Optimization of Imprecise Circuits Represented by Taylor Series and Real-Valued Polynomials
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Bibliographic record
Abstract
Arithmetic circuits in general do not match specifications exactly, leading to different implementations within allowed imprecision. We present a technique to search for the least expensive fixed-point implementations for a given error bound. The method is practical in real applications and overcomes traditional precision analysis pessimism, as it allows simultaneous selection of multiple word lengths and even some function approximation, primarily based on Taylor series. Starting from real-valued representation, such as Taylor series, we rely on arithmetic transform to explore maximum imprecision by a branch-and-bound search algorithm to investigate imprecision. We also adopt a new tight-bound interval scheme, and derive a precision optimization algorithm that explores multiple precision parameters to get an implementation with smallest area cost.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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