Fixed-rate entropy-coded vector quantization using linear (zero-one) programming
Bibliographic record
Abstract
Consider two sets of points X, A and their n-fold cartesian products {A}/sup n/, {X}n. A non-negative cost is associated with each element of A. A measure of distance is defined between an element of A and an element of X. It is assumed that the cost and also the distance in the n-fold space has an additive property. The shaped set is composed of a subset of elements of {A}/sup n/ of the least cost. Decoding of an element x/spl isin/{X}/sup n/ is the process of finding the element of the shaped set which has the minimum distance to x. Using the additivity property of cost and distance measures, the decoding problem is formulated as a linear program. Using the generalized upper bounding technique of linear programming in conjunction with some special features of the problem, we present methods to substantially reduce the complexity of the corresponding simplex search. The proposed method is used for the fixed-rate entropy-coded vector quantization of a Gaussian source. For n=128 (space dimensionality) using 8 points per dimension and for a rate of 2.5 bits/dimension, we need about 52 additions, 87 comparisons, 0.2 divisions, and 0.4 multiplications per dimension to achieve SNR=13.31 dB (the bound obtained from the rate-distortion curve is 13.52 dB). This is substantially less complex than the traditional methods based on the dynamic programming.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".