Generic convergence of methods for solving stochastic feasibility problems
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Bibliographic record
Abstract
We use an implementation of the generic approach to solve (generalized) stochastic feasibility problems. These are the problems of finding almost common fixed points of measurable (with respect to a probability measure) families of mappings. Such an implementation for a bounded set K has already been presented by Gabour, Reich and Zaslavski in 2001. Our strong convergence results provide iterative methods (in the case where the set K is not necessarily bounded) for finding an almost common fixed point of a generic measurable family of mappings. Some of our results involve the case where a subset of the almost common fixed point set is a nonexpansive retract of K. Our results are applicable to both the consistent case (that is, the case where the aforesaid almost common fixed points exist) and the inconsistent case (that is, the case where there are no common fixed points at all).
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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 | 0.004 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| 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