SO(3)-Equivariant Learning on CAD Boundary Representations

Boundary representations (B-reps) encode CAD geometry as parametric surface patches with explicit topological adjacency, forming information-rich geometric graphs. Yet existing methods encode coordinates and normals as scalars, making models rotation-sensitive, while invariant alternatives using per-face local frames discard the shared orientation reference needed to capture inter-face directional relationships. We introduce SO3brep, the first $SO(3)$-equivariant neural architecture for B-rep learning. Faces are represented by scalar, vector, and tensor irreducible representations constructed in per-face local frames, lifted to a shared global frame via Wigner $D$-matrices, and propagated through equivariant message passing. This preserves inter-face directional structure during message passing while guaranteeing $SE(3)$ invariance at the output. Across five CAD benchmarks for shape classification and per-face segmentation, SO3brep consistently outperforms prior B-rep and equivariant point-cloud methods while significantly improving data efficiency. These results demonstrate that $SO(3)$-equivariance is a powerful inductive bias for structured CAD geometry.