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In-Context Learning (ICL) ability has been found efficient across a wide range of applications, where the Large Language Models (LLM) learn to complete the tasks from the examples in the prompt without tuning the parameters. In this work, we conduct a comprehensive study to understand ICL from a statistical perspective. First, we show that the perfectly pretrained LLMs perform Bayesian Model Averaging (BMA) for ICL under a dynamic model of examples in the prompt. The average error analysis for ICL is then built for the perfectly pretrained LLMs with the analysis of BMA. Second, we demonstrate how the attention structure boosts the BMA implementation. With sufficient examples in the prompt, attention is proven to perform BMA under the Gaussian linear ICL model, which also motivates the explicit construction of the hidden concepts from the attention heads' values. Finally, we analyze the pretraining behavior of LLMs. The pretraining error is decomposed as the generalization error and the approximation error. The generalization error is upper bounded via the PAC-Bayes framework. Then the ICL average error of the pretrained LLMs is shown to be the sum of O(T^{-1}) and the pretraining error. In addition, we analyze the ICL performance of the pretrained LLMs with misspecified examples.
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Dual Operating Modes of In-Context Learning
In-context learning (ICL) exhibits dual operating modes: task learning, i.e., acquiring a new skill from in-context samples, and task retrieval, i.e., locating and activating a relevant pretrained skill. Recent theoretical work proposes various mathematical models to analyze ICL, but they cannot fully explain the duality. In this work, we analyze a generalized probabilistic model for pretraining data, obtaining a quantitative understanding of the two operating modes of ICL. Leveraging our analysis, we provide the first explanation of an unexplained phenomenon observed with real-world large language models (LLMs). Under some settings, the ICL risk initially increases and then decreases with more in-context examples. Our analysis offers a plausible explanation for this "early ascent" phenomenon: a limited number of in-context samples may lead to the retrieval of an incorrect skill, thereby increasing the risk, which will eventually diminish as task learning takes effect with more in-context samples. We also analyze ICL with biased labels, e.g., zero-shot ICL, where in-context examples are assigned random labels, and predict the bounded efficacy of such approaches. We corroborate our analysis and predictions with extensive experiments with Transformers and LLMs.
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- Award ID(s):
- 2339978
- PAR ID:
- 10596472
- Publisher / Repository:
- Proceedings of the 41st International Conference on Machine Learning
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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