From the 1 of 4 linked papers with an AI index.
4 papers
Minimum Block Width for Universal Approximation by Residual Neural Networks with Inner Width One
Qi Zhou, Xuan Zhou, Xiao-Song Yang
The paper analyzes the minimal block width required for residual neural networks with inner width one to achieve universal function approximation, proving it equals the larger of i…
On the mathematics table problem
Xiao-Song Yang, Xuan Zhou
In this paper we study the mathematical table problem from a geometric-topological point of view. We prove a zero-existence theorem on a cylinder, which gives a new proof of Fenn's…
Relocation of compact sets in by diffeomorphisms and linear separability of datasets in
Xiao-Song Yang, Xuan Zhou, Qi Zhou
Relocation of compact sets in an -dimensional manifold by self-diffeomorphism is of its own interest as well as significant potential applications to data classification in data…
Minimum Width of Deep Narrow Networks for Universal Approximation
Xiao-Song Yang, Qi Zhou, Xuan Zhou
Determining the minimum width of fully connected neural networks has become a fundamental problem in recent theoretical studies of deep neural networks. In this paper, we study the…