A shallow dense Transformer achieves uniform epsilon-approximation of alpha-Holder functions with O(epsilon^{-d/alpha}) parameters and near-minimax generalization error O(n^{-2alpha/(2alpha+d)} log n).
Optimal approximation of continuous functions by very deep relu networks
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Learning Theory of Transformers: Local-to-Global Approximation via Softmax Partition of Unity
A shallow dense Transformer achieves uniform epsilon-approximation of alpha-Holder functions with O(epsilon^{-d/alpha}) parameters and near-minimax generalization error O(n^{-2alpha/(2alpha+d)} log n).