Revisiting some classical linearizations of the quadratic binary optimization problem
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Bibliographic record
Abstract
In this paper, we present several new linearizations of a quadratic binary optimization problem (QBOP), primarily using the method of aggregations. Although aggregations were studied in the past in the context of solving system of Diophantine equations in non-negative variables, none of the approaches developed produced practical models, particularly due to the large size of associate multipliers. Exploiting the special structure of QBOP we show that selective aggregation of constraints provide valid linearizations with interesting properties. For our aggregations, multipliers can be any non-zero real numbers. Moreover, choosing the multipliers appropriately, we demonstrate that the resulting LP relaxations have value identical to the corresponding non-aggregated models. We also provide a review of existing explicit linearizations of QBOP and presents the first systematic study of such models. Theoretical and experimental comparisons of new and existing models are also provided.
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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 | 0.001 |
| 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 | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| 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