Universal approximation theorem for neural networks with inputs from a topological vector space
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913508393746432 |
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| author | Ismailov, Vugar |
| author_facet | Ismailov, Vugar |
| contents | We study feedforward neural networks with inputs from a topological vector space (TVS-FNNs). Unlike traditional feedforward neural networks, TVS-FNNs can process a broader range of inputs, including sequences, matrices, functions and more. We prove a universal approximation theorem for TVS-FNNs, which demonstrates their capacity to approximate any continuous function defined on this expanded input space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12913 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal approximation theorem for neural networks with inputs from a topological vector space Ismailov, Vugar Machine Learning Neural and Evolutionary Computing 41A30, 41A65, 68T05 We study feedforward neural networks with inputs from a topological vector space (TVS-FNNs). Unlike traditional feedforward neural networks, TVS-FNNs can process a broader range of inputs, including sequences, matrices, functions and more. We prove a universal approximation theorem for TVS-FNNs, which demonstrates their capacity to approximate any continuous function defined on this expanded input space. |
| title | Universal approximation theorem for neural networks with inputs from a topological vector space |
| topic | Machine Learning Neural and Evolutionary Computing 41A30, 41A65, 68T05 |
| url | https://arxiv.org/abs/2409.12913 |