We now turn our attention towards the rotation equivariant MatTEN model, which was shown to significantly outperform the invariant models (see Table ). Similar to the case of invariant models, there are a variety of output targets available for the equivariant model, of which there is not an a priori optimal choice. We focus on using an asymmetric Cartesian tensor, symmetric Cartesian tensor, asymmetric irreps (E, A ik , S ik ), or symmetric irreps (E, S ik ) as the target (refer to Eq. ( )). Additionally, the question of which loss function is suitable for learning chemical shift tensors has not, to our knowledge, been investigated for training ML models. There has, however, been substantial work by the MRI diffusion tensor community on optimal tensor metrics for diffusion tensors. The l n -norms offer a good balance of optimizing the shape, magnitude, and orientation of a tensor, and in our case we adopted the l 1 norm as the loss function. We found there is a small benefit to learning on a symmetric tensor versus an asymmetric tensor before symmetrizing. Additionally, there is a minor decrease in both epoch time and the loss when training on an irreps tensor versus a Cartesian tensor. Thus, the optimal space was chosen to be symmetric irreps tensor using an l 1 -norm loss function, and all subsequent results are obtained from models trained using this optimal space. The best performing equivariant MatTEN model exhibits an MAE of 1.05 ppm over the entire chemical shift Cartesian tensor. However, we admit that a MAE calculated for all the tensor components is challenging to interpret as asymmetric second rank tensor has six independent parameters which must be assessed in order to evaluate performance without loss of information. Therefore, we compare the predicted and DFT-calculated isotropic chemical shift, X, Y, and Euler angles (α, β, γ) (refer to Section for their definition). These parame-ters are chosen as they provide an intuitive view of the magnitude, shape, and orientation of the tensor, as described above. Additionally, because the shift tensor is very closely linked to the structural point group, 71 the results are grouped by Q n into three clusters reflecting the broad symmetry point group: T d , C 3 and C 2 . The results are summarized in Table . as shown in Fig. . The isotropic shift, however, performs considerably worse than the tetrahedral case as is clearly seen in Table (3.28 ppm and 8.58 ppm in Q 3 and Q 1 respectively vs. 1.52 ppm and 1.46 ppm in Q 4 and Q 0 respectively). Barring a cluster of 3 data points, the Q 3 isotropic shift tends to be over-predicted by MatTEN. The sites with over-predicted isotropic shift also correspond to the sites with poorly predicted Euler angles in Fig. .