Bibliographic record
Abstract
Any scalar quantizer of 2/sup h/ bins, where h is a positive integer, can be structured by a balanced binary quantizer tree T of h levels. Any pruned subtree /spl tau/ of T corresponds to an operational rate R(/spl tau/) and distortion D(/spl tau/) pair. Denote by S/sub n/ the set of all pruned subtrees of n leaf nodes, 1/spl les/n/spl les/2/sup h/. We consider the problem of designing a 2/sup h/-bin scalar quantizer that minimizes the weighted average distortion D~=/spl Sigma//sub n=1//sup 2(h)/ D(/spl tau/)W(n), where W(n) is a weighting function in the size of pruned subtrees (or the resolution of the underlying quantizer). We present an O(hN/sup 3/) algorithm to solve the underlying optimization problem (N is the number of points of the histogram that represents the source probability mass function), and call the resulting quantizer optimal multi-resolution scalar quantizer in the sense that it minimizes a global distortion measure averaged over all quantization resolutions of T. Interestingly, a similar quantizer design problem studied by Brunk et al. (1996) is a special case of our formulation, and can thus be solved exactly and efficiently using our algorithm. Furthermore, we present an algorithm to generate a sequence of 2/sup h/ nested pruned subtrees of T, from the root of T to the entire tree T itself, which minimizes an expected distortion over a range of operational rates. The resulting nested pruned subtree sequence generates an optimized embedded (rate-distortion scalable) code stream with maximum granularity of 2/sup h/ quantization stages, as opposed to existing successively refinable quantizers, such as the popular bit-plane coding scheme, which offer only h stages.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".