Learning curves for deep structured Gaussian feature models*
Why this work is in the frame
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Bibliographic record
Abstract
Abstract In recent years, significant attention in deep learning theory has been devoted to analyzing when models that interpolate their training data can still generalize well to unseen examples. Many insights have been gained from studying models with multiple layers of Gaussian random features, for which one can compute precise generalization asymptotics. However, few works have considered the effect of weight anisotropy; most assume that the random features are generated using independent and identically distributed Gaussian weights, and allow only for structure in the input data. Here, we use the replica trick from statistical physics to derive learning curves for models with many layers of structured Gaussian features. We show that allowing correlations between the rows of the first layer of features can aid generalization, while structure in later layers is generally detrimental. Our results shed light on how weight structure affects generalization in a simple class of solvable models.
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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