Variable-Length Insertion-Based Noisy Sorting
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Bibliographic record
Abstract
In this work, we study the problem of sorting n elements with pairwise comparisons under the presence of observation noise. We consider variable-length algorithms with a random number of queries M, and attempt to characterize the noisy sorting capacity defined as the maximal ratio $\frac{{n\log n}}{{{\text{E}}[M]}}$ such that the ordering can be correctly estimated with a vanishing error probability. This can be viewed as a generalization of the framework introduced in [1] to allow variable-length algorithms. We provide upper and lower bounds for the noisy sorting capacity. The proposed algorithm attaining the lower bound is based on the insertion sort algorithm for the sorting problem in the noiseless case and the variable-length version of the Burnashev–Zigangirov algorithm for coding over channels with feedback. Moreover, we also derive an upper bound on the maximal ratio that can be achieved by noisy sorting algorithms that are based on insertion sort.
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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 | 0.000 | 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 | 0.000 |
| Open science | 0.001 | 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