Provable weak-to-strong generalization via benign overfitting

David Xing Wu, Anant Sahai

Keywords: benign overfitting, spiked covariance models, overparameterized models, interpolation, pseudolabeling, weak-to-strong generalization, alignment

TL;DR: We use recent advances in benign overfitting for classification to prove weak-to-strong generalization in a toy setting.

Abstract:

The classic teacher-student model in machine learning posits that a strong teacher supervises a weak student to improve the student's capabilities. We instead consider the inverted situation, where a weak teacher supervises a strong student with imperfect pseudolabels. This paradigm was recently brought forth by \citet{burns2023weak} and termed \emph{weak-to-strong generalization}. We theoretically investigate weak-to-strong generalization for binary and multilabel classification in a stylized overparameterized spiked covariance model with Gaussian covariates where the weak teacher's pseudolabels are asymptotically like random guessing. Under these assumptions, we provably identify two asymptotic phases of the strong student's generalization after weak supervision: (1) successful generalization and (2) random guessing. Our techniques should eventually extend to weak-to-strong multiclass classification. Towards doing so, we prove a tight lower tail inequality for the maximum of correlated Gaussians, which may be of independent interest. Understanding the multilabel setting reinforces the value of using logits for weak supervision when they are available.

Primary Area: learning theory

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Submission Number: 8378