To validate our conclusions regarding the advantages of incorporating orbits in MLFFs across different system sizes, we extend our analysis to a larger system-a CsPbI 3 perovskite slab with 216 atoms per unit cell. As shown in Figure (a), the CsPbI 3 perovskite slab exhibits only reflective symmetry along the z-axis, resulting in three distinct, non-equivalent layers of PbI 2 and CsI: the outer layer, the in-between layer, and the middle layer. Consequently, despite containing only three chemical elements, the system features 12 distinct orbits defined by global permutational symmetry-six for iodine, three for cesium, and three for lead-providing a more granular structural representation for MACE models.