E(3)-equivariant networks have become central to materials machine learning because they encode spatial symmetries and achieve high accuracy for non-magnetic systems. Their underlying assumptions, however, break down for magnetic ordering, where spin degrees of freedom, time-reversal symmetry breaking, and near-degenerate magnetic states are essential to the physics but absent from coordinate-only representations. This paper argues that the mismatch between E(3) symmetry and the magnetic space-group structure of real materials makes standard equivariant architectures fundamentally unreliable for magnetic ordering tasks. We show that this mismatch produces systematic failures, including the collapse of distinct magnetic states, the erasure of hidden degeneracies, and the inability to capture finite-temperature ordering phenomena. By framing these limitations in symmetry-theoretic terms, the analysis clarifies why architectural modifications that incorporate spin, time reversal, and multi-valued outputs are necessary for physically faithful prediction in magnetic materials discovery.
Institute for Advanced Materials Research Press