  The predictive accuracy of Machine Learning (ML) models of molecular
properties depends on the choice of the molecular representation. Based on the
postulates of quantum mechanics, we introduce a hierarchy of representations
which meet uniqueness and target similarity criteria. To systematically control
target similarity, we rely on interatomic many body expansions, as implemented
in universal force-fields, including Bonding, Angular, and higher order terms
(BA). 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, heatcapacity, 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.
