Papers › Deep Graph Matching under Quadratic Constraint
Deep Graph Matching under Quadratic Constraint
Quankai Gao, Fudong Wang, Nan Xue, Jin-Gang Yu, Gui-Song Xia
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.
In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.
For agents, Syntology's MCP tool lists every function and class Syntology harvested from this paper and whether it ran (how to connect): get_harvested_code_for_paper(arxiv_id="2103.06643")
Code
Syntology Ran 2 of 2 code samples harvested from 1 repository linked to this paper; 0 have no recorded run. Of those that ran: 1 ran · our draft was wrong; 1 ran · fixture could not drive it.
By repository: official repository: 2 samples from 1 repository, 2 ran. The run record, sample by sample. “Ran” means executed on a synthesized input, not that the code is correct or reproduces the paper.
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
2 samples harvested; 2 ran; 0 honoured the contract we drafted; 0 have no recorded run. Read from Syntology's graph 2026-09-24; that is when this build read the record, not when the samples ran.
Licence: 2 of the 2 samples are pointer only, meaning Syntology does not serve that copy's text. This page shows no code text for any sample; each one links to its file in the repository.
Harvested from Zerg-Overmind/QC-DGM. “Ran” means the sample executed on a synthesized input. It does not mean the output is correct, and nothing here reproduces the paper's results. “Honoured” and “violated” refer to a contract Syntology drafted from the code itself; “our draft was wrong” and “fixture could not drive it” are failures of Syntology's instrument, not of the code.
Each sample ends with its code_sha256, Syntology's identity for that exact code. An agent fetches the stored sample with Syntology's MCP tool get_code(code_sha256="…") (how to connect); click an identity to copy that call.
Repository labels, per sample. official repository: The archive marks this repository official for the paper. named in the paper: The archive records that the paper mentions this repository; it is not marked official. community (archive-listed): In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper. found in paper text by Syntology: Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted. community: Not in the archive's code links for this paper; a community repository Syntology harvested. Samples from a repository marked official are listed first. Licence labels name the repository's licence as recorded at harvest. “Pointer only” means Syntology does not serve that copy's text, for one of four reasons: no licence file was found; the licence was not identified; the licence is recorded as permissive but that copy's record is not marked cleared; or the licence is outside the permissive list Syntology serves text under (MIT, Apache-2.0, BSD and similar). Some licences outside that list permit redistribution, such as WTFPL, and GPL-3.0 under its conditions; they are simply not on the list. Hover a licence label for the reason. File links open the file on GitHub at the default branch, which may have changed since the harvest.
4371ea418a77da94 · report
9810cb600fe4ff51 · report
Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Graph Matching | PASCAL VOC | qc-DGM2 | matching accuracy | 0.703 | #22 of 31 | Archive leaderboard | report |
| Graph Matching | PASCAL VOC | qc-DGM1 | matching accuracy | 0.693 | #23 of 31 | Archive leaderboard | report |
| Graph Matching | Willow Object Class | qc-DGM2 | matching accuracy | 0.977 | #8 of 23 | Archive leaderboard | report |
| Graph Matching | Willow Object Class | qc-DGM1 | matching accuracy | 0.960 | #15 of 23 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections