How Many Pretraining Tasks Are Needed for In-Context Learning of Linear Regression?
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914715188330496 |
|---|---|
| author | Wu, Jingfeng Zou, Difan Chen, Zixiang Braverman, Vladimir Gu, Quanquan Bartlett, Peter L. |
| author_facet | Wu, Jingfeng Zou, Difan Chen, Zixiang Braverman, Vladimir Gu, Quanquan Bartlett, Peter L. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_08391 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | How Many Pretraining Tasks Are Needed for In-Context Learning of Linear Regression? Wu, Jingfeng Zou, Difan Chen, Zixiang Braverman, Vladimir Gu, Quanquan Bartlett, Peter L. Machine Learning 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. |
| title | How Many Pretraining Tasks Are Needed for In-Context Learning of Linear Regression? |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2310.08391 |