Investigating the Zone of Proximal Development of Language Models for In-Context Learning

In this paper, we introduce a learning analytics framework to analyze the in-context learning (ICL) behavior of large language models (LLMs) through the lens of the Zone of Proximal Development (ZPD), an established theory in educational psychology. ZPD delineates the space between what a learner is capable of doing unsupported and what the learner cannot do even with support. We adapt this concept to ICL, measuring the ZPD of LLMs based on model performance on individual examples with and without ICL. Furthermore, we propose an item response theory (IRT) model to predict the distribution of zones for LLMs. Our findings reveal a series of intricate and multifaceted behaviors of ICL, providing new insights into understanding and leveraging this technique. Finally, we demonstrate how our framework can enhance LLM in both inference and fine-tuning scenarios: (1) By predicting a model's zone of proximal development, we selectively apply ICL to queries that are most likely to benefit from demonstrations, achieving a better balance between inference cost and performance; (2) We propose a human-like curriculum for fine-tuning, which prioritizes examples within the model's ZPD. The curriculum results in improved performance, and we explain its effectiveness through an analysis of the training dynamics of LLMs.