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).
Deep nonparametric estimation of intrinsic data structures by chart autoencoders: Generalization error and robustness.Applied and Computational Harmonic Analysis, 68:101602
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Tangent-bundle and inverse-consistency penalties derived from observed covariance improve autoencoder learning of nonlinear charts and latent SDEs, reducing radial mean first-passage time errors by 50-70% on embedded surfaces.
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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).
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Geometric regularization of autoencoders via observed stochastic dynamics
Tangent-bundle and inverse-consistency penalties derived from observed covariance improve autoencoder learning of nonlinear charts and latent SDEs, reducing radial mean first-passage time errors by 50-70% on embedded surfaces.