  Recent advances in machine-learned interatomic potentials largely benefit
from the atomistic representation and locally invariant many-body descriptors.
It was however recently argued that including three- (or even four-) body
features is incomplete to distinguish specific local structures. Utilizing an
embedded density descriptor made by linear combinations of neighboring atomic
orbitals and realizing that each orbital coefficient physically depends on its
own local environment, we propose a recursively embedded atom neural network
model. We formally prove that this model can efficiently incorporate complete
many-body correlations without explicitly computing high-order terms. This
model not only successfully addresses challenges regarding local completeness
and nonlocality in representative systems, but also provides an easy and
general way to update local many-body descriptors to have a message-passing
form without changing their basic structures.
