In recent years, pre-trained large language models have demonstrated remarkable efficiency in achieving an inference-time few-shot learning capability known as in-context learning. However, existing literature has highlighted the sensitivity of this capability to the selection of few-shot demonstrations. The underlying mechanisms by which this capability arises from regular language model pretraining objectives remain poorly understood. In this study, we aim to examine the in-context learning phenomenon through a Bayesian lens, viewing large language models as topic models that implicitly infer task-related information from demonstrations. On this premise, we propose an algorithm for selecting optimal demonstrations from a set of annotated data and demonstrate a significant 12.5% improvement relative to the random selection baseline, averaged over eight GPT2 and GPT3 models on eight different real-world text classification datasets. Our empirical findings support our hypothesis that large language models implicitly infer a latent concept variable.

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