Using generalized simplex methods to approximate derivatives
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Bibliographic record
Abstract
Abstract This paper presents two methods for approximating a proper subset of the entries of a Hessian using only function evaluations. It is also shown how to approximate a Hessian-vector product with a minimal number of function evaluations. These approximations are obtained using the techniques called generalized simplex Hessian and generalized centred simplex Hessian. We show how to choose the matrices of directions involved in the computation of these two techniques, depending on the entries of the Hessian of interest. We discuss the number of function evaluations required in each case and develop a general formula to approximate all order-$P$ partial derivatives. Since only function evaluations are required to compute the methods discussed in this paper they are suitable for use in derivative-free optimization methods.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.005 |
| 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) | 0.000 | 0.000 |
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 it