{"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/learning-constrained-structured-spaces-with","title":"Learning Constrained Structured Spaces with Application to Multi-Graph Matching","arxiv_id":null,"date":"2022-05-03","proceeding":"Proceedings of the 26th International Conference on Artificial Intelligence and Statistics (AISTATS) 2022 5","authors":["Hedda Cohen Indelman","Tamir Hazan"],"abstract":"Multi-graph matching is a prominent structured prediction task, in which the predicted label is constrained to the space of cycle-consistent matchings. While direct loss minimization is an effective method for learning predictors over structured label spaces, it cannot be applied efficiently to the problem at hand, since executing a specialized solver across sets of matching predictions is computationally prohibitive. Moreover,\r\nthere’s no supervision on the ground-truth matchings over cycle-consistent prediction sets.\r\nOur key insight is to strictly enforce the matching constraints in pairwise matching predictions and softly enforce the cycle-consistency constraints\r\nby casting them as weighted loss terms, such that the severity of inconsistency with global predictions is tuned by a penalty parameter.\r\nInspired by the classic penalty method, we prove that our method theoretically recovers the optimal multi-graph matching constrained solution.\r\nOur method's advantages are brought to light in experimental results on the popular keypoint matching task on the Pascal VOC and the Willow ObjectClass datasets.","url_abs":"https://proceedings.mlr.press/v206/indelman23a.html","url_pdf":"https://proceedings.mlr.press/v206/indelman23a/indelman23a.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":"learning-constrained-structured-spaces-with","repo_url":"https://github.com/HeddaCohenIndelman/Learning-Constrained-Structured-Spaces-with-Application-to-Multi-Graph-Matching","is_official":0,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"graph-matching","task_name":"Graph Matching"},{"task_slug":"structured-prediction","task_name":"Structured Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/graph-matching-on-pascal-voc","task":"Graph Matching","dataset":"PASCAL VOC","model":"Direct-2HGM","rank_in_archive_order":7,"of":31,"metrics":{"F1 score":"0.601"},"uses_additional_data":false},{"leaderboard":"/sota/graph-matching-on-pascal-voc","task":"Graph Matching","dataset":"PASCAL VOC","model":"Direct-2GM","rank_in_archive_order":9,"of":31,"metrics":{"F1 score":"0.597"},"uses_additional_data":false},{"leaderboard":"/sota/graph-matching-on-pascal-voc","task":"Graph Matching","dataset":"PASCAL VOC","model":"Direct-MGM","rank_in_archive_order":11,"of":31,"metrics":{"F1 score":"0.575"},"uses_additional_data":false},{"leaderboard":"/sota/graph-matching-on-willow-object-class","task":"Graph Matching","dataset":"Willow Object Class","model":"Direct-MGM","rank_in_archive_order":5,"of":23,"metrics":{"matching accuracy":"0.987"},"uses_additional_data":false},{"leaderboard":"/sota/graph-matching-on-willow-object-class","task":"Graph Matching","dataset":"Willow Object Class","model":"Direct-2HGM","rank_in_archive_order":7,"of":23,"metrics":{"matching accuracy":"0.981"},"uses_additional_data":false}],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}