Some density theorems in neural network with variable exponent
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917992209580032 |
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| author | Izuki, Mitsuo Noi, Takahiro Sawano, Yoshihiro Tanaka, Hirokazu |
| author_facet | Izuki, Mitsuo Noi, Takahiro Sawano, Yoshihiro Tanaka, Hirokazu |
| contents | In this paper, we extend several approximation theorems, originally formulated in the context of the standard $L^p$ norm, to the more general framework of variable exponent spaces. Our study is motivated by applications in neural networks, where function approximation plays a crucial role. In addition to these generalizations, we provide alternative proofs for certain well-known results concerning the universal approximation property. In particular, we highlight spaces with variable exponents as illustrative examples, demonstrating the broader applicability of our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14476 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some density theorems in neural network with variable exponent Izuki, Mitsuo Noi, Takahiro Sawano, Yoshihiro Tanaka, Hirokazu Functional Analysis 26A33, 42B35 In this paper, we extend several approximation theorems, originally formulated in the context of the standard $L^p$ norm, to the more general framework of variable exponent spaces. Our study is motivated by applications in neural networks, where function approximation plays a crucial role. In addition to these generalizations, we provide alternative proofs for certain well-known results concerning the universal approximation property. In particular, we highlight spaces with variable exponents as illustrative examples, demonstrating the broader applicability of our approach. |
| title | Some density theorems in neural network with variable exponent |
| topic | Functional Analysis 26A33, 42B35 |
| url | https://arxiv.org/abs/2504.14476 |