Optimizing the Parallel Tree-Search for Finding Shortest-Span Error-Correcting CDO Codes
Bibliographic record
Abstract
Finding optimal/short-span Convolutional Self-Doubly Orthogonal (CDO) codes and Simplified-CDO (S-CDO) codes for a specified order J is computationally very challenging. This paper describes several optimizations that were applied to an implicitly-exhaustive search algorithm in order to reduce the time required for finding these types of codes. The resulting high-performance parallel implementation provides an impressive speedup that is greater than 16 300 (CDO,${\rm J} = 7$) and 6300 (S-CDO,${\rm J} = 8$) over the reference implicitly-exhaustive search algorithm, and greater than 2000$({\rm J} = 17)$over the fastest published CDO validation function used in high-performance pseudorandom search algorithms. These speedups are achieved through enhancements in the deterministic search-space reduction, and a vastly improved validation function that makes use of a novel data structure for enabling data-reuse and incremental computations. The resulting validation function speedup is greater than 60 000 (S-CDO,${\rm J} = 17$) and 190 000 (CDO,${\rm J} = 17$) when compared to its reference implementation. The combination of optimizations and load-balancing techniques allowed us to leverage hundreds of processor cores in order to complete an exhaustive search over a search space that is some$10^{14}$times larger than what was previously possible.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".