Bibliographic record
Abstract
In this thesis, we implement several approximation algorithms for solving optimization problems on graphs. The result computed by the algorithm may or may not be optimal. The approximation factor of an algorithm indicates how close the computed result is to an optimal solution. We are going to verify two properties of each algorithm in this thesis.First, we show that the algorithm computes a solution to the problem, and, second, we show that the approximation factor is satisfied. To implement these algorithms, we use the algebraic theory of relations, i.e., the theory of allegories and various extension thereof. An implementation of various kinds of lattices and the theory of categories is required for the declaration of allegories. The programming language and interactive theorem prover Coq is used for the implementation purposes. This language is based on Higher-Order Logic (HOL) with dependent types which support both reasoning and program execution. In addition to the abstract theory, we provide the model of set-theoretic relations between finite sets. This model is executable and used in our examples. Finally, we provide an example for each of the approximation algorithm.
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.005 |
| Open science | 0.002 | 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".