Explicit C2-smooth approximate Kolmogorov superpositions are constructed via translated dilated inner functions and piecewise C2 outer interpolation, achieving N^{-alpha} accuracy for alpha-Holder functions.
The optimal linear b-splines approximation via kolmogorov super- position theorem and its application
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Transformers achieve approximation and generalization error bounds for noisy manifold regression that scale with the intrinsic dimension of the task-level manifold.
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Explicit Construction of Approximate Kolmogorov Superpositions with C2 Smoothness
Explicit C2-smooth approximate Kolmogorov superpositions are constructed via translated dilated inner functions and piecewise C2 outer interpolation, achieving N^{-alpha} accuracy for alpha-Holder functions.
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Transformers for Learning on Noisy and Task-Level Manifolds: Approximation and Generalization Insights
Transformers achieve approximation and generalization error bounds for noisy manifold regression that scale with the intrinsic dimension of the task-level manifold.