Understanding Emergent In-Context Learning from a Kernel Regression Perspective
This work provides theoretical insights into ICL phenomena for researchers in machine learning and natural language processing, but it is incremental as it builds on existing understanding without introducing a new method.
The paper tackles the problem of understanding how large language models (LLMs) acquire in-context learning (ICL) capabilities by proposing a kernel regression perspective, showing that Bayesian inference on in-context prompts asymptotically behaves like kernel regression and empirically validating this with attention and hidden features in LLMs.
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.