Bridging Tokens and Geometry: Token-wise 3D Supervision for CAD Generation

Yijia Guan, Jianhua Sun
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:37518-37537, 2026.

Abstract

Computer-Aided Design (CAD) generation is typically formulated as a sequence modeling task over parametric tokens. Recent studies introduce visual information through additional visual inputs or rendering of the final generated programs. However, these methods provide no intermediate visual feedback, hindering the association of individual tokens with their geometric effects. In this work, we propose an Argument-induced 3D Point Loss (A3PL) that maps argument tokens to corresponding 3D points, enabling dense token-wise geometric supervision. To reduce learning complexity and invalid sequences, we further introduce a Grammar-constrained Operator (GCO) that leverages the structured nature of CAD programs to regulate sequence generation. We evaluate our approach on five CAD generation tasks with diverse input modalities, including text, Scalable Vector Graphics (SVG) sketches, point clouds, and CAD sequences. Our approach improves generation accuracy and program validity across different input modalities. Code is available at https://github.com/JumpJumpTigger-GYJ/A3PL.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-guan26g, title = {Bridging Tokens and Geometry: Token-wise 3{D} Supervision for {CAD} Generation}, author = {Guan, Yijia and Sun, Jianhua}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {37518--37537}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/guan26g/guan26g.pdf}, url = {https://proceedings.mlr.press/v306/guan26g.html}, abstract = {Computer-Aided Design (CAD) generation is typically formulated as a sequence modeling task over parametric tokens. Recent studies introduce visual information through additional visual inputs or rendering of the final generated programs. However, these methods provide no intermediate visual feedback, hindering the association of individual tokens with their geometric effects. In this work, we propose an Argument-induced 3D Point Loss (A3PL) that maps argument tokens to corresponding 3D points, enabling dense token-wise geometric supervision. To reduce learning complexity and invalid sequences, we further introduce a Grammar-constrained Operator (GCO) that leverages the structured nature of CAD programs to regulate sequence generation. We evaluate our approach on five CAD generation tasks with diverse input modalities, including text, Scalable Vector Graphics (SVG) sketches, point clouds, and CAD sequences. Our approach improves generation accuracy and program validity across different input modalities. Code is available at https://github.com/JumpJumpTigger-GYJ/A3PL.} }
Endnote
%0 Conference Paper %T Bridging Tokens and Geometry: Token-wise 3D Supervision for CAD Generation %A Yijia Guan %A Jianhua Sun %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-guan26g %I PMLR %P 37518--37537 %U https://proceedings.mlr.press/v306/guan26g.html %V 306 %X Computer-Aided Design (CAD) generation is typically formulated as a sequence modeling task over parametric tokens. Recent studies introduce visual information through additional visual inputs or rendering of the final generated programs. However, these methods provide no intermediate visual feedback, hindering the association of individual tokens with their geometric effects. In this work, we propose an Argument-induced 3D Point Loss (A3PL) that maps argument tokens to corresponding 3D points, enabling dense token-wise geometric supervision. To reduce learning complexity and invalid sequences, we further introduce a Grammar-constrained Operator (GCO) that leverages the structured nature of CAD programs to regulate sequence generation. We evaluate our approach on five CAD generation tasks with diverse input modalities, including text, Scalable Vector Graphics (SVG) sketches, point clouds, and CAD sequences. Our approach improves generation accuracy and program validity across different input modalities. Code is available at https://github.com/JumpJumpTigger-GYJ/A3PL.
APA
Guan, Y. & Sun, J.. (2026). Bridging Tokens and Geometry: Token-wise 3D Supervision for CAD Generation. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:37518-37537 Available from https://proceedings.mlr.press/v306/guan26g.html.

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