EquiCAD: A Geometric Equivariant Neural Network for 3D Shape Classification

Three-dimensional (3D) shape classification plays a central role in computer vision and computer-aided design (CAD), underpinning applications in intelligent manufacturing, automated inspection, and digital engineering. Despite recent progress with 3D CNNs and graph-based approaches, existing methods often overlook the geometric-topological regularities and symmetry principles intrinsic to CAD boundary representations (B-reps). To address this challenge, we introduce EquiCAD, a symmetry-aware learning framework that integrates equivariant representations with graph-based reasoning. By leveraging group-theoretic decomposition of curve and surface descriptors, EquiCAD enforces consistent $SO(3)/O(3)$-equivariance while preserving rich geometric details. The model further exploits hierarchical message passing to capture interactions between local features and global structure. Experimental results across multiple datasets, including SolidLetters, Parts, the Machining Feature benchmark, and our newly constructed Features dataset, demonstrate substantial improvements over prior state-of-the-art approaches, particularly on industrially relevant shapes with fine-grained attributes. These findings highlight the value of symmetry-aware modeling for robust and generalizable 3D shape analysis.