Complete and Efficient Covariants for 3D Point Configurations with Application to Learning Molecular Quantum Properties
This provides a foundational improvement for machine learning in quantum chemistry and other domains involving 3D data, enabling more accurate and scalable property predictions.
The paper tackles the problem of modeling molecular quantum properties with machine learning by developing complete and efficient SO(3)-covariant features for 3D point configurations, proving that 6k-5 features suffice for up to k atoms and reducing computational scaling from O(l^6) to O(l^3).
When modeling physical properties of molecules 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 $O(l^6)$ to $O(l^3)$ in the degree of the features. We apply this to quantum chemistry, but the proposed methods are generally applicable for problems involving 3D point configurations.