Numerical Analysis of $\mathcal{V}\mathcal{U}$-Decomposition, $\mathcal{U}$-Gradient, and $\mathcal{U}$-Hessian Approximations
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Advances in bundle methods for nonsmooth optimization have lead to the development of $\mathcal{V}\mathcal{U}$-decompositions, the $\mathcal{U}$-gradient, and the $\mathcal{U}$-Hessian. These variational analysis constructs have proven extremely valuable and lead to the development of the superlinearly convergent $\mathcal{V}\mathcal{U}$-algorithm for nonsmooth optimization. In this paper we examine these constructs from the viewpoint of derivative-free optimization. We show that, given a finite max function $f(x) = \max_{i=0, 1, \ldots m} f_i(x)$ and a black-box which returns function values for each $f_i$, it is possible to construct approximations of the $\mathcal{V}\mathcal{U}$-decompositions, $\mathcal{U}$-gradient and $\mathcal{U}$-Hessian. The approximations do not require excessive black-box calls, and the accuracy of the approximations is directly related to the accuracy of the approximate gradient and Hessians for each $f_i$.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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