Bibliographic record
Abstract
ABSTRACT In this paper, we establish a matrix Freedman inequality for martingales with sub‐Weibull tails. Under conditional control of the increments, the top eigenvalue admits a non‐asymptotic tail bound with explicit, dimension‐aware constants. Via Hermitian dilation, our result extends to rectangular matrices, recovers the sub‐Gaussian case at and admits a time‐uniform (supremum‐over‐time) form. Relative to recent Bennett/Bernstein bounds for sub‐Weibull matrix martingales, our thresholds depend only on a variance proxy and a radius. Concretely, in high‐confidence regimes with , these new thresholds match or improve the corresponding modern envelopes at the same confidence level. We illustrate the utility of our bound in two applications: (i) self‐normalized confidence sets for stochastic linear bandits with heavy‐tailed noise and (ii) operator‐norm error bounds for covariance estimation. We corroborate the theory and highlight constant‐level effects through simulations over a range of tail indices and variance levels.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".