3 citations · 3 across the 3 of their papers we have counts for
4 papers
On the Dimension-Free Approximation of Deep Neural Networks for Symmetric Korobov Functions
Yulong Lu, Tong Mao, Jinchao Xu +1
Deep neural networks have been widely used as universal approximators for functions with inherent physical structures, including permutation symmetry. In this paper, we construct s…
Generalization Guarantees for Multi-Input Neural Operator Learning in Sobolev Spaces
Yahong Yang, Zecheng Zhang, Wei Zhu +2
We develop approximation and generalization error estimates for multi-input neural operators, with the output error measured in Sobolev norms. In contrast to standard operator-lear…
Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Loss
Yahong Yang, Juncai He
Constructing the architecture of a neural network is a challenging pursuit for the machine learning community, and the dilemma of whether to go deeper or wider remains a persistent…
Deep Neural Networks with General Activations: Super-Convergence in Sobolev Norms
Yahong Yang, Juncai He
This paper establishes a comprehensive approximation result for deep fully-connected neural networks with commonly-used and general activation functions in Sobolev spaces $W^{n,\in…