论文标题
Wasserstein度量标准用于改进具有邻接矩阵表示的QML
Wasserstein metric for improved QML with adjacency matrix representations
论文作者
论文摘要
我们研究了Wasserstein指标，用于测量由原子指数依赖性邻接“ Coulomb”基质代表的分子之间的距离，该基质用于基于内核脊回归的监督学习。由此产生的量子机学习模型表现出提高的训练效率，并导致分子畸变的预测更平稳。我们首先证明了从某些有机分子中连续提取原子的平滑度。从QM9数据集中得出数万个有机分子，已经获得了学习曲线，量化了雾化能量的预测误差的衰减，这是训练集大小的函数。与常规使用的指标（$ l_1 $和$ l_2 $ norm）相比，我们的数值结果表明，在学习曲线方面进行了系统的改进。我们的发现表明，该度量对应于一个有利的相似性度量，该度量依靠邻接矩阵表示，在任何基于内核的模型中引入了索引不变性。
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 quantum machine learning models exhibit improved training efficiency and result in smoother predictions of molecular distortions. We first demonstrate 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. Our findings suggest that this metric corresponds to a favorable similarity measure which introduces index-invariance in any kernel based model relying on adjacency matrix representations.
