4 papers
Minimum Block Width for Universal Approximation by Residual Neural Networks with Inner Width One
Qi Zhou, Xuan Zhou, Xiao-Song Yang
In this paper, we study the universal approximation property of residual neural networks. For input and output dimensions and , and LeakyReLU, ReLU, ReLU-like activation…
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…