Deep Neural Networks: A Formulation Via Non-Archimedean Analysis
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912986962067456 |
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| author | Zúñiga-Galindo, W. A. |
| author_facet | Zúñiga-Galindo, W. A. |
| contents | We introduce a new class of deep neural networks (DNNs) with multilayered tree-like architectures. The architectures are codified using numbers from the ring of integers of non-Archimdean local fields. These rings have a natural hierarchical organization as infinite rooted trees. Natural morphisms on these rings allow us to construct finite multilayered architectures. The new DNNs are robust universal approximators of real-valued functions defined on the mentioned rings. We also show that the DNNs are robust universal approximators of real-valued square-integrable functions defined in the unit interval. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_00094 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deep Neural Networks: A Formulation Via Non-Archimedean Analysis Zúñiga-Galindo, W. A. Neural and Evolutionary Computing Artificial Intelligence Machine Learning Primary 68T07, 65D15, Secondary 41A30, 11S85 We introduce a new class of deep neural networks (DNNs) with multilayered tree-like architectures. The architectures are codified using numbers from the ring of integers of non-Archimdean local fields. These rings have a natural hierarchical organization as infinite rooted trees. Natural morphisms on these rings allow us to construct finite multilayered architectures. The new DNNs are robust universal approximators of real-valued functions defined on the mentioned rings. We also show that the DNNs are robust universal approximators of real-valued square-integrable functions defined in the unit interval. |
| title | Deep Neural Networks: A Formulation Via Non-Archimedean Analysis |
| topic | Neural and Evolutionary Computing Artificial Intelligence Machine Learning Primary 68T07, 65D15, Secondary 41A30, 11S85 |
| url | https://arxiv.org/abs/2402.00094 |