Multipath Greedy Algorithm-for Canonical Representation of Numbers-in the Double Base Number System
Bibliographic record
Abstract
The double base number system (DBNS) has been used in applications such as cryptography and digital filters. Two important properties of this type of representation are high redundancy and sparseness, which are key in eliminating carry propagation in basic arithmetic operations. High redundancy poses challenges in determining the canonical double base number representation (CDBNR) of an algebraic value. An exhaustive search for this representation can be computationally intensive, even for relatively small values. The greedy algorithm is very fast and simple to implement, but only allows for a single near canonical double base number representation (NCDBNR). The multipath greedy (MG) algorithm discussed in this paper is much faster than exhaustive search and gives better performance since it dramatically increases the likelihood of finding canonical representations. Since multiple starting points are used, this algorithm is able to find more than one NCDBNR in a single run.
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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 | 0.000 |
| Open science | 0.001 | 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".