Adaptive Higher-Order Graph Learning for Molecular Property Prediction: Investigating Learned Importance of Molecular Substructures

Abstract

Molecular property prediction is central to computational drug discovery and quantum chemistry, yet standard graph neural networks are limited by their reliance on pairwise atomic interactions. Existing hypergraph approaches extend this framework to multi-atom structures but rely on fixed, fingerprint-derived motif vocabularies that cannot adapt to the prediction task. This thesis presents AdaptiveHON, a framework that generates candidate multi-atom subgraphs via depth-first search, represents each candidate by a 36-dimensional structural feature vector, and uses a learned scoring network to assign continuous relevance weights that gate higher-order message passing. AdaptiveHON improves on a pairwise MPNN baseline on all 19 QM9 targets and outperforms the fixed hypergraph baseline HyperMol on 6 of 19 targets, with the most consistent gains on electronic structure properties including the HOMO energy (5.1% reduction in MAE), the LUMO energy (17.0%), the HOMO–LUMO gap (14.1%) and ZPVE (74.9%) compared to the simple MPNN. On the αxx polarizability tensor component, Adaptive- HON achieves a 55.0% reduction in MAE relative to the MPNN and is the only condition to outperform geometry-aware SchNet on any target. Ablation studies show that learned scoring contributes up to 35% of the gain on targets where the signal is concentrated in a subset of distinct subgraphs. These results suggest that adaptive higher-order representations can capture structure that pairwise methods miss, and that which substructures to model matters as much as the message-passing architecture itself.