A Theoretical Interpretation of In-Context Learning via Probabilistic Modeling

2026-06-27

AI Summary

This work addresses the lack of a unified modeling framework and rigorous theoretical analysis for in-context learning (ICL). It proposes the first general probabilistic modeling framework grounded in statistical inference and exponential family distribution theory. Within this framework, the authors systematically derive performance bounds for ICL under both general and exponential-family parameter distributions. They further provide a quantitative analysis of how key factors—such as the number of demonstration examples, model parameter sensitivity, and similarity between demonstrations and query inputs—affect ICL effectiveness. By identifying the critical determinants of ICL performance, this study establishes an interpretable theoretical foundation for understanding the contextual learning mechanisms of large language models.

Abstract

In-context learning (ICL) is an emerging paradigm that employs the semantic information inherent in large language models (LLMs) for generating answers to user queries. While the remarkable performance of ICL has been widely known, a general modeling and a rigorous theoretical analysis of this paradigm are still lacking. This work presents a probabilistic model for ICL and derives the performance of ICL for both general parametric distributions and exponential families. Based on the derived results, the work explains the impact of multiple factors such as the number of demonstrations, the sensitivity of the probabilistic model to the variation of its parameters, as well as the similarity between the demonstrations and the query on the performance of ICL.

Problem

• in-context learning
• probabilistic modeling
• theoretical analysis
• large language models
• exponential families

Innovation

• in-context learning
• probabilistic modeling
• theoretical analysis
• large language models
• exponential families