A 2-digit DBNS filter architecture
Bibliographic record
Abstract
We have previously reported on a novel number representation using 2 bases which we refer to as the double-base number system (DBNS). Our preferred implementation uses the relatively prime bases {2,3}. If we allow the exponents of the bases to be arbitrarily large signed integers, then we can represent any real number to any arbitrary precision by a single digit DBNS representation. By representing the digit position by the exponent values, we generate a logarithmic-like representation which we can manipulate using an index calculus. A multiplier accumulator architecture for a FIR filter application has been reported which uses a half-index domain to remove the problem of addition within the index calculus. In this paper we show that using a 2-digit DBNS representation for both the input data and the filter coefficients can result in substantial hardware savings compared to both the single-digit a DBNS approach and an equivalent binary implementation of a general multiplier accumulator. In the paper we discuss the filter architecture, techniques for converting between binary and the 2-digit DBNS representations, and also the design technique used to generate the 2-digit DBNS FIR filter coefficients.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.009 | 0.003 |
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".