An efficient CGA_ADMM for the metric nearness problem
Why this work is in the frame
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Bibliographic record
Abstract
The metric nearness problem aims to find a metric matrix nearest to a given dissimilarity matrix with the triangle inequalities valid.In this paper, we consider the metric nearness problem with the distance measured by the vector p (p = 1, 2, ) norm.Due to the O(n 3 ) constraints and O(n 2 ) variables, the main difficulty of solving this kind of large scale problems is the high memory requirement.We design a constraint generation based alternating direction method of multipliers (CGA ADMM) and take full advantage of the special structure of the constraint matrix so that the memory requirement of the CGA ADMM is moderate.Numerical experiments of the real world graph data sets involving up to 10 8 variables and 10 12 constraints demonstrate that our algorithm has a better performance than the current state-of-the-art algorithms.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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