Genetic Algorithms Applied to Problems of Forbidden Configurations
Bibliographic record
Abstract
A simple matrix is a (0,1)-matrix with no repeated columns. For a (0,1)-matrix $F$, we say a (0,1)-matrix $A$ avoids $F$ (as a configuration) if there is no submatrix of $A$ which is a row and column permutation of $F$. Let $\|{A}\|$ denote the number of columns of $A$. We define $\mathrm{forb}(m,F)=\max\{\|{A}\|\ : A$ is an $m$-rowed simple matrix that avoids $F \}$. Define an extremal matrix as an $m$-rowed simple matrix $A$ with that avoids $F$ and $\|{A}\|=\mathrm{forb}(m,F)$. We describe the use of Local Search Algorithms (in particular a Genetic Algorithm) for finding extremal matrices. We apply this technique to two forbidden configurations in turn, obtaining a guess for the structure of an $m\times\mathrm{forb}(m,F)$ simple matrix avoiding $F$ and then proving the guess is indeed correct. The Genetic Algorithm was also helpful in finding the proof.
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".