Bibliographic record
Abstract
It's well known that there is a so-called exponential-type error bound for Gaussian interpolation which is the most powerful error bound hitherto. It's of the formj f (x) s(x)j c1(c2d) c3 dk fk h where f and s are the interpolated and interpolating functions respectively, c1; c2; c3 are positive constants, d is the fill distance which roughly speaking measures the spacing of the data points, andk fkh is the h-norm of f where h is the Gaussian function. The error bound is suitable for x 2 R n ; n 1, and gets small rapidly as d ! 0. The drawback is that the crucial constants c2 and c3 get worse rapidly as n increases in the sense c2! 1 and c3! 0 as n! 1. In this paper we raise an error bound of the form j f (x) s(x)j c 0 (c 0 d) c0 d p dk fk h; where c 0 and c 0 are independent of the dimension n. Moreover, c 0 << c2; c3 << c 0 , and c 0 is only slightly di erent from c1. What's important is that all constants c 0 ; c 0 and c 0 can be computed without slight di culty.
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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 | 0.010 | 0.034 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.003 | 0.008 |
| Research integrity | 0.003 | 0.008 |
| Insufficient payload (model declined to judge) | 0.006 | 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; 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".