# Measure theoretic results for approximation by neural networks with limited weights

arXiv: https://arxiv.org/abs/2304.01880 · HTML: https://mlsanity.com/paper/2304.01880/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 34 references that are in the map.
- First posted on arXiv 4 Apr 2023.

## Built on by (most cited first, 2 of 2)

- [Universal approximation with complex-valued deep narrow neural networks](https://mlsanity.com/paper/2305.16910/) (2023)
- [Numerical Approximation Capacity of Neural Networks with Bounded Parameters: Do Limits Exist, and How Can They Be Measured?](https://mlsanity.com/paper/2409.16697/) (2024)

## Abstract (arXiv)

In this paper, we study approximation properties of single hidden layer neural networks with weights varying on finitely many directions and thresholds from an open interval. We obtain a necessary and at the same time sufficient measure theoretic condition for density of such networks in the space of continuous functions. Further, we prove a density result for neural networks with a specifically constructed activation function and a fixed number of neurons.