1. Asymptotic theory of in-context learning by linear attention
- Author
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Lu, Yue M., Letey, Mary I., Zavatone-Veth, Jacob A., Maiti, Anindita, and Pehlevan, Cengiz
- Subjects
Statistics - Machine Learning ,Condensed Matter - Disordered Systems and Neural Networks ,Computer Science - Machine Learning - 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 in-context learning 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., Comment: 20 pages, 5 figures, and supplementary information
- Published
- 2024