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 preserves symmetry-consistent feature transformations while retaining 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.

Many products around us, from machine parts to consumer devices, are first designed as three-dimensional digital models. Helping computers understand these models is important for smarter manufacturing, automatic inspection, and faster engineering design. However, existing methods can struggle when the same object is rotated, mirrored, or represented with complex fine details. In this paper, we present EquiCAD, a new learning method for recognizing 3D CAD models more reliably. The key idea is to teach the model to respect natural geometric symmetries, so that a part can still be recognized correctly even when it is viewed from a different direction. EquiCAD also studies how small local elements of a model are connected to form the overall shape, allowing it to capture both detailed features and global structure. We test EquiCAD on several 3D shape datasets, including industrial parts and challenging fine-grained design features. The results show that EquiCAD performs better than previous methods, especially on complex engineering shapes. This suggests that building symmetry awareness into 3D learning systems can make them more accurate and robust for real-world CAD understanding.