Statistics of the Synchrosqueezing Transform
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We investigate the synchrosqueezing transform applied to complex gaussian white noise, as well as signals consisting of a single harmonic component contaminated with complex gaussian white noise. First, this involves analyzing the reassignment rule, which is built from a quotient of improper, correlated complex gaussians. We provide a new formula for the general density of said quotient and use this to carefully clarify the decay rate of the covariance of the reassignment rule. Next, for a fixed time $t$, we analyze the synchrosqueezing integrand $Y_{\alpha,\eta}$ at different frequencies $\eta$ and resolutions $\alpha$. A detailed asymptotic analysis of the covariance between $Y_{\alpha,\eta}$ and $Y_{\alpha,\eta'}$ is provided. By appealing to an $M$-dependent approximation argument, we obtain a central-limit theorem for the synchrosqueezing transform at time $t=0$ and fixed frequency $\xi$ and give an interpretation within the context of kernel regression. Finally, we provide a number of open problems whose resolution may lend themselves to further results in the vein of this work.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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