Reduction of Distributions: Definitions, Properties, and Applications
Bibliographic record
Abstract
In this work, a notion of reduction of distributions is proposed as a technical tool for improving the complexity of decomposability verification and supporting parallel verification of decomposability, by exploiting the rich structures of distributions. We provide some results that reduce the search space of candidate reductions, as a first step toward efficiently computing optimal reductions. It is then shown that a distribution has a reduction if and only if a particular candidate reduction is indeed a reduction. We then provide a sound substitution-based proof technique that can be used for (automatic) reduction verification. Techniques for refuting candidate reductions are also provided. We then explain an application of the decomposability verification problem in the lower bound proofs for the problem of supervisor decomposition and the problem of existence of a decentralized supervisor. Finally, some other applications of the notion of reduction of distributions are also shown.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.007 |
| Scholarly communication | 0.002 | 0.007 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.001 | 0.005 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".