We study the Wasserstein metric to measure distances between molecules represented by the atom index dependent adjacency ‘Coulomb’ matrix, used in kernel ridge regression based supervised learning. Resulting machine learning models of quantum properties, a.k.a. quantum machine learning models exhibit improved training efficiency and result in smoother predictions of energies related to molecular distortions. We first illustrate smoothness for the continuous extraction of an atom from some organic molecule. Learning curves, quantifying the decay of the atomization energy’s prediction error as a function of training set size, have been obtained for tens of thousands of organic molecules drawn from the QM9 data set. In comparison to conventionally used metrics ( L 1 and L 2 norm), our numerical results indicate systematic improvement in terms of learning curve off-set for random as well as sorted (by norms of row) atom indexing in Coulomb matrices...

中文翻译：

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Wasserstein度量，用于使用邻接矩阵表示的改进量子机器学习

我们研究了Wasserstein度量来测量由原子指数依赖的邻接“ Coulomb”矩阵表示的分子之间的距离，该距离用于基于核岭回归的监督学习中。由此产生的量子属性机器学习模型（又名量子机器学习模型）显示出提高的训练效率，并能更平稳地预测与分子变形有关的能量。我们首先说明从某些有机分子中连续提取原子的光滑度。对于从QM9数据集中提取的成千上万的有机分子，已经获得了学习曲线，该曲线将雾化能量的预测误差的衰减作为训练集大小的函数进行了量化。与常规使用的指标（L 1和L 2范数）相比，