  Large language models (LLMs) exhibit remarkable in-context learning (ICL)
capabilities. However, the underlying working mechanism of ICL remains poorly
understood. Recent research presents two conflicting views on ICL: One
attributes it to LLMs' inherent ability of task recognition, deeming label
correctness and shot numbers of demonstrations as not crucial; the other
emphasizes the impact of similar examples in the demonstrations, stressing the
need for label correctness and more shots. In this work, we provide a
Two-Dimensional Coordinate System that unifies both views into a systematic
framework. The framework explains the behavior of ICL through two orthogonal
variables: whether LLMs can recognize the task and whether similar examples are
presented in the demonstrations. We propose the peak inverse rank metric to
detect the task recognition ability of LLMs and study LLMs' reactions to
different definitions of similarity. Based on these, we conduct extensive
experiments to elucidate how ICL functions across each quadrant on multiple
representative classification tasks. Finally, we extend our analyses to
generation tasks, showing that our coordinate system can also be used to
interpret ICL for generation tasks effectively.
