Transformers perform kernel-based prediction for Hölder regression on manifolds and achieve intrinsic-dimension-dependent minimax rates with sufficient training tasks.
The existence of a length-minimizing geodesic γ : [t, t′] → M between any two points x = γ(t), x′ = γ(t′) is guaranteed by the Hopf–Rinow theorem [Hopf and Rinow, 1931]
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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.