弱教师也能教会强学生，线性模型中几乎必然发生。
Weak-to-Strong Generalization is Nearly Inevitable (in Linear Models)
- 在线性逻辑回归中，弱教师可指导强学生提升性能。
- 在温和数据假设下，多数师生组合都能实现超越。
- 无需模型容量差异，颠覆传统认知的理论基础。
弱到强泛化是一种后训练现象，即强学生模型仅通过弱教师的反馈进行微调时，不仅能超越教师，还能自我提升。近期研究（Burns 等，2023）在前沿语言模型中验证了该现象，引发大量实证与理论探索。本文证明，在标准线性逻辑回归设置下，只要数据满足轻微分布假设，弱到强泛化就会发生。事实上，对大多数师生组合而言，这种现象近乎必然。值得注意的是，该结果不依赖于学生模型在表达能力或容量上超过教师，这与当前主流理论认为的模型容量不匹配是核心机制的观点相悖。
原文摘要 · Abstract (English)
Weak-to-strong generalization is a phenomenon in post-training whereby a strong student model, when finetuned solely with feedback from a weaker teacher, can not only surpass the teacher, but can improve upon its own capabilities. Recent work of Burns et al. (2023) demonstrated that this can occur in the setting of frontier language models, and subsequently there has been a flurry of both empirical work trying to exploit this phenomenon, as well as theoretical work attempting to understand it. In this work, we demonstrate that weak-to-strong generalization occurs in standard linear logistic regression, under mild distributional assumptions on the data. In fact, we show that this happens for most student-teacher pairs, suggesting that weak-to-strong generalization is in fact \emph{almost inevitable}, even in this basic setting. Notably, our setting does not require the student to be more expressive or have more model capacity in any way compared to the teacher, which runs contrary to the prevailing theoretical belief that a mismatch in model capacity is a central mechanism to weak-to-strong generalization.
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