Sobolev duals of random frames
Bibliographic record
Abstract
Sobolev dual frames have recently been proposed as optimal alternative reconstruction operators that are specifically tailored for Sigma-Delta (¿¿) quantization of frame coefficients. While the canonical dual frame of a given analysis (sampling) frame is optimal for the white-noise type quantization error of Pulse Code Modulation (PCM), the Sobolev dual offers significant reduction of the reconstruction error for the colored-noise of ¿¿ quantization. However, initial quantitative results concerning the use of Sobolev dual frames required certain regularity assumptions on the given analysis frame in order to deduce improvements of performance on reconstruction that are similar to those achieved in the standard setting of bandlimited functions. In this paper, we show that these regularity assumptions can be lifted for (Gaussian) random frames with high probability on the choice of the analysis frame. Our results are immediately applicable in the traditional oversampled (coarse) quantization scenario, but also extend to compressive sampling of sparse signals.
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How this classification was reachedexpand
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 | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".