Bibliographic record
Abstract
We consider the SUMT (Sequential Unconstrained Minimization Technique) method using extrapolations to link successive unconstrained sub-problems. The case when the extrapolation is obtained by a first order Taylor estimate and Newton's method is used as a correction in this predictor-corrector scheme was analyzed in [1]. It yields a two-steps super-linear asymptotic convergence with limiting order of 4/3 for the logarithmic barrier and order two for the quadratic loss penalty. We explore both lower order variants (approximate extrapolations correction computations) as well as higher order variants (second order and further) Taylor estimate. First, we address inexact solutions of the linear systems arising within the extrapolation and the Newton's correction steps. Depending on the inexactness allowed, asymptotic convergence order reduces, more severely so for interior variants. Second, we investigate the use of higher order path following strategies in those methods. We consider the approach based on a high order expansion of the so-called central path, somewhat reminiscent of Chebyshev's third order method and its generalizations. The use of higher order representation of the path yields spectacular improvement in the convergence property, even more so for the interior variants.
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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 | 0.003 | 0.016 |
| 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 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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".