# Neural networks with superexpressive activations and integer weights

arXiv: https://arxiv.org/abs/2105.09917 · HTML: https://mlsanity.com/paper/2105.09917/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 7 references that are in the map.
- First posted on arXiv 20 May 2021.

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

- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Elementary superexpressive activations](https://mlsanity.com/paper/2102.10911/) (2021)
- [Statistical Guarantees for Regularized Neural Networks](https://mlsanity.com/paper/2006.00294/) (2020)
- [Function approximation by deep neural networks with parameters 0,± frac12, ± 1, 2](https://mlsanity.com/paper/2103.08659/) (2021)

## Built on by (most cited first, 3 of 3)

- [Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer](https://mlsanity.com/paper/2201.13094/) (2022)
- [Do ReLU Networks Have An Edge When Approximating Compactly-Supported Functions?](https://mlsanity.com/paper/2204.11231/) (2022)
- [On Explicit Super-Expressive Approximation for Neural Networks](https://mlsanity.com/paper/2607.06781/) (2026)

## Abstract (arXiv)

An example of an activation function σ is given such that networks with activations σ, lfloor·rfloor, integer weights and a fixed architecture depending on d approximate continuous functions on [0,1]d. The range of integer weights required for varepsilon-approximation of H"older continuous functions is derived, which leads to a convergence rate of order n^frac-2β2β+dlog2n for neural network regression estimation of unknown β-H"older continuous function with given n samples.