Accelerating Floating-Point Lattice Reduction: A Preprocessing Block Reduction Framework
Bibliographic record
Abstract
Lattice reduction is a fundamental technique in computational mathematics with applications in cryptography, integer programming, and wireless communications.The Lenstra-Lenstra-Lovász (LLL) algorithm is among the most widely used lattice reduction algorithms.However, the efficiency of its floating-point implementations is insufficient for practical applications, particularly for high-dimensional lattices.This thesis proposes a block lattice reduction (BLR) algorithm, which can be used as a preprocessing step to accelerate existing floating-point LLL algorithms such as the L 2 and H-LLL algorithms.While designed primarily for speed improvement, BLR often achieves better reduction quality as well.Moreover, the BLR algorithm is not limited to LLL reduction; it provides a general framework that can also reduce the running time of other lattice reduction algorithms, such as HKZ, BKZ, Self-Dual BKZ, and Slide reduction.We demonstrate the efficiency and effectiveness of our approach through extensive runtime comparisons, leveraging the widely used floating-point lattice reduction library fplll.
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.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.013 | 0.008 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".