When physical properties of molecules are being modeled with machine learning, it is desirable to incorporate SO(3)-covariance. While such models based on low body order features are not complete, we formulate and prove general completeness properties for higher order methods and show that 6k – 5 of these features are enough for up to k atoms. We also find that the Clebsch–Gordan operations commonly used in these methods can be replaced by matrix multiplications without sacrificing completeness, lowering the scaling from O(l⁶) to O(l³) in the degree of the features. We apply this to quantum chemistry, but the proposed methods are generally applicable for problems involving three-dimensional point configurations.

中文翻译：

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三维点构型的完整高效协变及其在学习分子量子性质中的应用


当使用机器学习对分子的物理性质进行建模时，需要结合 SO（3） 协方差。虽然这种基于低体顺序特征的模型并不完整，但我们制定并证明了高阶方法的一般完备性，并表明这些特征中的 6k – 5 足以用于多达 k 个原子。我们还发现，这些方法中常用的 Clebsch-Gordan 运算可以用矩阵乘法代替，而不会牺牲完整性，从而将特征程度从 O（l⁶） 降低到 O（l³）。我们将其应用于量子化学，但所提出的方法通常适用于涉及三维点构型的问题。