Geometric separation and constructive universal approximation with two hidden layers
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908831773097984 |
|---|---|
| author | Sung, Chanyoung |
| author_facet | Sung, Chanyoung |
| contents | We give a geometric construction of neural networks that separate disjoint compact subsets of $\Bbb R^n$, and use it to obtain a constructive universal approximation theorem. Specifically, we show that networks with two hidden layers and either a sigmoidal activation (i.e., strictly monotone bounded continuous) or the ReLU activation can approximate any real-valued continuous function on an arbitrary compact set $K\subset\Bbb R^n$ to any prescribed accuracy in the uniform norm. For finite $K$, the construction simplifies and yields a sharp depth-2 (single hidden layer) approximation result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12482 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometric separation and constructive universal approximation with two hidden layers Sung, Chanyoung Machine Learning Classical Analysis and ODEs 41A46, 68T07, 54D15 We give a geometric construction of neural networks that separate disjoint compact subsets of $\Bbb R^n$, and use it to obtain a constructive universal approximation theorem. Specifically, we show that networks with two hidden layers and either a sigmoidal activation (i.e., strictly monotone bounded continuous) or the ReLU activation can approximate any real-valued continuous function on an arbitrary compact set $K\subset\Bbb R^n$ to any prescribed accuracy in the uniform norm. For finite $K$, the construction simplifies and yields a sharp depth-2 (single hidden layer) approximation result. |
| title | Geometric separation and constructive universal approximation with two hidden layers |
| topic | Machine Learning Classical Analysis and ODEs 41A46, 68T07, 54D15 |
| url | https://arxiv.org/abs/2602.12482 |