Learning Linear Regression with Low-Rank Tasks in-Context
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866911617697972224 |
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| author | Takanami, Kaito Takahashi, Takashi Kabashima, Yoshiyuki |
| author_facet | Takanami, Kaito Takahashi, Takashi Kabashima, Yoshiyuki |
| contents | In-context learning (ICL) is a key building block of modern large language models, yet its theoretical mechanisms remain poorly understood. It is particularly mysterious how ICL operates in real-world applications where tasks have a common structure. In this work, we address this problem by analyzing a linear attention model trained on low-rank regression tasks. Within this setting, we precisely characterize the distribution of predictions and the generalization error in the high-dimensional limit. Moreover, we find that statistical fluctuations in finite pre-training data induce an implicit regularization. Finally, we identify a sharp phase transition of the generalization error governed by task structure. These results provide a framework for understanding how transformers learn to learn the task structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04548 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning Linear Regression with Low-Rank Tasks in-Context Takanami, Kaito Takahashi, Takashi Kabashima, Yoshiyuki Disordered Systems and Neural Networks Machine Learning In-context learning (ICL) is a key building block of modern large language models, yet its theoretical mechanisms remain poorly understood. It is particularly mysterious how ICL operates in real-world applications where tasks have a common structure. In this work, we address this problem by analyzing a linear attention model trained on low-rank regression tasks. Within this setting, we precisely characterize the distribution of predictions and the generalization error in the high-dimensional limit. Moreover, we find that statistical fluctuations in finite pre-training data induce an implicit regularization. Finally, we identify a sharp phase transition of the generalization error governed by task structure. These results provide a framework for understanding how transformers learn to learn the task structure. |
| title | Learning Linear Regression with Low-Rank Tasks in-Context |
| topic | Disordered Systems and Neural Networks Machine Learning |
| url | https://arxiv.org/abs/2510.04548 |