  Atomistic machine learning focuses on the creation of models which obey
fundamental symmetries of atomistic configurations, such as permutation,
translation, and rotation invariances. In many of these schemes, translation
and rotation invariance are achieved by building on scalar invariants, e.g.,
distances between atom pairs. There is growing interest in molecular
representations that work internally with higher rank rotational tensors, e.g.,
vector displacements between atoms, and tensor products thereof. Here we
present a framework for extending the Hierarchically Interacting Particle
Neural Network (HIP-NN) with Tensor Sensitivity information (HIP-NN-TS) from
each local atomic environment. Crucially, the method employs a weight tying
strategy that allows direct incorporation of many-body information while adding
very few model parameters. We show that HIP-NN-TS is more accurate than HIP-NN,
with negligible increase in parameter count, for several datasets and network
sizes. As the dataset becomes more complex, tensor sensitivities provide
greater improvements to model accuracy. In particular, HIP-NN-TS achieves a
record mean absolute error of 0.927 kcal/mol for conformational energy
variation on the challenging COMP6 benchmark, which includes a broad set of
organic molecules. We also compare the computational performance of HIP-NN-TS
to HIP-NN and other models in the literature.
