Approximation Theory for Neural Networks: Old and New
Universal approximation theorems provide a mathematical explanation for the expressive power of neural networks. They assert that, under mild conditions on the activation function, feedforward neural networks are dense in broad function classes, such as continuous functions on compact subsets of $\mathbb{R}^d$, $L^p$ spaces, or Sobolev spaces. Over the past four decades, these qualitative universality results have evolved into a rich quantitative theory addressing approximation rates, parameter efficiency, and the role of architectural features such as depth and width. This survey presents several glimpses into this theory. We review classical density results for single-hidden-layer netwo...
| Authors | Soumendu Sundar Mukherjee, Himasish Talukdar |
|---|---|
| Primary category | cs.LG |
| Published | 20 May 2026 |
| Last updated at source | 20 May 2026 |
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