Understanding Emergent In-Context Learning from a Kernel Regression Perspective

• URL: http://arxiv.org/abs/2305.12766v3
• Date: Fri, 12 Sep 2025 22:18:33 GMT
• Title: Understanding Emergent In-Context Learning from a Kernel Regression Perspective
• Authors: Chi Han, Ziqi Wang, Han Zhao, Heng Ji,
• Abstract summary: Large language models (LLMs) have initiated a paradigm shift in transfer learning.<n>This paper proposes a kernel-regression perspective of understanding LLMs' ICL bahaviors when faced with in-context examples.<n>We find that during ICL, the attention and hidden features in LLMs match the behaviors of a kernel regression.
• Score: 55.95455089638838
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Large language models (LLMs) have initiated a paradigm shift in transfer learning. In contrast to the classic pretraining-then-finetuning procedure, in order to use LLMs for downstream prediction tasks, one only needs to provide a few demonstrations, known as in-context examples, without adding more or updating existing model parameters. This in-context learning (ICL) capability of LLMs is intriguing, and it is not yet fully understood how pretrained LLMs acquire such capabilities. In this paper, we investigate the reason why a transformer-based language model can accomplish in-context learning after pre-training on a general language corpus by proposing a kernel-regression perspective of understanding LLMs' ICL bahaviors when faced with in-context examples. More concretely, we first prove that Bayesian inference on in-context prompts can be asymptotically understood as kernel regression $\hat y = \sum_i y_i K(x, x_i)/\sum_i K(x, x_i)$ as the number of in-context demonstrations grows. Then, we empirically investigate the in-context behaviors of language models. We find that during ICL, the attention and hidden features in LLMs match the behaviors of a kernel regression. Finally, our theory provides insights into multiple phenomena observed in the ICL field: why retrieving demonstrative samples similar to test samples can help, why ICL performance is sensitive to the output formats, and why ICL accuracy benefits from selecting in-distribution and representative samples. Code and resources are publicly available at https://github.com/Glaciohound/Explain-ICL-As-Kernel-Regression.

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