs](https://mlsanity.com/paper/2002.03230/) (2020)
- [Learning Gradient Fields for Molecular Conformation Generation](https://mlsanity.com/paper/2105.03902/) (2021)
- [A Survey on Graph Kernels](https://mlsanity.com/paper/1903.11835/) (2019)
- [3D Infomax improves GNNs for Molecular Property Prediction](https://mlsanity.com/paper/2110.04126/) (2021)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensembles](https://mlsanity.com/paper/2106.07802/) (2021)
- [Learning Neural Generative Dynamics for Molecular Conformation Generation](https://mlsanity.com/paper/2102.10240/) (2021)
- [Molecular Property Prediction: A Multilevel Quantum Interactions Modeling Perspective](https://mlsanity.com/paper/1906.11081/) (2019)
- [Covariant Compositional Networks For Learning Graphs](https://mlsanity.com/paper/1801.02144/) (2018)
- [PotentialNet for Molecular Property Prediction](https://mlsanity.com/paper/1803.04465/) (2018)
- [Persistence Curves: A canonical framework for summarizing persistence diagrams](https://mlsanity.com/paper/1904.07768/) (2019)
- [Molecular machine learning with conformer ensembles](https://mlsanity.com/paper/2012.08452/) (2020)
- [Optimal Transport Graph Neural Networks](https://mlsanity.com/paper/2006.04804/) (2020)
- [Multi-View Graph Neural Networks for Molecular Property Prediction](https://mlsanity.com/paper/2005.13607/) (2020)
- [ToDD: Topological Compound Fingerprinting in Computer-Aided Drug Discovery](https://mlsanity.com/paper/2211.03808/) (2022)
- [Utilizing Edge Features in Graph Neural Networks via Variational Information Maximization](https://mlsanity.com/paper/1906.05488/) (2019)
- [Drug-Target Interaction Prediction with Graph Attention networks](https://mlsanity.com/paper/2107.06099/) (2021)
- [Lipophilicity Prediction with Multitask Learning and Molecular Substructures Representation](https://mlsanity.com/paper/2011.12117/) (2020)

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

- [SE(3)-Invariant Multiparameter Persistent Homology for Chiral-Sensitive Molecular Property Prediction](https://mlsanity.com/paper/2312.07633/) (2023)
- [MacroGuide: Topological Guidance for Macrocycle Generation](https://mlsanity.com/paper/2602.14977/) (2026)

## Abstract (arXiv)

In this study, we present a novel molecular fingerprint generation method based on multiparameter persistent homology. This approach reveals the latent structures and relationships within molecular geometry, and detects topological features that exhibit persistence across multiple scales along multiple parameters, such as atomic mass, partial charge, and bond type, and can be further enhanced by incorporating additional parameters like ionization energy, electron affinity, chirality and orbital hybridization. The proposed fingerprinting method provides fresh perspectives on molecular structure that are not easily discernible from single-parameter or single-scale analysis. Besides, in comparison with traditional graph neural networks, multiparameter persistent homology has the advantage of providing a more comprehensive and interpretable characterization of the topology of the molecular data. We have established theoretical stability guarantees for multiparameter persistent homology, and have conducted extensive experiments on the Lipophilicity, FreeSolv, and ESOL datasets to demonstrate its effectiveness in predicting molecular properties.