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Dimensionality reduction and width of deep neural networks based on topological degree theory
Xiao-Song Yang
https://arxiv.org/abs/2511.06821 https://arxiv.org/pdf/2511.06821 https://arxiv.org/html/2511.06821
arXiv:2511.06821v1 Announce Type: new
Abstract: 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.
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A general framework for adaptive nonparametric dimensionality reduction
Antonio Di Noia, Federico Ravenda, Antonietta Mira
https://arxiv.org/abs/2511.09486 https://