Loading the bases: a new number representation with applications
Bibliographic record
Abstract
A number system has recently been introduced that uses two orthogonal bases (Double-base Number System-DBNS). In its direct form the system provides a very sparse two-dimensional number representation which appears, initially, to be a curiosity. After some research by our group, however, the number system has proved to have some interesting and potentially far-reaching applications. The number system has been extended to more than 2 bases and a logarithmic version, which we refer to as the Multi-dimensional Logarithmic Number System (MDLNS), has also proved useful for implementing digital filters. An important property of the MDLNS, that the computational complexity associated with each base reduces both as the number of bases and as the number of digits (or logarithmic components) increase, gives rise to some simple implementation procedures. In this article we will explore some of the theory of the linear and logarithmic systems associated with this new representation, and provide examples of applications in cryptography and digital filter implementation.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.010 | 0.005 |
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".