Gaussian mixture error estimation for approximate circuits
Bibliographic record
Abstract
In application domains where perceived quality is limited by human senses, where data are inherently noisy, or where models are naturally inexact, approximate computing offers an attractive tradeoff between accuracy and energy or performance. While several approximate functional units have been proposed to date, the question of how these techniques can be systematically integrated into a design flow remains open. Ideally, units like adders or multipliers could be automatically replaced with their approximate counterparts as part of the design flow. This, however, requires accurately modelling approximation errors to avoid compromising output quality. Prior proposals have either focused on describing errors per-bit or significantly limited estimation accuracy to reduce otherwise exponential storage requirements. When multiple approximate modules are chained, these limitations become critical, and propagated error estimates can be orders of magnitude off. In this paper, we propose an approach where both input distributions and approximation errors are modelled as Gaussian mixtures. This naturally represents the multiple sources of error that arise in many approximate circuits while maintaining reasonable memory requirements. Estimation accuracy is significantly better than prior art (up to 7.2× lower Hellinger distance) and errors can be accurately propagated through a cascade of approximate operations; estimates of quality metrics like MSE and MED are within a few percent of simulation-derived values.
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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 | 0.003 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".