General purpose FIR filter arrays using optimized redundancy over direct product polynomial rings
Bibliographic record
Abstract
This paper presents architectures for implementing general purpose FIR arrays, using enhanced Fermat ALU theory. The structure is based on a direct product finite polynomial ring mapping of a redundant binary representation of the input data; in effect we exploit a double redundancy of the input representation and the mapped polynomial representation. By exploiting this redundancy, with attendant reductions in coefficient growth due to the polynomial multiplication, we are able to considerably reduce the probability of overflow error. The direct product computational channels all operate over the single Fermat prime, 257, and the silicon area overhead for the input/output mappings is less than 10%. This a considerable reduction compared to conventional and previous RNS designs of inner product processor array for DSP applications. We present results of test chips and 53 tap filter array designs using both a 0.5 micron and 0.35 micron CMOS technology. Power reduction estimates over equivalent binary implementations are at least 50%.
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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 | 0.000 |
| 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 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".