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This work develops a theoretical framework for characterizing the approximation and generalization errors of transformer-based operator learning, and derives a universal approximation error of transformer-based operator learning for H\"older-regular operators".
This work characterize task-space complexity through covering numbers under a prescribed metric, thereby quantifying the low-dimensional cross-task structure without requiring an explicit parametric representation and explicitly construct a Transformer that exploits their low-dimensional structure to perform ICL.
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