Bigger Is Safer: Provable Robustness in In-Context Learning Scales with Capacity

Abstract

In-context learning (ICL) allows large language models to adapt to new tasks from a few examples without updating their parameters. Existing theories explain ICL by assuming the test task distribution matches pretraining -- an assumption that breaks down under adversarial distribution shifts. We introduce a distributionally robust meta-learning framework that provides worst-case guarantees for ICL under Wasserstein-based distribution shifts. Focusing on linear self-attention Transformers, we derive a non-asymptotic bound connecting adversarial perturbation strength ($\ddot{I}$), model capacity ($m$), and the number of in-context examples ($N$). The analysis reveals that the maximum safe perturbation radius scales as $\ddot{I}{}_{\max }\propto \sqrt{m}$, while maintaining performance under adversarial shift requires additional in-context examples with $N_{\ddot{I}}-N_0\propto \ddot{I}{}^2$. Experiments on synthetic tasks confirm these scaling laws, and experiments on 21 real pretrained models (0.1B--7B parameters, 5 families) provide qualitative evidence consistent with the theory's predictions, while revealing that ICL capability is a prerequisite for robustness. These findings advance the theoretical understanding of ICL under adversarial conditions and formalize the sense in which larger models are safer under distributional shift.

27 pages