Dimensionality reduction and width of deep neural networks based on topological degree theory
Xiao-Song Yang
在本文中,我们提出了一个数学框架,将紧凑的拓扑空间嵌入到欧几里得空间中,并在特定类别的减少尺寸映射下链接嵌入的可分离性。 作为既定理论的应用,我们在深度神经网络的设置中,对深度学习理论中的分类和近似问题提供了一些迷人的见解。
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 specific class of dimension reduction maps. As applications of the established theory, we provide some fascinating insights into classification and approximation problems in deep learning theory in the setting of deep neural networks.
