Distributionally robust approximation property of neural networks
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917002008854528 |
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| author | Ceylan, Mihriban Prömel, David J. |
| author_facet | Ceylan, Mihriban Prömel, David J. |
| contents | The universal approximation property uniformly with respect to weakly compact families of measures is established for several classes of neural networks. To that end, we prove that these neural networks are dense in Orlicz spaces, thereby extending classical universal approximation theorems even beyond the traditional $L^p$-setting. The covered classes of neural networks include widely used architectures like feedforward neural networks with non-polynomial activation functions, deep narrow networks with ReLU activation functions and functional input neural networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09177 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distributionally robust approximation property of neural networks Ceylan, Mihriban Prömel, David J. Machine Learning Functional Analysis Probability The universal approximation property uniformly with respect to weakly compact families of measures is established for several classes of neural networks. To that end, we prove that these neural networks are dense in Orlicz spaces, thereby extending classical universal approximation theorems even beyond the traditional $L^p$-setting. The covered classes of neural networks include widely used architectures like feedforward neural networks with non-polynomial activation functions, deep narrow networks with ReLU activation functions and functional input neural networks. |
| title | Distributionally robust approximation property of neural networks |
| topic | Machine Learning Functional Analysis Probability |
| url | https://arxiv.org/abs/2510.09177 |