# Efficient uniform approximation using Random Vector Functional Link networks

arXiv: https://arxiv.org/abs/2306.17501 · HTML: https://mlsanity.com/paper/2306.17501/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 17 references that are in the map.
- First posted on arXiv 30 Jun 2023.

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

- [Random vector functional link network: recent developments, applications, and future directions](https://mlsanity.com/paper/2203.11316/) (2022)
- [On the Approximation Power of Two-Layer Networks of Random ReLUs](https://mlsanity.com/paper/2102.02336/) (2021)
- [Random Vector Functional Link Networks for Function Approximation on Manifolds](https://mlsanity.com/paper/2007.15776/) (2020)
- [A Corrective View of Neural Networks: Representation, Memorization and Learning](https://mlsanity.com/paper/2002.00274/) (2020)

## Built on by (most cited first, 1 of 1)

- [A Neural Network Algorithm for KL Divergence Estimation with Quantitative Error Bounds](https://mlsanity.com/paper/2510.05386/) (2025)

## Abstract (arXiv)

A Random Vector Functional Link (RVFL) network is a depth-2 neural network with random inner weights and biases. Only the outer weights of such an architecture are to be learned, so the learning process boils down to a linear optimization task, allowing one to sidestep the pitfalls of nonconvex optimization problems. In this paper, we prove that an RVFL with ReLU activation functions can approximate Lipschitz continuous functions in L_∞ norm. To the best of our knowledge, our result is the first approximation result in L_∞ norm using nice inner weights; namely, Gaussians. We give a nonasymptotic lower bound for the number of hidden-layer nodes to achieve a given accuracy with high probability, depending on, among other things, the Lipschitz constant of the target function, the desired accuracy, and the input dimension. Our method of proof is rooted in probability theory and harmonic analysis.