Transformers are Minimax Optimal Nonparametric In-Context Learners

• URL: http://arxiv.org/abs/2408.12186v2
• Date: Wed, 2 Oct 2024 16:58:37 GMT
• Title: Transformers are Minimax Optimal Nonparametric In-Context Learners
• Authors: Juno Kim, Tai Nakamaki, Taiji Suzuki,
• Abstract summary: In-context learning of large language models has proven to be a surprisingly effective method of learning a new task from only a few demonstrative examples. We develop approximation and generalization error bounds for a transformer composed of a deep neural network and one linear attention layer. We show that sufficiently trained transformers can achieve -- and even improve upon -- the minimax optimal estimation risk in context.
• Score: 36.291980654891496
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 study the efficacy of ICL from the viewpoint of statistical learning theory. We develop approximation and generalization error bounds for a transformer 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. 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. Furthermore, we establish information-theoretic lower bounds for meta-learners w.r.t. both the number of tasks and in-context examples. These findings shed light on the roles of task diversity and representation learning for ICL.

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