$\mathcal{C}^1$-approximation with rational functions and rational neural networks
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916920899403776 |
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| author | Morina, Erion Holler, Martin |
| author_facet | Morina, Erion Holler, Martin |
| contents | We show that suitably regular functions can be approximated in the $\mathcal{C}^1$-norm both with rational functions and rational neural networks, including approximation rates with respect to width and depth of the network, and degree of the rational functions. As consequence of our results, we further obtain $\mathcal{C}^1$-approximation results for rational neural networks with the $\text{EQL}^÷$ and ParFam architecture, both of which are important in particular in the context of symbolic regression for physical law learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19672 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathcal{C}^1$-approximation with rational functions and rational neural networks Morina, Erion Holler, Martin Machine Learning Information Theory Numerical Analysis 33F05, 41A20, 41A25, 26C15 We show that suitably regular functions can be approximated in the $\mathcal{C}^1$-norm both with rational functions and rational neural networks, including approximation rates with respect to width and depth of the network, and degree of the rational functions. As consequence of our results, we further obtain $\mathcal{C}^1$-approximation results for rational neural networks with the $\text{EQL}^÷$ and ParFam architecture, both of which are important in particular in the context of symbolic regression for physical law learning. |
| title | $\mathcal{C}^1$-approximation with rational functions and rational neural networks |
| topic | Machine Learning Information Theory Numerical Analysis 33F05, 41A20, 41A25, 26C15 |
| url | https://arxiv.org/abs/2508.19672 |