What can we learn from No Free Lunch? a first attempt to characterize the concept of a searchable function
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
The No Free Lunch theorem has had considerable impact in the field of optimization research. A terse definition of this theorem is that no algorithm can outperform any other algorithm when performance is amortized over all functions. Once that theorem has been proven, the next logical step is to characterize how effective optimization can be under reasonable restrictions. We operationally define a technique for approaching the question of what makes a function searchable in practice. This technique involves defining a scalar field over the space of all functions that enables one to make decisive claims concerning the performance of an associated algorithm. We then demonstrate the effectiveness of this technique by giving such a field and a corresponding algorithm; the algorithm performs better than random search for small values of this field. We then show that this algorithm will be effective over many, perhaps most functions of interest to optimization researchers. We conclude with a discussion about how such regularities are exploited in many popular optimization algorithms. 1
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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