Sigma-Delta quantization of sub-Gaussian frame expansions and its\n application to compressed sensing
Bibliographic record
Abstract
Suppose that the collection $\\{e_i\\}_{i=1}^m$ forms a frame for $\\R^k$, where\neach entry of the vector $e_i$ is a sub-Gaussian random variable. We consider\nexpansions in such a frame, which are then quantized using a Sigma-Delta\nscheme. We show that an arbitrary signal in $\\R^k$ can be recovered from its\nquantized frame coefficients up to an error which decays root-exponentially in\nthe oversampling rate $m/k$. Here the quantization scheme is assumed to be\nchosen appropriately depending on the oversampling rate and the quantization\nalphabet can be coarse. The result holds with high probability on the draw of\nthe frame uniformly for all signals. The crux of the argument is a bound on the\nextreme singular values of the product of a deterministic matrix and a\nsub-Gaussian frame. For fine quantization alphabets, we leverage this bound to\nshow polynomial error decay in the context of compressed sensing. Our results\nextend previous results for structured deterministic frame expansions and\nGaussian compressed sensing measurements.\n
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".