{"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/deep-graph-matching-under-quadratic","title":"Deep Graph Matching under Quadratic Constraint","arxiv_id":"2103.06643","date":"2021-03-11","proceeding":"CVPR 2021 1","authors":["Quankai Gao","Fudong Wang","Nan Xue","Jin-Gang Yu","Gui-Song Xia"],"abstract":"Recently, deep learning based methods have demonstrated promising results on the graph matching problem, by relying on the descriptive capability of deep features extracted on graph nodes. However, one main limitation with existing deep graph matching (DGM) methods lies in their ignorance of explicit constraint of graph structures, which may lead the model to be trapped into local minimum in training. In this paper, we propose to explicitly formulate pairwise graph structures as a \\textbf{quadratic constraint} incorporated into the DGM framework. The quadratic constraint minimizes the pairwise structural discrepancy between graphs, which can reduce the ambiguities brought by only using the extracted CNN features. Moreover, we present a differentiable implementation to the quadratic constrained-optimization such that it is compatible with the unconstrained deep learning optimizer. To give more precise and proper supervision, a well-designed false matching loss against class imbalance is proposed, which can better penalize the false negatives and false positives with less overfitting. Exhaustive experiments demonstrate that our method competitive performance on real-world datasets.","url_abs":"https://arxiv.org/abs/2103.06643v2","url_pdf":"https://arxiv.org/pdf/2103.06643v2.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":"deep-graph-matching-under-quadratic","repo_url":"https://github.com/Zerg-Overmind/QC-DGM","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"descriptive","task_name":"Descriptive"},{"task_slug":"graph-matching","task_name":"Graph Matching"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/graph-matching-on-pascal-voc","task":"Graph Matching","dataset":"PASCAL VOC","model":"qc-DGM2","rank_in_archive_order":22,"of":31,"metrics":{"matching accuracy":"0.703"},"uses_additional_data":false},{"leaderboard":"/sota/graph-matching-on-pascal-voc","task":"Graph Matching","dataset":"PASCAL VOC","model":"qc-DGM1","rank_in_archive_order":23,"of":31,"metrics":{"matching accuracy":"0.693"},"uses_additional_data":false},{"leaderboard":"/sota/graph-matching-on-willow-object-class","task":"Graph Matching","dataset":"Willow Object Class","model":"qc-DGM2","rank_in_archive_order":8,"of":23,"metrics":{"matching accuracy":"0.977"},"uses_additional_data":false},{"leaderboard":"/sota/graph-matching-on-willow-object-class","task":"Graph Matching","dataset":"Willow Object Class","model":"qc-DGM1","rank_in_archive_order":15,"of":23,"metrics":{"matching accuracy":"0.960"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2103.06643","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2103.06643"}},"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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