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This research establishes a theoretical link between model capacity and safety in in-context learning (ICL), demonstrating that larger models offer provable robustness against adversarial distribution shifts. By deriving scaling laws for perturbation tolerance, the study confirms that increasing parameter count directly expands the safe operating radius of LLMs without updating weights. These findings provide critical mathematical grounding for deploying ICL methods in high-stakes environments where reliability under data drift is essential.
Bigger Is Safer: Provable Robustness in In-Context Learning Scales with Capacity
arXiv:2602.17743v2 Announce Type: replace 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 ($\rho$), model capacity ($m$), and the number of in-context examples ($N$). The analysis reveals that the maximum safe perturbation radius scales as $\rho_{\max} \propto \sqrt{m}$, while maintaining performance under adversarial shift requires additional in-context examples with $N_\rho - N_0 \propto \rho^2$. 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.
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 ($\rho$), model capacity ($m$), and the number of in-context examples ($N$). The analysis reveals that the maximum safe perturbation radius scales as $\rho_{\max} \propto \sqrt{m}$, while maintaining performance under adversarial shift requires additional in-context examples with $N_\rho - N_0 \propto \rho^2$. 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.
Machine Learning (cs.LG); Machine Learning (stat.ML)
I.2.6; G.3; F.2.1
arXiv:2602.17743 [cs.LG]
(or arXiv:2602.17743v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2602.17743 Focus to learn more arXiv-issued DOI via DataCite
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