Numerical methods for underdetermined box-constrained integer least squares problems
Why this work is in the frame
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Bibliographic record
Abstract
Integer least squares (ILS) is an important class of optimization problems, which can arise in many applications, such as communications, cryptography and cryptanalysis and global navigation satellite systems. This thesis is concerned with solving the underdetermined box constrained ILS (UBILS) problems. For the two existing algorithms, the direct tree search (DTS) algorithm and the partial regularization (PR) algorithm, we propose to incorporate some lower bounds to speed up the search process. Simulation results show that the proposed lower bounds can make the search process of the DTS algorithm perform more efficiently than the original one. Then we propose a modified DTS algorithm by partially using a best-first search strategy in the search process. Numerical tests results indicate that the new search algorithm is very effective in improving the efficiency of the DTS algorithm with or without incorporating the proposed lower bounds.
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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 | 0.002 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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