6 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…
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…
Dimensionality reduction and width of deep neural networks based on topological degree theory
Xiao-Song Yang
In this paper we present a mathematical framework on linking of embeddings of compact topological spaces into Euclidean spaces and separability of linked embeddings under a specifi…
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…
RM-Dijkstra: A surface optimal path planning algorithm based on Riemannian metric
Yu Zhang, Xiao-Song Yang
The Dijkstra algorithm is a classic path planning method, which operates in a discrete graph space to determine the shortest path from a specified source point to a target node or…