# Fourier Neural Networks for Function Approximation

arXiv: https://arxiv.org/abs/2111.08438 · HTML: https://mlsanity.com/paper/2111.08438/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 8 references that are in the map.
- First posted on arXiv 21 Oct 2021.

## Builds on (most cited first, 7 of 7)

- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [Benefits of depth in neural networks](https://mlsanity.com/paper/1602.04485/) (2016)
- [Universal Approximation with Deep Narrow Networks](https://mlsanity.com/paper/1905.08539/) (2019)
- [The Power of Depth for Feedforward Neural Networks](https://mlsanity.com/paper/1512.03965/) (2015)
- [Approximating Continuous Functions by ReLU Nets of Minimal Width](https://mlsanity.com/paper/1710.11278/) (2017)
- [Why Deep Neural Networks for Function Approximation?](https://mlsanity.com/paper/1610.04161/) (2016)
- [Are ResNets Provably Better than Linear Predictors?](https://mlsanity.com/paper/1804.06739/) (2018)

## Abstract (arXiv)

The success of Neural networks in providing miraculous results when applied to a wide variety of tasks is astonishing. Insight in the working can be obtained by studying the universal approximation property of neural networks. It is proved extensively that neural networks are universal approximators. Further it is proved that deep Neural networks are better approximators. It is specifically proved that for a narrow neural network to approximate a function which is otherwise implemented by a deep Neural network, the network take exponentially large number of neurons. In this work, we have implemented existing methodologies for a variety of synthetic functions and identified their deficiencies. Further, we examined that Fourier neural network is able to perform fairly good with only two layers in the neural network. A modified Fourier Neural network which has sinusoidal activation and two hidden layer is proposed and the results are tabulated.