{"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/relaxed-rotational-equivariance-via-g-biases","title":"Relaxed Rotational Equivariance via $G$-Biases in Vision","arxiv_id":"2408.12454","date":"2024-08-22","proceeding":null,"authors":["Zhiqiang Wu","Yingjie Liu","Licheng Sun","Jian Yang","Hanlin Dong","Shing-Ho J. Lin","Xuan Tang","Jinpeng Mi","Bo Jin","Xian Wei"],"abstract":"Group Equivariant Convolution (GConv) can capture rotational equivariance from original data. It assumes uniform and strict rotational equivariance across all features as the transformations under the specific group. However, the presentation or distribution of real-world data rarely conforms to strict rotational equivariance, commonly referred to as Rotational Symmetry-Breaking (RSB) in the system or dataset, making GConv unable to adapt effectively to this phenomenon. Motivated by this, we propose a simple but highly effective method to address this problem, which utilizes a set of learnable biases called $G$-Biases under the group order to break strict group constraints and then achieve a Relaxed Rotational Equivariant Convolution (RREConv). To validate the efficiency of RREConv, we conduct extensive ablation experiments on the discrete rotational group $\\mathcal{C}_n$. Experiments demonstrate that the proposed RREConv-based methods achieve excellent performance compared to existing GConv-based methods in both classification and 2D object detection tasks on the natural image datasets.","url_abs":"https://arxiv.org/abs/2408.12454v3","url_pdf":"https://arxiv.org/pdf/2408.12454v3.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":"relaxed-rotational-equivariance-via-g-biases","repo_url":"https://github.com/wuer5/rrenet","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"2d-object-detection","task_name":"2D Object Detection"},{"task_slug":"object-detection","task_name":"Object Detection"},{"task_slug":"object-detection-1","task_name":"object-detection"}],"methods":[{"method_slug":"convolution","method_name":"Convolution"},{"method_slug":"set","method_name":"SET"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2408.12454","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2408.12454"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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