Title: EquiCAD: A Geometric Equivariant Neural Network for 3D Shape Classification
Primary area: learning on graphs and other geometries & topologies
Keywords: Equivariant Neural Networks, O(3)/SO(3) Rotational Symmetry, CAD B-rep Shape Classification, Geometric Deep Learning, Graph Neural Networks, UV-Parameterized Surface Features, Industrial Feature Recognition, 3D Solid Modeling

Abstract: 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, and a newly constructed benchmark, 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.

TL;DR: EquiCAD introduces a symmetry-aware framework combining  SO(3)/O(3)-equivariant neural networks and graph-based reasoning for robust 3D CAD shape classification.