The Modulus Replication RNS (MRRNS): A Comparative Study
Bibliographic record
Abstract
There have been several recent initiatives to use computations on finite polynomial rings as a tool for evaluating digital signal processing algorithms. A technique was recently introduced, by the authors [9], that allows a direct mapping from the bit pattern of the input numbers to the polynomial coefficients. The mapping strategy is simple, and some of the magnitude information of the resulting computations is preserved in the resulting finite ring operations. This is in contrast to the use of a standard residue number system where magnitude information requires invoking the Chinese Remainder Theorem (or some mixed radix counterpart) across the entire dynamic range of the calculation. Disadvantages of the technique are associated with the relatively large redundancy required in the finite ring computational hardware compared to that required for nonredundant integer calculations (binary, RNS etc.). This paper performs a comparative study of the RNS and MRRNS techniques to show that this redundancy in computational hardware is adequately compensated by the simplicity in mapping, scaling and redundancy considerations for WSI implementation.
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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 | 0.000 |
| 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".