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The predictive accuracy of Machine Learning (ML) models of molecularproperties depends on the choice of the molecular representation. Based on thepostulates of quantum mechanics, we introduce a hierarchy of representationswhich meet uniqueness and target similarity criteria. To systematically controltarget similarity, we rely on interatomic many body expansions, as implementedin universal force-fields, including Bonding, Angular, and higher order terms(BA). Addition of higher order contributions systematically increasessimilarity to the true potential energy and predictive accuracy of theresulting ML models. We report numerical evidence for the performance of BAMLmodels trained on molecular properties pre-calculated at electron-correlatedand density functional theory level of theory for thousands of small organicmolecules. Properties studied include enthalpies and free energies ofatomization, heatcapacity, zero-point vibrational energies, dipole-moment,polarizability, HOMO/LUMO energies and gap, ionization potential, electronaffinity, and electronic excitations. After training, BAML predicts energies orelectronic properties of out-of-sample molecules with unprecedented accuracyand speed.

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