Universal approximation results for neural networks with non-polynomial activation function over non-compact domains
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913928675590144 |
|---|---|
| author | Neufeld, Ariel Schmocker, Philipp |
| author_facet | Neufeld, Ariel Schmocker, Philipp |
| contents | This paper extends the universal approximation property of single-hidden-layer feedforward neural networks beyond compact domains, which is of particular interest for the approximation within weighted $C^k$-spaces and weighted Sobolev spaces over unbounded domains. More precisely, by assuming that the activation function is non-polynomial, we establish universal approximation results within function spaces defined over non-compact subsets of a Euclidean space, including $L^p$-spaces, weighted $C^k$-spaces, and weighted Sobolev spaces, where the latter two include the approximation of the (weak) derivatives. Moreover, we provide some dimension-independent rates for approximating a function with sufficiently regular and integrable Fourier transform by neural networks with non-polynomial activation function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14759 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal approximation results for neural networks with non-polynomial activation function over non-compact domains Neufeld, Ariel Schmocker, Philipp Machine Learning Neural and Evolutionary Computing Classical Analysis and ODEs This paper extends the universal approximation property of single-hidden-layer feedforward neural networks beyond compact domains, which is of particular interest for the approximation within weighted $C^k$-spaces and weighted Sobolev spaces over unbounded domains. More precisely, by assuming that the activation function is non-polynomial, we establish universal approximation results within function spaces defined over non-compact subsets of a Euclidean space, including $L^p$-spaces, weighted $C^k$-spaces, and weighted Sobolev spaces, where the latter two include the approximation of the (weak) derivatives. Moreover, we provide some dimension-independent rates for approximating a function with sufficiently regular and integrable Fourier transform by neural networks with non-polynomial activation function. |
| title | Universal approximation results for neural networks with non-polynomial activation function over non-compact domains |
| topic | Machine Learning Neural and Evolutionary Computing Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2410.14759 |