Design of General Entropy-Constrained Successively Refinable Unrestricted Polar Quantizer
Bibliographic record
Abstract
This paper presents an algorithm for the optimal design of general entropy-constrained successively refinable unrestricted polar quantizer, i.e., with arbitrary number L of refinement levels, for bivariate circularly symmetric sources. The optimization problem is formulated as the minimization of a weighted sum of distortions and entropies for the scenario where the magnitude quantizers' thresholds are confined to a predefined finite set. The proposed solution algorithm is globally optimal. It involves L stages, where each stage corresponds to an unrestricted polar quantizer (UPQ) level, and includes solving the minimum-weight path problem for multiple node pairs in a series of weighted directed acyclic graphs. Additionally, we derive an upper bound P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(l)</sup> , l ∈ [1 : L], on the possible number of phase levels in any phase quantizer of the l-th level UPQ, which grows linearly with l. The time complexity of the proposed approach is O(L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(l)</sup> ), where K is the cardinality of the predefined set of possible magnitude thresholds. Finally, the experimental results for L = 3 demonstrate the effectiveness in practice of the proposed scheme.
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How this classification was reachedexpand
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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.003 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".