As an equivariant model, MACE effectively handles symmetry by converting discrete permutation symmetry into a continuous representation subject to rotational symmetry. Although such a conversion allows for efficient parameterization using irreps of the rotation group SO(3), it also imposes a constraint. The network is forced to work with the full rotation group and cannot explicitly focus on specific subgroups of the symmetry (like certain atom swaps). By maintaining a direct connection to permutation symmetry, it becomes possible to treat both the discrete permutation and continuous rotation symmetries explicitly. This enables a finer control over the symmetry treatment, improving MACE's accuracy and efficiency by employing equivalence classes-atoms with persistent neighborhood chemical compositions.