A model of double descent for high-dimensional binary linear classification
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Bibliographic record
Abstract
Abstract We consider a model for logistic regression where only a subset of features of size $p$ is used for training a linear classifier over $n$ training samples. The classifier is obtained by running gradient descent on logistic loss. For this model, we investigate the dependence of the classification error on the ratio $\kappa =p/n$. First, building on known deterministic results on the implicit bias of gradient descent, we uncover a phase-transition phenomenon for the case of Gaussian features: the classification error of the gradient descent solution is the same as that of the maximum-likelihood solution when $\kappa <\kappa _\star $, and that of the support vector machine when $\kappa>\kappa _\star $, where $\kappa _\star $ is a phase-transition threshold. Next, using the convex Gaussian min–max theorem, we sharply characterize the performance of both the maximum-likelihood and the support vector machine solutions. Combining these results, we obtain curves that explicitly characterize the classification error for varying values of $\kappa $. The numerical results validate the theoretical predictions and unveil double-descent phenomena that complement similar recent findings in linear regression settings as well as empirical observations in more complex learning scenarios.
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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 | 0.000 | 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