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…
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…
An RRT* algorithm based on Riemannian metric model for optimal path planning
Yu Zhang, Qi Zhou, Xiao-Song Yang
This paper presents a Riemannian metric-based model to solve the optimal path planning problem on two-dimensional smooth submanifolds in high-dimensional space. Our model is based…