Optimal In-context Adaptivity and Distributional Robustness of Transformers

We study in-context learning problems where a Transformer is pretrained on tasks drawn from a mixture distribution $π=\sum_{α\in\mathcal{A}} λ_α π_α$, called the pretraining prior, in which each mixture component $π_α$ is a distribution on tasks of a specific difficulty level indexed by $α$. Our goa