Learnability of convolutional neural networks for infinite dimensional input via mixed and anisotropic smoothness

no code implementations • ICLR 2022 • Sho Okumoto, Taiji Suzuki

Although the approximation and estimation errors of neural networks are affected by the curse of dimensionality in the existing analyses for typical function spaces such as the \Holder and Besov spaces, we show that, by considering anisotropic smoothness, they can alleviate exponential dependency on the dimensionality but they only depend on the smoothness of the target functions.

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