Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Loss

no code implementations • 31 Jan 2024 • 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 question.

Optimal Deep Neural Network Approximation for Korobov Functions with respect to Sobolev Norms

no code implementations • 8 Nov 2023 • Yahong Yang, Yulong Lu

This paper establishes the nearly optimal rate of approximation for deep neural networks (DNNs) when applied to Korobov functions, effectively overcoming the curse of dimensionality.

Homotopy Relaxation Training Algorithms for Infinite-Width Two-Layer ReLU Neural Networks

no code implementations • 26 Sep 2023 • Yahong Yang, Qipin Chen, Wenrui Hao

In this paper, we present a novel training approach called the Homotopy Relaxation Training Algorithm (HRTA), aimed at accelerating the training process in contrast to traditional methods.

Approximation of Functionals by Neural Network without Curse of Dimensionality

no code implementations • 28 May 2022 • Yahong Yang, Yang Xiang

In this paper, we establish a neural network to approximate functionals, which are maps from infinite dimensional spaces to finite dimensional spaces.