The research explores the potential of leveraging curvature, specifically Ollivier-Ricci curvature, to distinguish chemical molecules treated as graph structures. Traditional methods in graph neural networks (GNNs) have shown promise but need help with challenges, such as the need for abundant labeled data and theoretical expressivity limitations. By incorporating molecular geometry through curvature, the aim is to lay a stable mathematical foundation to characterize molecules, providing improved data for neural networks and ultimately contributing to more efficient drug discovery processes.
The analysis reveals patterns within individual molecules as well as across different molecules. Notably, the analysis of node-to-node curvature exposes analogous intramolecular patterns. Moreover, within the intermolecular context, especially when considering the Zinc Chemistry dataset, the application of manifold embeddings like UMAP showcases the clustering of similar molecular structures. These findings suggest that curvature can be effectively utilized as a feature for distinguishing molecules.