Reliable Minimum Finding Comparator Networks
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Bibliographic record
Abstract
We consider the problem of constructing reliable comparator networks built from unreliable comparators. In case of a faulty comparator inputs are directly output without comparison. A trivial lower bound of Ω(logn + k) on the depth of n-input k-fault tolerant sorting network is well known. We are interested in establishing exact lower bounds on the depth of such networks. To this end we consider fairly simple minimum-finding networks. Our main result is the first nontrivial lower bound on depths of networks computing minimum among n > 2 items in the presence of k > 0 faulty comparators. We prove that the depth of any such network is at least max([logn] + 2k, logn + klog logn/k+1). We also describe a network whose depth nearly matches the lower bound.
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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 | 0.000 |
| 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) | 0.002 | 0.002 |
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