  Message passing neural networks have become a method of choice for learning
on graphs, in particular the prediction of chemical properties and the
acceleration of molecular dynamics studies. While they readily scale to large
training data sets, previous approaches have proven to be less data efficient
than kernel methods. We identify limitations of invariant representations as a
major reason and extend the message passing formulation to rotationally
equivariant representations. On this basis, we propose the polarizable atom
interaction neural network (PaiNN) and improve on common molecule benchmarks
over previous networks, while reducing model size and inference time. We
leverage the equivariant atomwise representations obtained by PaiNN for the
prediction of tensorial properties. Finally, we apply this to the simulation of
molecular spectra, achieving speedups of 4-5 orders of magnitude compared to
the electronic structure reference.
