Transformers perform kernel-based prediction for Hölder regression on manifolds and achieve intrinsic-dimension-dependent minimax rates with sufficient training tasks.
We prove it using a series of concentration inequalities [Hoeffding, 1994, Vershynin, 2018]
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Understanding In-Context Learning on Structured Manifolds: Bridging Attention to Kernel Methods
Transformers perform kernel-based prediction for Hölder regression on manifolds and achieve intrinsic-dimension-dependent minimax rates with sufficient training tasks.