# Distributionally robust approximation property of neural networks

arXiv: https://arxiv.org/abs/2510.09177 · HTML: https://mlsanity.com/paper/2510.09177/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 19 references that are in the map.
- First posted on arXiv 10 Oct 2025.

## Builds on (most cited first, 4 of 4)

- [Understanding Deep Neural Networks with Rectified Linear Units](https://mlsanity.com/paper/1611.01491/) (2016)
- [Global universal approximation of functional input maps on weighted spaces](https://mlsanity.com/paper/2306.03303/) (2023)
- [Wasserstein distributional robustness of neural networks](https://mlsanity.com/paper/2306.09844/) (2023)
- [Universal approximation results for neural networks with non-polynomial activation function over non-compact domains](https://mlsanity.com/paper/2410.14759/) (2024)

## Abstract (arXiv)

The universal approximation property uniformly with respect to weakly compact families of measures is established for several classes of neural networks. To that end, we prove that these neural networks are dense in Orlicz spaces, thereby extending classical universal approximation theorems even beyond the traditional Lp-setting. The covered classes of neural networks include widely used architectures like feedforward neural networks with non-polynomial activation functions, deep narrow networks with ReLU activation functions and functional input neural networks.