On Weighted Cross-Entropy for Label-Imbalanced Separable Data: An Algorithmic-Stability Study
Bibliographic record
Abstract
Implicit bias theory characterizes notions of simplicity in the weights learned by gradient descent when training without explicit regularization beyond zero training error, and has served as a cornerstone result for theoretically justifying good generalization of interpolating models. However, its asymptotic nature (in number of gradient steps) limits its practical relevance. This motivates developing finite-time generalization bounds. Specifically, recent works have proposed bounding the generalization error indirectly by controlling the corresponding test loss via the algorithmic-stability framework. Concretely, for cross-entropy (CE) training on separable balanced data, they show that the CE test loss decays as fast (up to logarithmic factors) as the test error. In this paper, we study generalization under label imbalances. Motivated by our empirical observation that weighted CE (wCE) can significantly outperform the max-margin classifier at early training phases, we ask whether the stability framework can prove this early-stopping result. To this end, we extend the analysis to the imbalanced setting and bound the test loss of wCE. For Gaussian mixtures, we show this bound is orderwise the same as the balanced error of the max-margin classifier, suggesting the test loss might not be a good proxy of balanced error for wCE under imbalances. We further support this conjecture with empirical results.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 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".