Bibliographic record
Abstract
We introduce a new software tool and library named Lattice Builder, written in C++, that implements a variety of construction algorithms for good rank-1 lattice rules. It supports exhaustive and random searches, as well as component-by-component (CBC) and random CBC constructions, for any number of points, and for various measures of (non)uniformity of the points. The measures currently implemented are all shift-invariant and represent the worst-case integration error for certain classes of integrands. They include, for example, the weighted Pα square discrepancy, the Rα criterion, and figures of merit based on the spectral test, with projection-dependent weights. Each of these measures can be computed as a finite sum. For the Pα and Rα criteria, efficient specializations of the CBC algorithm are provided for projection-dependent, order-dependent, and product weights. For numbers of points that are integer powers of a prime base, the construction of embedded rank-1 lattice rules is supported through any of these algorithms, and through a fast CBC algorithm, with a variety of possibilities for the normalization of the merit values of individual embedded levels and for their combination into a single merit value. The library is extensible, thanks to the decomposition of the algorithms into decoupled components, which makes it easy to implement new types of weights, new search domains, new figures of merit, and so on.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.004 | 0.003 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.137 | 0.072 |
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".