{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/projective-manifold-gradient-layer-for-deep-1","title":"Projective Manifold Gradient Layer for Deep Rotation Regression","arxiv_id":"2110.11657","date":"2021-10-22","proceeding":"CVPR 2022 1","authors":["Jiayi Chen","Yingda Yin","Tolga Birdal","Baoquan Chen","Leonidas Guibas","He Wang"],"abstract":"Regressing rotations on SO(3) manifold using deep neural networks is an important yet unsolved problem. The gap between the Euclidean network output space and the non-Euclidean SO(3) manifold imposes a severe challenge for neural network learning in both forward and backward passes. While several works have proposed different regression-friendly rotation representations, very few works have been devoted to improving the gradient backpropagating in the backward pass. In this paper, we propose a manifold-aware gradient that directly backpropagates into deep network weights. Leveraging Riemannian optimization to construct a novel projective gradient, our proposed regularized projective manifold gradient (RPMG) method helps networks achieve new state-of-the-art performance in a variety of rotation estimation tasks. Our proposed gradient layer can also be applied to other smooth manifolds such as the unit sphere. Our project page is at https://jychen18.github.io/RPMG.","url_abs":"https://arxiv.org/abs/2110.11657v3","url_pdf":"https://arxiv.org/pdf/2110.11657v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"projective-manifold-gradient-layer-for-deep-1","repo_url":"https://github.com/jychen18/rpmg","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"riemannian-optimization","task_name":"Riemannian optimization"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2110.11657","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}