Weak-to-Strong Generalization via Bregman Bias–Variance Decomposition

Weak-to-strong generalization (W2SG) is the phenomenon in which a powerful student model, trained on labels produced by a weaker teacher, ultimately outperforms the teacher on the target task. In this work, we theoretically investigate how W2SG can arise via a generalized bias–variance decomposition under Bregman divergence. We show that the expected population risk gap between the student and the teacher is characterized by the expected misfit between the two models. Unlike earlier misfit-based analyses, our theory removes several restrictive assumptions, e.g., it does not require the student hypothesis class to be convex. Our results indicate that W2SG is more likely when the student effectively approximates the teacher's posterior mean. Specializing to squared loss, we provide a sufficient condition (illustrated through a concrete example) under which the student converges to its posterior mean teacher; in particular, increasing the student model size can ensure this convergence. For cross-entropy loss, our analysis further suggests that lowering the entropy of the student's predictive distribution can promote W2SG. We also find that the reverse cross-entropy, unlike the standard forward cross-entropy, is less sensitive to the teacher's predictive uncertainty. Finally, we verify these theoretical insights empirically and demonstrate that incorporating reverse cross-entropy consistently improves student performance.

Superalignment asks how humans can guide AI systems that may become much more capable than humans. Weak-to-strong generalization provides a simplified analogy of this problem by asking whether a strong model can learn from a weaker model and eventually outperform it. We study when this kind of improvement can happen. Our work suggests that the strong model should not simply imitate one teacher, but should instead learn from the common signal behind weak supervision. We also find that larger and more confident student models are more likely to achieve weak-to-strong generalization. In addition, our analysis suggests that training should account for how confident the weak model is, rather than treating all weak labels as equally reliable. These insights help explain when weak supervision can still lead to stronger AI systems. They also lead to an algorithmic improvement that consistently enhances student performance in our experiments.