@inproceedings{
kim2024transformers,
title={Transformers are Minimax Optimal Nonparametric In-Context Learners},
author={Juno Kim and Tai Nakamaki and Taiji Suzuki},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=hF6vatntqc}
}
In-context learning (ICL) of large language models has proven to be a surprisingly effective method of learning a new task from only a few demonstrative examples. In this paper, we shed light on the efficacy of ICL from the viewpoint of statistical learning theory. We develop approximation and generalization error analyses for a transformer model composed of a deep neural network and one linear attention layer, pretrained on nonparametric regression tasks sampled from general function spaces including the Besov space and piecewise $\gamma$-smooth class. In particular, we show that sufficiently trained transformers can achieve -- and even improve upon -- the minimax optimal estimation risk in context by encoding the most relevant basis representations during pretraining. Our analysis extends to high-dimensional or sequential data and distinguishes the \emph{pretraining} and \emph{in-context} generalization gaps, establishing upper and lower bounds w.r.t. both the number of tasks and in-context examples. These findings shed light on the effectiveness of few-shot prompting and the roles of task diversity and representation learning for ICL.
Transformers are Minimax Optimal Nonparametric In-Context Learners
Juno Kim Tai Nakamaki Taiji Suzuki