Graph matching with low-rank regularization
Why this work is in the frame
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Bibliographic record
Abstract
Graph matching is a widely researched topic which has been utilized in various applications of computer vision. Due to the combinatorial nature of graph matching, it is NP-hard to find an exact solution. So exact graph matching is always relaxed to inexact graph matching which seeks to find an approximate solution for the original problem. For a matching problem in quadratic form, semidefinite programming (SDP) relaxation is proven to be effective. However, previous SDP relaxation methods discard the constraint that the solution matrix is rank one, because the rank of a matrix is non-convex. In this paper, we explore some good properties of the solution matrix. By relaxing the rank into convex form using the properties, we propose to reformulate the graph matching with low rank constraint into a standard SDP, which can be easily solved. We test our method on both synthetic and real world data. The experimental results demonstrate that our method effectively handles low rank constraint and achieves competitive performance on robustness test against state-of-the-art counterparts.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it