An explicit randomized training pipeline is claimed to yield uniform approximators from noisy data with minimax-optimal trainable parameters, but key sample-complexity claims are algebraically reversed and the proof statements are garbled.
Nonlocal techniques for the analysis of deep ReLU neural network approximations
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
Recently, Daubechies, DeVore, Foucart, Hanin, and Petrova introduced a system of piece-wise linear functions, which can be easily reproduced by artificial neural networks with the ReLU activation function and which form a Riesz basis of $L_2([0,1])$. This work was generalized by two of the authors to the multivariate setting. We show that this system serves as a Riesz basis also for Sobolev spaces $W^s([0,1]^d)$ and Barron classes ${\mathbb B}^s([0,1]^d)$ with smoothness $0<s<1$. We apply this fact to re-prove some recent results on the approximation of functions from these classes by deep neural networks. Our proof method avoids using local approximations and allows us to track also the implicit constants as well as to show that we can avoid the curse of dimension. Moreover, we also study how well one can approximate Sobolev and Barron functions by ANNs if only function values are known.
citation-role summary
background 1
citation-polarity summary
fields
stat.ML 1years
2025 1verdicts
REJECT 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data
An explicit randomized training pipeline is claimed to yield uniform approximators from noisy data with minimax-optimal trainable parameters, but key sample-complexity claims are algebraically reversed and the proof statements are garbled.