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arXiv · 2504.12991

A Theoretical Framework for OOD Robustness in Transformers using Gevrey Classes

Yu Wang·Fu-Chieh Chang·Pei-Yuan Wu
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Abstract

We study the robustness of Transformer language models under semantic out-of-distribution (OOD) shifts, where training and test data lie in disjoint latent spaces. Using Wasserstein-1 distance and Gevrey-class smoothness, we derive sub-exponential upper bounds on prediction error. Our theoretical framework explains how smoothness governs generalization under distributional drift. We validate these findings through controlled experiments on arithmetic and Chain-of-Thought tasks with latent permutations and scalings. Results show empirical degradation aligns with our bounds, highlighting the geometric and functional principles underlying OOD generalization in Transformers.

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Yu Wang, Fu-Chieh Chang, Pei-Yuan Wu. 2025-05-30. A Theoretical Framework for OOD Robustness in Transformers using Gevrey Classes. https://arxiv.org/abs/2504.12991

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