Weak-to-Strong Generalization (Burns et al., 2023) is the phenomenon whereby a strong student, say GPT-4, learns a task from a weak teacher, say GPT-2, and ends up significantly outperforming the teacher. We show that this phenomenon does not require a strong and complex learner like GPT-4, nor pre-training. We consider students and teachers that are random feature models, described by two-layer networks with a random and fixed bottom layer and trained top layer. A ‘weak’ teacher, with a small number of units (i.e. random features), is trained on the population, and a ‘strong’ student, with a much larger number of units (i.e. random features), is trained only on labels generated by the weak teacher. We demonstrate, prove and understand, how the student can outperform the teacher, even though trained only on data labeled by the teacher, with no pretraining or other knowledge or data advantage over the teacher. We explain how such weak-to-strong generalization is enabled by early stopping. Importantly, we also show the quantitative limits of weak-to-strong generalization in this model.
Joint work with Marko Medvedev, Kaifeng Lyu, Dingli Yu, Sanjeev Arora and Zhiyuan Li.