Towards the Law of Capacity Gap in Distilling Language Models

Language model (LM) distillation aims at distilling the knowledge in a large teacher LM to a small student one. As a critical issue facing LM distillation, a superior student often arises from a teacher of a relatively small scale instead of a larger one, especially in the presence of substantial capacity gap between the teacher and student. This issue, often referred to as the \textit{curse of capacity gap}, suggests that there is likely an optimal teacher yielding the best-performing student along the scaling course of the teacher. Consequently, distillation trials on teachers of a wide range of scales are called for to determine the optimal teacher, which becomes computationally intensive in the context of large LMs (LLMs). This paper addresses this critical bottleneck by providing the \textit{law of capacity gap} inducted from a preliminary study on distilling a broad range of small-scale (<3B) LMs, where the optimal teacher consistently scales linearly with the student scale across different model and data scales. By extending the law to LLM distillation on a larger scale (7B), we succeed in obtaining versatile LLMs that outperform a wide array of competitors.