**Theoretical Analysis of Weak-to-Strong Generalization** This paper presents a theoretical analysis of weak-to-strong generalization, where a strong student model can learn from weaker teacher models. The key phenomena are pseudolabel correction, where the student model performs better than the pseudolabels used for training, and coverage expansion, where the model performs well on examples not covered by the teacher's pseudolabels. Existing weak supervision theory fails to account for these effects, which are crucial for the success of weak supervision. The authors introduce new bounds based on expansion properties of the data distribution and student hypothesis class that directly account for pseudolabel correction and coverage expansion. These bounds capture the intuition that weak-to-strong generalization occurs when the strong model cannot fit the mistakes of the weak teacher without incurring additional error. The expansion properties can be checked from finite data, and empirical evidence shows they hold in practice. The paper also discusses related work, highlighting the limitations of existing bounds in the weak supervision literature. It introduces definitions of expansion and robustness, and provides theoretical bounds for weakly-supervised classifiers. The results show that the error of the student model on the true labels can be bounded based on the error on the weak labels, expansion parameters, and robustness parameters. The authors also present a statistical theory for checking the expansion properties of the population distribution from finite data. This involves estimating the expansion of set families using a neighborhood oracle and empirical data. The results show that expansion is present and correlates with performance in real-world examples. The experiments demonstrate that the proposed bounds and expansion-based theory can differentiate between cases where pseudolabel correction occurs and where it does not. The results also show that the student model has nontrivial performance on the uncovered sets, even when the teacher model is not confident. In conclusion, the paper provides a theoretical foundation for understanding weak-to-strong generalization and offers a framework for encouraging this effect through appropriate neighborhood structures and student hypothesis classes. The results highlight the importance of expansion properties in weak supervision and provide a basis for further research in this area.**Theoretical Analysis of Weak-to-Strong Generalization** This paper presents a theoretical analysis of weak-to-strong generalization, where a strong student model can learn from weaker teacher models. The key phenomena are pseudolabel correction, where the student model performs better than the pseudolabels used for training, and coverage expansion, where the model performs well on examples not covered by the teacher's pseudolabels. Existing weak supervision theory fails to account for these effects, which are crucial for the success of weak supervision. The authors introduce new bounds based on expansion properties of the data distribution and student hypothesis class that directly account for pseudolabel correction and coverage expansion. These bounds capture the intuition that weak-to-strong generalization occurs when the strong model cannot fit the mistakes of the weak teacher without incurring additional error. The expansion properties can be checked from finite data, and empirical evidence shows they hold in practice. The paper also discusses related work, highlighting the limitations of existing bounds in the weak supervision literature. It introduces definitions of expansion and robustness, and provides theoretical bounds for weakly-supervised classifiers. The results show that the error of the student model on the true labels can be bounded based on the error on the weak labels, expansion parameters, and robustness parameters. The authors also present a statistical theory for checking the expansion properties of the population distribution from finite data. This involves estimating the expansion of set families using a neighborhood oracle and empirical data. The results show that expansion is present and correlates with performance in real-world examples. The experiments demonstrate that the proposed bounds and expansion-based theory can differentiate between cases where pseudolabel correction occurs and where it does not. The results also show that the student model has nontrivial performance on the uncovered sets, even when the teacher model is not confident. In conclusion, the paper provides a theoretical foundation for understanding weak-to-strong generalization and offers a framework for encouraging this effect through appropriate neighborhood structures and student hypothesis classes. The results highlight the importance of expansion properties in weak supervision and provide a basis for further research in this area.