Globally Optimal Design of a Distributed Scalar Quantizer for Linear Classification
Bibliographic record
Abstract
This work is concerned with the design of a distributed scalar quantizer (DSQ) with two encoders, for linear classification. The objective of the optimization is to minimize the classification error of the classifier applied to the quantized inputs in the training sequence with respect to the classifier applied on unquantized inputs. We prove that the optimal DSQ design problem is equivalent to a minimum weight path problem with some constraints on the number and types of edges in a certain weighted directed acyclic graph. Further, we propose a solution algorithm with time complexity$O(K_{1}K_{2}N^{4})$, where$N$is the size of the training sequence while$K_{1}$and$K_{2}$are the numbers of cells of the two encoders, respectively. In addition, we develop faster design algorithms for the equal-rate case (i.e.,$K_{1}=K_{2}=K$). Specifically, when the training sequence is symmetric, we prove that there exists an optimal DSQ where the thresholds of the encoders' partitions are interleaved. By leveraging this property and the symmetry of the training sequence, we propose a$O(KN^{2})$time solution algorithm. For the case when the training sequence is not symmetric, we propose an algorithm with the same time complexity that minimizes an upper bound on the misclassification ratio. Experimental results prove the considerable superiority of the proposed approaches in comparison with prior work in both symmetric and asymmetric scenarios.
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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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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) | 0.003 | 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".