[Submitted on 3 Nov 2026]
Title:SO(3)-Equivariant Learning on CAD Boundary Representations
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Abstract:Learning on boundary representations (B-reps) requires robustness to the pose of a part, since CAD models are not stored in a canonical orientation. Existing B-rep networks either operate on world-frame coordinates and normals, and thus degrade under rotation, or encode each face in a local reference frame. Local frames yield invariance, but reduce inter-face messages to scalars and discard the relative orientation of adjacent faces. We propose SO3brep, an SO(3)-equivariant graph neural network on the B-rep face-adjacency graph. Node features are computed in local frames and mapped into a shared frame by Wigner D-matrices. Clebsch-Gordan tensor products couple these features with the directions between adjacent faces, so that relative orientation is preserved throughout message passing and the output remains SE(3)-invariant. Across three face-segmentation and two classification benchmarks with randomly rotated test parts, SO3brep achieves the highest accuracy among the compared B-rep networks and equivariant point cloud networks, with the fewest parameters. Its advantage is largest with few labeled parts, a setting typical of industrial CAD. Code is available at this https URL.
Comments: Accepted to NeurIPS 2026 main track
Subjects:
Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG)
Cite as: arXiv:2611.05449 [cs.CV]
(or arXiv:2611.05449v1 [cs.CV] for this version)
https://doi.org/10.48550/arXiv.2611.05449
arXiv-issued DOI via DataCite
Submission history
From: Matteo Ballegeer Mr. [view email] [v1] Tue, 3 Nov 2026 17:51:02 UTC (2,154 KB)
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