Integer least squares search and reduction strategies
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
This thesis is concerned with integer least squares problems, also referred to as closest vector problems. One often used approach to solving these problems is the discrete search method, which typically involves two stages, the reduction and the search. The main purpose of the reduction is to make the search faster. Reduction strategies for box-constrained integer least squares problems involve column reordering of the input matrix. There are currently two algorithms for column reordering that are most effective for the search stage, referred to here as SW and CH. Although both use all available information in the problem, the SW and CH algorithms look different and were derived respectively from geometric and algebraic points of view. In this thesis we modify the SW algorithm to make it more computationally efficient and easier to comprehend. We then prove that the SW and CH algorithms actually give the same column reordering in theory. Finally, we propose a new mathematically equivalent algorithm, which is more computationally efficient and is still easy to understand. This thesis also extends the column permutation idea to ordinary integer least squares problems. A new reduction algorithm which combines the well-known LenstraâLenstraâLovász (LLL) reduction and the new column reordering strategy is proposed. The new reduction can be much more effective than the LLL reduction in some cases. The thesis also reviews some common search algorithms. A new one is proposed, which is based on two previous algorithms, the depth-first search and the best-first search. This hybrid algorithm makes use of the advantages of both originals, is more efficient than either and is easier to implement than other previous hybrid algorithms.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.003 |
| 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