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.

We propose a variational autoencoder (VAE)-based model for building forward and inverse structure-property linkages, a problem of paramount importance in computational materials science. Our model systematically combines VAE with regression, linking the two models through a two-level prior conditioned on the regression variables. The regression loss is optimized jointly with the reconstruction loss of the variational autoencoder, learning microstructure features relevant for property prediction and reconstruction. The resultant model can be used for both forward and inverse prediction i.e., for predicting the properties of a given microstructure as well as for predicting the microstructure required to obtain given properties. Since the inverse problem is ill-posed (one-to-many), we derive the objective function using a multi-modal Gaussian mixture prior enabling the model to infer multiple microstructures for a target set of properties. We show that for forward prediction, our model is as accurate as state-of-the-art forward-only models. Additionally, our method enables direct inverse inference. We show that the microstructures inferred using our model achieve desired properties reasonably accurately, avoiding the need for expensive optimization loops.