Sharpened Generalization Bounds based on Conditional Mutual Information and an Application to Noisy, Iterative Algorithms
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Bibliographic record
Abstract
The information-theoretic framework of Russo and J. Zou (2016) and Xu and Raginsky (2017) provides bounds on the generalization error of a learning algorithm in terms of the mutual information between the algorithm's output and the training sample. In this work, we study the proposal, by Steinke and Zakynthinou (2020), to reason about the generalization error of a learning algorithm by introducing a super that contains the training as a random subset and computing mutual information conditional on the super sample. We first show that these new bounds based on the conditional mutual information are tighter than those based on the unconditional mutual information. We then introduce yet tighter bounds, building on the individual sample idea of Bu, S. Zou, and Veeravalli (2019) and the data dependent ideas of Negrea et al. (2019), using disintegrated mutual information. Finally, we apply these bounds to the study of Langevin dynamics algorithm, showing that conditioning on the super allows us to exploit information in the optimization trajectory to obtain tighter bounds based on hypothesis tests.
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.002 | 0.009 |
| 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