An ADMM based method for underdetermined box-constrained integer least squares problems
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Bibliographic record
Abstract
To solve underdetermined box-constrained integer least squares (UBILS) problems, we propose an integer-constrained alternating direction method of multipliers (IADMM), which can be much more accurate than the ADMM method. To guarantee to find the optimal solution, then we incorporate IADMM to DTS, a tree search method, to make the latter more efficient. Numerical tests show that the combined method IADMM-DTS can be much faster than the original DTS method. Finally, we apply the combined method to a practical communication problem. Numerical results indicate that IADMM-DTS typically performs better than the commercial solvers CPLEX and MOSEK in terms of both efficiency and accuracy, and it can be used as an alternative to the commercial solver Gurobi for UBILS problems.
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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