Generalized Max-Cut and the Approximation Ratio
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
<p>In this thesis, we formulate a new problem based on Max-Cut called Generalized Max-Cut. This problem requires a graph as input and two real numbers (a, b) where a > 0 and −a < b < a and outputs a number. The restriction on the pair (a, b) is to avoid trivializing the problem. We formulate a quadratic program for Generalized Max-Cut and relax it to a semi-definite program. Most algorithms in this thesis will require solving this semi-definite program. The main algorithm in this thesis is the 2-Dimensional Rounding algorithm, designed by Avidor and Zwick, with the restriction that the semi-definite program of the input graph must have 2-Dimensional solutions. This algorithm uses a factor of randomness, β ∈ [0, 1], that is dependent on the integer input to Generalized Max-Cut. We improve the performance of this algorithm by numerically finding better β.</p>
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.005 |
| 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