揭示Transformer在上下文学习中的泛化边界，发现跨任务泛化弱但同任务内泛化强。

Large language models (LLMs) like GPT-4 and LLaMA-3 utilize the powerful in-context learning (ICL) capability of Transformer architecture to learn on the fly from limited examples. While ICL underpins many LLM applications, its full potential remains hindered by a limited understanding of its generalization boundaries and vulnerabilities. We present a systematic investigation of transformers' generalization capability with ICL relative to training data coverage by defining a task-centric framework along three dimensions: inter-problem, intra-problem, and intra-task generalization. Through extensive simulation and real-world experiments, encompassing tasks such as function fitting, API calling, and translation, we find that transformers lack inter-problem generalization with ICL, but excel in intra-task and intra-problem generalization. When the training data includes a greater variety of mixed tasks, it significantly enhances the generalization ability of ICL on unseen tasks and even on known simple tasks. This guides us in designing training data to maximize the diversity of tasks covered and to combine different tasks whenever possible, rather than solely focusing on the target task for testing.