Superiorization: The asymmetric roles of feasibility-seeking and objective function reduction
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Bibliographic record
Abstract
The superiorization methodology can be thought of as lying conceptually between feasibilityseeking and constrained minimization.It is not trying to solve the full-fledged constrained minimization problem composed from the modeling constraints and the chosen objective function.Rather, the task is to find a feasible point which is "superior" (in a well-defined manner) with respect to the objective function, to one returned by a feasibility-seeking only algorithm.We telegraphically review the superiorization methodology and where it stands today and propose a rigorous formulation of its, yet only partially resolved, guarantee problem.The real-world situation in an application field is commonly represented by constraints defined by the modeling process and the data, obtained from measurements or otherwise dictated by the model-user.The feasibility-seeking problem requires to find a point in the intersection of all constraints without using any objective function to aim at any specific feasible point.At the heart of the superiorization methodology lies the modeler desire to use an objective function, that is exogenous to the constraints, in order to seek a feasible solution that will have lower (not necessarily minimal) objective function value.This aim is less demanding than full-fledged constrained minimization but more demanding than plain feasibility-seeking.Putting emphasis on the need to satisfy the constraints, because they represent the real-world situation, one recognizes the "asymmetric roles of feasibility-seeking and objective function reduction", namely, that fulfilling the constraints is the main task while reduction of the exogenous objective function plays only a secondary role.There are two research directions in the superiorization methodology that nourish from this same general principle: Weak superiorization and strong superiorization.Since its inception in 2007, the superiorization methodology has evolved and gained ground, as can be seen from the, compiled and continuously updated, bibliography at: http://math.haifa.ac.il/yair/bib-
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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 | 0.003 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.007 |
| 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