In the era of large language models (LLMs), fine-tuning pretrained models has become ubiquitous. Yet the theoretical underpinning remains an open question. A central question is why only a few epochs of fine-tuning are typically sufficient to achieve strong performance on many different tasks. In this work, we approach this question by developing a statistical framework, combining rigorous early stopping theory with the attention-based Neural Tangent Kernel (NTK) for LLMs, offering new theoretical insights on fine-tuning practices. Specifically, we formally extend classical NTK theory [Jacot et al., 2018] to non-random (i.e., pretrained) initializations and provide a convergence guarantee for attention-based fine-tuning. One key insight provided by the theory is that the convergence rate with respect to sample size is closely linked to the eigenvalue decay rate of the empirical kernel matrix induced by the NTK. We also demonstrate how the framework can be used to explain task vectors for multiple tasks in LLMs. Finally, experiments with modern language models on real-world datasets provide empirical evidence supporting our theoretical insights.

翻译：在大语言模型（LLM）时代，对预训练模型进行微调已成为普遍做法，但其理论基础仍是一个开放性问题。一个核心问题是：为何通常仅需少数几个训练周期（epoch）的微调，即可在许多不同任务上取得强劲性能。本研究通过构建一个统计框架来探讨此问题，该框架将严格的早期停止理论与适用于大语言模型的注意力机制神经正切核（NTK）相结合，从而为微调实践提供了新的理论见解。具体而言，我们正式将经典NTK理论[Jacot et al., 2018]扩展至非随机（即预训练）初始化情形，并为基于注意力机制的微调提供了收敛性保证。该理论提供的一个关键见解是：相对于样本量的收敛速率，与NTK所诱导的经验核矩阵的特征值衰减速率密切相关。我们还展示了如何利用该框架解释大语言模型中多任务的任务向量。最后，基于现代语言模型在真实数据集上的实验，为我们的理论见解提供了实证支持。