Noisy Computing of the OR and MAX Functions
Why this work is in the frame
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Bibliographic record
Abstract
We consider the problem of computing a function of n variables using noisy queries, where each query is incorrect with some fixed and known probability p(0,1/2). Specifically, we consider the computation of the OR function of n bits (where queries correspond to noisy readings of the bits) and the MAX function of n real numbers (where queries correspond to noisy pairwise comparisons). We show that an expected number of queries of (1±o(1))nlog1/δDKL(p||1-p) is both sufficient and necessary to compute both functions with a vanishing error probability δ=o(1), where DKL(p||1-p) denotes the Kullback-Leibler divergence between Bern(p) and Bern(1-p) distributions. Compared to previous work, our results tighten the dependence on p in both the upper and lower bounds for the two functions.
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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