Analysis of Mean-Square-Error (MSE) for fixed-point FFT units
Bibliographic record
Abstract
Range and precision analysis are important steps in assigning suitable integer and fractional bit-widths to the fixed-point variables in a design such that no overflow occurs and a given error bound on maximum mismatch and (or) Mean-Square-Error (MSE) is satisfied. Although, range and maximum mismatch analysis of linear arithmetic circuits has been studied before [8], regarding analysis of MSE, the previous works [9,10,12] cannot analyze the error, when it is defined as the difference between the fixed-point circuit and the reference model, e.g., floating-point format. This paper presents an efficient analysis of MSE for linear arithmetic circuits narrowing on Fast Fourier Transform (FFT) units. Furthermore, an optimization algorithm is introduced to set the bit-widths in an FFT unit while satisfying a given maximum bound on MSE. Experimental results prove the robustness of our MSE analysis and the efficiency of the optimization algorithm compared to [12] for an 8K FFT unit.
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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 | 0.001 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".