  Large language models (LLMs) have emerged as powerful tools for many AI
problems and exhibit remarkable in-context learning (ICL) capabilities.
Compositional ability, solving unseen complex tasks that combine two or more
simple tasks, is an essential reasoning ability for Artificial General
Intelligence. Despite LLM's tremendous success, how they approach composite
tasks, especially those not encountered during the pretraining phase, remains
an open question and largely ununderstood. In this study, we delve into the ICL
capabilities of LLMs on composite tasks, with only simple tasks as in-context
examples. We develop a test suite of composite tasks that include linguistic
and logical challenges and perform empirical studies across different LLM
families. We observe that models exhibit divergent behaviors: (1) For simpler
composite tasks that apply distinct mapping mechanisms to different input
segments, the models demonstrate decent compositional ability, while scaling up
the model enhances this ability; (2) for more complex composite tasks that
involving reasoning multiple steps, where each step represent one task, models
typically underperform, and scaling up generally provide no improvements. We
offer theoretical analysis in a simplified setting, explaining that models
exhibit compositional capability when the task handles different input parts
separately. We believe our work sheds new light on the capabilities of LLMs in
solving composite tasks regarding the nature of the tasks and model scale. Our
dataset and code are available at
{\url{https://github.com/OliverXUZY/LLM_Compose}}.
