Singular vector distribution of sample covariance matrices
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Bibliographic record
Abstract
Abstract We consider a class of sample covariance matrices of the form Q = TXX * T *, where X = ( x ij ) is an M × N rectangular matrix consisting of independent and identically distributed entries, and T is a deterministic matrix such that T * T is diagonal. Assuming that M is comparable to N , we prove that the distribution of the components of the right singular vectors close to the edge singular values agrees with that of Gaussian ensembles provided the first two moments of x ij coincide with the Gaussian random variables. For the right singular vectors associated with the bulk singular values, the same conclusion holds if the first four moments of x ij match those of the Gaussian random variables. Similar results hold for the left singular vectors if we further assume that T is diagonal.
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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 | 0.001 | 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 it