Bibliographic record
Abstract
A square system of linear equations is \\ill-conditioned" when the norm of the corresponding inverse matrix is large. This norm bounds the size of the solution, and measures how close the system is to being inconsistent: it is thus of fundamental computational signicance. We generalize this idea from linear equations to inclusions governed by closed convex processes, and hence to \\conic linear systems". 1 Research partially supported by the Natural Sciences and Engineering Research Council of Canada. The author thanks the University of Montpellier II for their hospitality while this work was completed. 1 1 Introduction Given an invertible n n real matrix F and a vector b in R n , consider the linear system Fx = b; x 2 R n : It is a simple consequence of the Eckart-Young theorem (see [7], for example) that the smallest operator norm of a matrix G making the perturbed matrix F +G singular is just kF 1 k 1 . This quantity is a fundamental measure of the \\conditioning...
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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) | 0.008 | 0.002 |
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; both teacher heads agree on what is shown here.
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".