Large language models (LLMs) can adapt to new tasks through in-context learning (ICL) based on a few examples presented in dialogue history without any model parameter update. Despite such convenience, the performance of ICL heavily depends on the quality of the in-context examples presented, which makes the in-context example selection approach a critical choice. This paper proposes a novel Bayesian in-Context example Selection method (ByCS) for ICL. Extending the inference probability conditioned on in-context examples based on Bayes' theorem, ByCS focuses on the inverse inference conditioned on test input. Following the assumption that accurate inverse inference probability (likelihood) will result in accurate inference probability (posterior), in-context examples are selected based on their inverse inference results. Diverse and extensive cross-tasking and cross-modality experiments are performed with speech, text, and image examples. Experimental results show the efficacy and robustness of our ByCS method on various models, tasks and modalities.

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