The models are categorized according to the symmetries of its internal embeddings and its final target, labeled as "Embedding Symmetry" and "Target Symmetry", respectively, in Table . Of the invariant target models, DimeNet++ performs the best, and LRR-SOAP and MatTEN are on par with each other. However, if a fully equivariant MatTEN model (equivarant embedding and equivariant target) is used to predict the full shift tensor and then diagonalized to yield the eignevalues, significant improvement over the invariant target models can be achieved. For example, the total MAE reduces to 3.05 ppm, which is less than half of that from the DimeNet++ model (6.44 ppm). Comparing the MatTEN models trained using invariant versus equivariant target symmetry, it is clear that the boost in performance is due to the additional constraint afforded by learning a second rank tensor rather than three independent scalars. The fully equivariant model will be further discussed in the next section, and here we focus on the invariant models.