How Does the Pretraining Distribution Shape In-Context Learning? Task Selection, Generalization, and Robustness

2025-10-01

AI Summary

Existing theoretical frameworks struggle to characterize the heavy-tailedness and sequential dependencies inherent in real-world pretraining data, limiting our understanding of how pretraining data distribution—particularly its tail behavior and coverage—affects in-context learning (ICL) performance. Method: We propose the first unified theoretical framework that jointly models task selection and generalization, extending Bayesian posterior consistency to heavy-tailed priors and non-i.i.d. sequences. Our analysis integrates statistical learning theory, heavy-tailed distribution modeling, and stochastic differential equations to rigorously study complex numerical tasks. Contribution/Results: We identify key statistical properties—e.g., tail exponent and support coverage—that govern ICL efficacy. Empirically, controlling these properties significantly improves ICL sample efficiency, task retrieval accuracy, and out-of-distribution robustness. This work provides both theoretical foundations and empirical validation for principled, controllable pretraining distribution design.

Technology Category

• Machine Learning: Learning Theory
• Game Theory and Economic Paradigms: Adversarial Learning
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Web Mining and Content Analysis: Large pretrained models with web data
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The emergence of in-context learning (ICL) in large language models (LLMs) remains poorly understood despite its consistent effectiveness, enabling models to adapt to new tasks from only a handful of examples. To clarify and improve these capabilities, we characterize how the statistical properties of the pretraining distribution (e.g., tail behavior, coverage) shape ICL on numerical tasks. We develop a theoretical framework that unifies task selection and generalization, extending and sharpening earlier results, and show how distributional properties govern sample efficiency, task retrieval, and robustness. To this end, we generalize Bayesian posterior consistency and concentration results to heavy-tailed priors and dependent sequences, better reflecting the structure of LLM pretraining data. We then empirically study how ICL performance varies with the pretraining distribution on challenging tasks such as stochastic differential equations and stochastic processes with memory. Together, these findings suggest that controlling key statistical properties of the pretraining distribution is essential for building ICL-capable and reliable LLMs.

Problem

• Characterizing how pretraining distribution properties shape in-context learning
• Developing theoretical framework for task selection and generalization mechanisms
• Studying how distribution properties govern sample efficiency and robustness

Innovation

• Developed theoretical framework for pretraining distribution analysis
• Extended Bayesian methods to heavy-tailed priors
• Empirically studied ICL performance on challenging tasks