Decoder Reduction Approximation Scheme for Booth Multipliers
Bibliographic record
Abstract
Existing approximate Booth multipliers fail to keep up with modern approximate multipliers such as truncation-based approximate logarithmic multipliers. This paper introduces a new approximation scheme for Booth multipliers that can operate with negligible error rates using only$N/4$Booth decoders, instead of the traditional$N/2$Booth decoders. The proposed 16-bit BD16.4 approximate Booth multiplier reduces the Normalized Mean Error Deviation (NMED) by 96.5% and the Power-Area-Product (PAP) by 69.6%, when compared to a state-of-the-art approximate logarithmic multiplier. Additionally, the proposed BD16.4 approximate multiplier reduces the NMED by 94.4% and PAP by 74.8%, when compared to a state-of-the-art higher-radix approximate Booth multiplier. The proposed 8-bit approximate Booth multipliers reduce the NMED by up to 74% and PAP by up to 5% when compared to the existing state-of-the-art approximate logarithmic multipliers. We validated the results derived in this paper through a neural network inference experiment, where the proposed approximate multipliers showed a negligible drop in inference accuracy compared to the exact Booth multipliers and the state-of-the-art approximate logarithmic multipliers (ALM). The proposed approximate multipliers achieved a Power-Delay-Product reduction of 63% (vs. exact) and 21.22% (vs. ALM) in 16-bit experiments and a reduction of 67% (vs. exact) and 8.75% (vs. ALM) in 8-bit experiments.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 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 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 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".