Dimensionality reduction and width of deep neural networks based on topological degree theory
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909895638384640 |
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| author | Yang, Xiao-Song |
| author_facet | Yang, Xiao-Song |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06821 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimensionality reduction and width of deep neural networks based on topological degree theory Yang, Xiao-Song General Topology Machine Learning 55P99, 68T01, 68T07 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. |
| title | Dimensionality reduction and width of deep neural networks based on topological degree theory |
| topic | General Topology Machine Learning 55P99, 68T01, 68T07 |
| url | https://arxiv.org/abs/2511.06821 |