AI RESEARCH
Approximation Theory for Neural Networks: Old and New
arXiv CS.LG
•
ArXi:2605.21451v1 Announce Type: 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 Sobole spaces.