SpinGTP Boosts Scalability and Expressivity for 3D Equivariant Networks.

E(3)-equivariant networks are highly promising for modeling 3D atomistic systems, but their scalability has been hampered by the high computational complexity of the Clebsch-Gordan Tensor Product (CGTP). While the Gaunt Tensor Product (GTP) offered a reduction in complexity, it lacked the ability to capture antisymmetric paths, leading to incomplete expressivity. This research presents SpinGTP, a novel method designed to address this limitation. SpinGTP generalizes from scalar functions to Spin-Weighted Spherical Harmonics (SWSH), leveraging their algebraic properties to recover the missing antisymmetric interactions. This approach maintains the asymptotic efficiency of GTP while providing a more expressive equivariant basis that naturally accounts for parity-odd components. Evaluated across diverse benchmarks, SpinGTP achieves accuracies comparable to the more complex CGTP. Notably, its explicit capture of antisymmetric paths results in superior performance for tasks involving chiral materials and non-centrosymmetric geometries, offering a complete, scalable, and mathematically rigorous path for high-order equivariance in large-scale 3D simulations.