When Do Geometric Algebra Layers Beat Scalarization? A Controlled Study on SO(3)-Equivariant Vector Laws
Compact networks built from Clifford algebra Cl(3,0) primitives are exactly SO(3)-equivariant and learn synthetic 3D vector laws from few samples. We ask whether the geometric algebra structure itself contributes anything beyond exact equivariance. We compare against a minimal scalarization baseline: invariant dot products fed to a small MLP that outputs coefficients on the equivariant basis {v_i, v_i x v_j}, which is also exactly equivariant. On single-stage laws (rotation by axis-angle, cross product, central force), scalarization matches or beats the Cl(3,0) network at a fraction of the training cost, so the geometric algebra adds nothing there. On compositional targets whose computati...
| Authors | Fabien Polly |
|---|---|
| Primary category | cs.LG |
| Published | 7 July 2026 |
| Last updated at source | 7 July 2026 |
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