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This paper introduces topology-aligned architectures for molecular property prediction, specifically through a variational quantum circuit (Iso-QGNN) and a classical message-passing model (Iso-CGNN). By aligning the model architecture with the molecular bond graph, the authors achieve significant parameter efficiency, demonstrating that both models can reach 90% of their asymptotic performance with only 64 trainable parameters. The results show that the quantum model achieves an AUC of approximately 0.88, while the classical model achieves 0.91 on the HOMO-LUMO gap task, highlighting the effectiveness of the topology-aligned inductive bias in low-data scenarios typical of quantum chemistry.
Achieving 90% of asymptotic performance with just 64 parameters challenges conventional wisdom about model complexity in molecular property prediction.
For low-data and resource-constrained regimes typical of quantum chemistry, parameter-efficient learning is a key objective. Here, we propose a topology-aligned inductive bias in which the model architecture mirrors the molecular bond graph: atoms map to a fixed register of computational units, and bonds determine which pairs interact through shared learnable parameters. This principle is instantiated in two architectures: a variational quantum circuit (Iso-QGNN), and a parameter-matched classical message-passing model (Iso-CGNN). The models are benchmarked on HOMO-LUMO and dipole moment binary classification tasks over the QM9 benchmark. With 64 trainable parameters, the implementations achieve test AUCs of approximately 0.88 (quantum) and 0.91 (classical) on the gap task, and close to 0.78 (both) on the dipole task. The models reach 90% of asymptotic performance within about 250 training molecules and gradient norms remain stable throughout training. These results indicate that the topology-aligned inductive bias is the active ingredient driving parameter efficiency at QM9 scale, with implications for matched-baseline benchmarking in quantum machine learning.
