Work

Asymptotic theory of in-context learning by linear attention

Year: 2025

Type: article

Abstract: Transformers have a remarkable ability to learn and execute tasks based on examples provided within the input itself, without explicit prior training. It has been argued that this capability, known as in-context learning (ICL), is a cornerstone of Transformers' success, yet questions about the necessary sample complexity, pretraining task diversity, and context length for successful ICL remain unresolved. Here, we provide a precise answer to these questions in an exactly solvable model of ICL of a linear regression task by linear attention. We derive sharp asymptotics for the learning curve in a phenomenologically rich scaling regime where the token dimension is taken to infinity; the context length and pretraining task diversity scale proportionally with the token dimension; and the number of pretraining examples scales quadratically. We demonstrate a double-descent learning curve with increasing pretraining examples, and uncover a phase transition in the model's behavior between low and high task diversity regimes: in the low diversity regime, the model tends toward memorization of training tasks, whereas in the high diversity regime, it achieves genuine ICL and generalization beyond the scope of pretrained tasks. These theoretical insights are empirically validated through experiments with both linear attention and full nonlinear Transformer architectures.

Source: Proceedings of the National Academy of Sciences

DOI: 10.1073/pnas.2502599122

Authors: Yue M. Lu, Mary Letey, Jacob A. Zavatone-Veth, Anindita Maiti, Cengiz Pehlevan

Institutions: Harvard University, Perimeter Institute

Language: English

Topic: Domain Adaptation and Few-Shot Learning

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid