How Many Pretraining Tasks Are Needed for In-Context Learning of Linear Regression?
This provides theoretical insights into the foundations of in-context learning, which is incremental but clarifies statistical efficiency for researchers in machine learning.
The paper tackles the problem of understanding the statistical requirements for effective in-context learning in transformers by analyzing a simplified linear regression setup, showing that pretraining requires only a small number of tasks and achieves nearly Bayes optimal risk.
Transformers pretrained on diverse tasks exhibit remarkable in-context learning (ICL) capabilities, enabling them to solve unseen tasks solely based on input contexts without adjusting model parameters. In this paper, we study ICL in one of its simplest setups: pretraining a linearly parameterized single-layer linear attention model for linear regression with a Gaussian prior. We establish a statistical task complexity bound for the attention model pretraining, showing that effective pretraining only requires a small number of independent tasks. Furthermore, we prove that the pretrained model closely matches the Bayes optimal algorithm, i.e., optimally tuned ridge regression, by achieving nearly Bayes optimal risk on unseen tasks under a fixed context length. These theoretical findings complement prior experimental research and shed light on the statistical foundations of ICL.