Fast Test Error Rates for Gradient-Based Algorithms on Separable Data
Bibliographic record
Abstract
In recent research aimed at understanding the strong generalization performance of simple gradient-based methods on overparameterized models, it has been demonstrated that when training a linear predictor on separable data with an exponentially-tailed loss function, the predictor converges towards the max-margin classifier direction, explaining its resistance to overfitting asymptotically. Moreover, recent findings have shown that overfitting is not a concern even in finite-time scenarios (non-asymptotically), as finite-time generalization bounds have been derived for gradient flow, gradient descent (GD), and stochastic GD. In this work, we extend this line of research and obtain new finite-time generalization bounds for other popular first-order methods, namely normalized GD and Nesterov’s accelerated GD. Our results reveal that these methods, as they converge more rapidly in terms of training loss, also exhibit enhanced generalization performance in terms of test error.
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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) | 0.000 | 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 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".