Compositional generalization--understanding unseen combinations of seen primitives--is an essential reasoning capability in human intelligence. The AI community mainly studies this capability by fine-tuning neural networks on lots of training samples, while it is still unclear whether and how in-context learning--the prevailing few-shot paradigm based on large language models--exhibits compositional generalization. In this paper, we present CoFe, a test suite to investigate in-context compositional generalization. We find that the compositional generalization performance can be easily affected by the selection of in-context examples, thus raising the research question what the key factors are to make good in-context examples for compositional generalization. We study three potential factors: similarity, diversity and complexity. Our systematic experiments indicate that in-context examples should be structurally similar to the test case, diverse from each other, and individually simple. Furthermore, two strong limitations are observed: in-context compositional generalization on fictional words is much weaker than that on commonly used ones; it is still critical that the in-context examples should cover required linguistic structures, even though the backbone model has been pre-trained on large corpus. We hope our analysis would facilitate the understanding and utilization of in-context learning paradigm.

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