aiqbench analysis
This research introduces a novel metric for evaluating graph neural networks in materials science by analyzing their dependence on trainable parameter-space directions rather than just final accuracy. By testing models like CGCNN and ALIGNN across random subspaces, the study reveals critical distinctions in how different tasks—such as band-gap prediction versus metallic classification—utilize optimization resources. This approach offers a rigorous stress test for understanding the intrinsic dimensional demands of AI architectures applied to material property prediction.
Measuring trainable degrees of freedom in materials graph neural networks: a random-subspace intrinsic dimension analysis
arXiv:2609.36084v1 Announce Type: cross Abstract: Final predictive accuracy is the standard basis for comparing graph neural networks (GNNs) in materials-property prediction, but it does not show how strongly performance depends on access to trainable parameter-space directions. Here, we introduce trainable-degree dependence as a complementary characterization of materials GNN learning. Using random-subspace intrinsic-dimension analysis, we train CGCNN, ALIGNN, and DimeNet++ in randomly oriented parameter subspaces across six prediction tasks and measure how performance recovers as independent trainable degrees of freedom are restored. The resulting recovery curves separate endpoint accuracy from the trainable-dimensional demand required to recover it. They reveal distinctions that final errors alone miss: metallic classification and log-bulk-modulus regression recover near-reference performance from small fractional subspaces, formation-energy and band-gap prediction show stronger architecture dependence, and phonon prediction is most sensitive to dimensional restriction. Dataset-size sweeps show that band-gap models require larger fractional subspaces as training data grows, whereas formation-energy and bulk-modulus responses are more stable. A width sweep shows that fractional thresholds can remain stable while absolute threshold dimensions increase with model size. Random-subspace analysis therefore provides a targeted stress test for how materials GNNs use their optimization space.
Abstract:Final predictive accuracy is the standard basis for comparing graph neural networks (GNNs) in materials-property prediction, but it does not show how strongly performance depends on access to trainable parameter-space directions. Here, we introduce trainable-degree dependence as a complementary characterization of materials GNN learning. Using random-subspace intrinsic-dimension analysis, we train CGCNN, ALIGNN, and DimeNet++ in randomly oriented parameter subspaces across six prediction tasks and measure how performance recovers as independent trainable degrees of freedom are restored. The resulting recovery curves separate endpoint accuracy from the trainable-dimensional demand required to recover it. They reveal distinctions that final errors alone miss: metallic classification and log-bulk-modulus regression recover near-reference performance from small fractional subspaces, formation-energy and band-gap prediction show stronger architecture dependence, and phonon prediction is most sensitive to dimensional restriction. Dataset-size sweeps show that band-gap models require larger fractional subspaces as training data grows, whereas formation-energy and bulk-modulus responses are more stable. A width sweep shows that fractional thresholds can remain stable while absolute threshold dimensions increase with model size. Random-subspace analysis therefore provides a targeted stress test for how materials GNNs use their optimization space.
Materials Science (cond-mat.mtrl-sci); Artificial Intelligence (cs.AI)
arXiv:2609.36084 [cond-mat.mtrl-sci]
(or arXiv:2609.36084v1 [cond-mat.mtrl-sci] for this version)
https://doi.org/10.48550/arXiv.2609.36084 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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