Randomized quantization and optimal design with a marginal constraint
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Bibliographic record
Abstract
We consider the problem of optimal randomized vector quantization under a constraint on the output's distribution. The problem is formalized by introducing a general representation of randomized quantization via probability measures over the space of joint distributions on the source and reproduction alphabets. Using this representation and results from optimal transport theory, we show the existence of an optimal (minimum distortion) randomized quantizer having a fixed output distribution under various conditions. For sources with densities and the mean square distortion measure, we show that this optimum can be attained by randomizing quantizers having convex code cells. We also consider a relaxed version of the problem where the output marginal must belong to some neighborhood (in the weak topology) of a fixed probability measure. We demonstrate that finitely randomized quantizers form an optimal class for the relaxed problem.
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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 | 0.001 |
| Open science | 0.000 | 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