While the hetero-GNN exhibits superior performance to the CNN, the image representation has the physically intuitive property that arbitrarily subdividing a given nanoparticle region (e.g. dividing a shell into two smaller shells, where both have the same dopant concentrations as the originally undivided region) has no impact on the model's structural representation or subsequent label prediction. This property, which we call "subdivision invariance", is physically motivated by the fact that region subdivision is arbitrary and leaves the nanoparticle being described completely unchanged. However, neither our heterogeneous graph nor any of the other non-image representations are inherently subdivision invariant. For example, as shown in Figure , subdividing an originally core-only particle into a core and a shell dramatically changes the heterogeneous graph, and thus our hetero-GNN model may predict very different latent representations for physically identical nanoparticles. This is clearly undesirable and may be detrimental to both the learning process and subsequent structural optimization. On the other hand, the voxelization that makes the image representation subdivision invariant simultaneously causes layer dimensions to only be present in the model implicitly, preventing UCNP emission from being differentiated with respect to layer thicknesses and precluding gradient-based optimization of UCNP heterostructure. Thus, any DL model that aims to enable inverse design of nanomaterial heterostructure via gradient-based optimization will need to reckon with the problem of subdivision invariance.