How Does the Pretraining Distribution Shape In-Context Learning? A Fundamental Trade-Off

Waı̈ss Azizian, Ali Hasan
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:4549-4605, 2026.

Abstract

The factors driving the performance of in-context learning (ICL) in large language models (LLMs) remain poorly understood despite ICL’s surprising 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. We develop a theoretical framework that encompasses generalization and task selection and show how distributional properties govern sample efficiency, task retrieval, and robustness. To this end, we generalize existing concentration results to heavy-tailed priors and dependent sequences, better reflecting the structure of LLM pretraining data. Our framework reveals a fundamental design trade-off: heavy-tailed pretraining distributions facilitate robust task selection under distribution shifts but are detrimental to generalization, especially in low-data regimes. We then empirically evaluate our predictions by studying 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-azizian26a, title = {How Does the Pretraining Distribution Shape In-Context Learning? {A} Fundamental Trade-Off}, author = {Azizian, Wa\"{\i}ss and Hasan, Ali}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {4549--4605}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/azizian26a/azizian26a.pdf}, url = {https://proceedings.mlr.press/v306/azizian26a.html}, abstract = {The factors driving the performance of in-context learning (ICL) in large language models (LLMs) remain poorly understood despite ICL’s surprising 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. We develop a theoretical framework that encompasses generalization and task selection and show how distributional properties govern sample efficiency, task retrieval, and robustness. To this end, we generalize existing concentration results to heavy-tailed priors and dependent sequences, better reflecting the structure of LLM pretraining data. Our framework reveals a fundamental design trade-off: heavy-tailed pretraining distributions facilitate robust task selection under distribution shifts but are detrimental to generalization, especially in low-data regimes. We then empirically evaluate our predictions by studying 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.} }
Endnote
%0 Conference Paper %T How Does the Pretraining Distribution Shape In-Context Learning? A Fundamental Trade-Off %A Waı̈ss Azizian %A Ali Hasan %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-azizian26a %I PMLR %P 4549--4605 %U https://proceedings.mlr.press/v306/azizian26a.html %V 306 %X The factors driving the performance of in-context learning (ICL) in large language models (LLMs) remain poorly understood despite ICL’s surprising 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. We develop a theoretical framework that encompasses generalization and task selection and show how distributional properties govern sample efficiency, task retrieval, and robustness. To this end, we generalize existing concentration results to heavy-tailed priors and dependent sequences, better reflecting the structure of LLM pretraining data. Our framework reveals a fundamental design trade-off: heavy-tailed pretraining distributions facilitate robust task selection under distribution shifts but are detrimental to generalization, especially in low-data regimes. We then empirically evaluate our predictions by studying 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.
APA
Azizian, W. & Hasan, A.. (2026). How Does the Pretraining Distribution Shape In-Context Learning? A Fundamental Trade-Off. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:4549-4605 Available from https://proceedings.mlr.press/v306/azizian26a.html.

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