Encoding and decoding algorithms for LP-decodable multipermutation codes
Bibliographic record
Abstract
LP-decodable multipermutation codes are a class of multipermutation codes that can be decoded using linear programming (LP). These codes are defined using linearly constrained multipermutation matrices, which are binary matrices that satisfy particular row sum and column sum constraints. Although generic LP solvers are capable of solving the LP decoding problem, they are not efficient in general because they do not leverage structures of the problem. This motivates us to study efficient decoding algorithms. In this paper, we focus on encoding and decoding algorithms for LP-decodable multipermutation codes. We first describe an algorithm that “ranks” multipermutations. In other words, it maps consecutive integers, one by one, to an ordered list of multipermutations. By leveraging this algorithm, we develop an encoding algorithm for a code proposed by Shieh and Tsai. Regarding decoding algorithms we propose an iterative decoding algorithm based on the alternating direction method of multipliers (ADMM), each iteration of which can be solved efficiently using off-the-shelf techniques. Finally, we study decoding performances of different decoders via simulation.
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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 | 0.001 | 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 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".