The model must make predictions of the final energies without knowledge of the final structure; i.e., any structural information derived from the relaxed vacancy crystal structures (C s or C e ) or image crystal structures (C pi ) cannot be utilized as input to the model. Figure 2a conceptualizes this procedure, whereby symmetrically distinct paths in a unit cell are projected within a supercell, decorated with path image nodes, and subsequently used to predict all sequence energies directly in one shot. This one-to-many prediction must also address several subtle symmetry constraints, also illustrated schematically in Figure . For symmetrically inequivalent paths, p ̸ = p ′ ̸ = p ′′ , within the same crystal structure that share symmetrically equivalent end points, the predicted vacancy formation energies in different sequence predictions must be equivalent,