Asymptotic Minimax Bounds for Stochastic Deconvolution Over Groups
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
This paper examines stochastic deconvolution over noncommutative compact Lie groups. This involves Fourier analysis on compact Lie groups as well as convolution products over such groups. An observation process consisting of a known impulse response function convolved with an unknown signal with additive white noise is assumed. Data collected through the observation process then allow us to construct an estimator of the signal. Signal recovery is then assessed through integrated mean squared error for which the main results show that asymptotic minimaxity depends on smoothness properties of the impulse response function. Thus, if the Fourier transform of the impulse response function is bounded polynomially, then the asymptotic minimax signal recovery is polynomial, while if the Fourier transform of the impulse response function is exponentially bounded, then the asymptotic minimax signal recovery is logarithmic. Such investigations have been previously considered in both the engineering and statistics literature with applications in among others, medical imaging, robotics, and polymer science.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 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) | 0.001 | 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