General purpose FIR filter arrays using optimized redundancy over direct product polynomial rings
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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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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it