Dimensionality reduction and width of deep neural networks based on topological degree theory
This work addresses theoretical challenges in deep learning for researchers, offering foundational mathematical insights that could be incremental in advancing the understanding of neural network properties.
The paper tackles the problem of classification and approximation in deep neural networks by developing a mathematical framework based on topological degree theory for linking embeddings and separability under dimension reduction maps, providing new insights into these areas.
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.