Communication: Understanding molecular representations in machine learning: The role of uniqueness and target similarity.

The predictive accuracy of Machine Learning (ML) models of molecular properties depends on the choice of the molecular representation. Inspired by the postulates of quantum mechanics, we introduce a hierarchy of representations which meet uniqueness and target similarity criteria. To systematically control target similarity, we simply rely on interatomic many body expansions, as implemented in universal force-fields, including Bonding, Angular (BA), and higher order terms. Addition of higher order contributions systematically increases similarity to the true potential energy and predictive accuracy of the resulting ML models. We report numerical evidence for the performance of BAML models trained on molecular properties pre-calculated at electron-correlated and density functional theory level of theory for thousands of small organic molecules. Properties studied include enthalpies and free energies of atomization, heat capacity, zero-point vibrational energies, dipole-moment, polarizability, HOMO/LUMO energies and gap, ionization potential, electron affinity, and electronic excitations. After training, BAML predicts energies or electronic properties of out-of-sample molecules with unprecedented accuracy and speed.