材料图神经网络中可训练自由度的测量：随机子空间本征维数分析

中文摘要 AI 辅助

最终预测精度是材料性质预测中比较图神经网络（GNNs）的标准基础，但它并不能显示性能对可训练参数空间方向的可用性依赖程度。在此，我们引入可训练度依赖性作为材料GNN学习的一种补充表征。利用随机子空间本征维数分析，我们在六个预测任务中于随机定向的参数子空间内训练CGCNN、ALIGNN和DimeNet++，并测量随着独立可训练自由度的恢复，性能如何恢复。由此得到的恢复曲线将端点精度与恢复该精度所需的可训练维数需求区分开来。它们揭示了仅凭最终误差无法看到的差异：金属分类和对数体积模量回归能从较小的分数子空间恢复接近参考的性能，形成能和带隙预测显示出更强的架构依赖性，而声子预测对维数限制最为敏感。数据集大小扫描显示，随着训练数据的增长，带隙模型需要更大的分数子空间，而形成能和体积模量的响应则更为稳定。宽度扫描显示，分数阈值可以保持稳定，而绝对阈值维数随模型大小增加。因此，随机子空间分析为材料GNN如何利用其优化空间提供了一个针对性的压力测试。

英文摘要

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.

发表机构

• King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
• King Fahd University of Petroleum and Minerals（法赫德国王石油与矿业大学）

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