Perturbative corrections to stochastic resonant quantizers
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Bibliographic record
Abstract
This communication considers perturbative effects on 2-level and 3-level stochastic resonant (SR) quantizers. Such quantizers are briefly reviewed in the small input signal-to-noise ratio (SNR) limit. First order perturbative corrections to the optimal SNR gain and normalized threshold due to small, non-zero input SNRs and a drift in the noise probability density function (PDF) are derived. The noise PDF is assumed to belong to the family of generalized Gaussians indexed by the parameter p e [1, ∞). For p > 1, it is established that these corrections are: (i) bounded, indicating that SR quantizers are stable to such perturbative effects and (ii) can be evaluated numerically using standard mathematical functions and improper integrals. For p → 1+, the corrections are found to be singular, indicating that regular perturbation theory becomes inapplicable for such PDFs. In the limit of heavy-tailed noise PDFs two important results are as follows: (i) the corrections to the SNR gains of 2-level and 3-level quantizers due to a variation in the PDF are equal; (ii) the correction to the normalized threshold of the 2-level quantizer due to a variation in the PDF vanish, but that of the 3-level quantizer do not, implying that 2-level quantizers are stabler than 3-level quantizers to variations in the PDF.
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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 | 0.000 | 0.000 |
| 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