This paper explores the phenomenon of weak-to-strong generalization, where a strong model (like GPT-4) trained on weakly labeled data generated by a weaker model (like GPT-2) outperforms the weaker model on the true task. The authors present a theoretical framework to understand this phenomenon, showing that the improvement in performance is quantified by the "misfit error" between the strong and weak models. The misfit error represents the amount of erroneous knowledge that the strong model does not obtain from the weak model. The theory reveals several algorithmic insights, such as predicting the amount of improvement and choosing the best weak model for training the strong model based on its misfit error. The findings are validated through empirical assessments on synthetic and real-world datasets. The paper also discusses the limitations of the current framework and suggests directions for future research, including the extension to classification tasks and larger-scale experiments.This paper explores the phenomenon of weak-to-strong generalization, where a strong model (like GPT-4) trained on weakly labeled data generated by a weaker model (like GPT-2) outperforms the weaker model on the true task. The authors present a theoretical framework to understand this phenomenon, showing that the improvement in performance is quantified by the "misfit error" between the strong and weak models. The misfit error represents the amount of erroneous knowledge that the strong model does not obtain from the weak model. The theory reveals several algorithmic insights, such as predicting the amount of improvement and choosing the best weak model for training the strong model based on its misfit error. The findings are validated through empirical assessments on synthetic and real-world datasets. The paper also discusses the limitations of the current framework and suggests directions for future research, including the extension to classification tasks and larger-scale experiments.