# Fourier Neural Networks: A Comparative Study

arXiv: https://arxiv.org/abs/1902.03011 · HTML: https://mlsanity.com/paper/1902.03011/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2019.

## Built on by (most cited first, 14 of 14)

- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://mlsanity.com/paper/2211.14680/) (2022)
- [Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization](https://mlsanity.com/paper/2412.17739/) (2024)
- [Fully Learnable Deep Wavelet Transform for Unsupervised Monitoring of High-Frequency Time Series](https://mlsanity.com/paper/2105.00899/) (2021)
- [Periodic Activation Functions Induce Stationarity](https://mlsanity.com/paper/2110.13572/) (2021)
- [SineKAN: Kolmogorov-Arnold Networks Using Sinusoidal Activation Functions](https://mlsanity.com/paper/2407.04149/) (2024)
- [FAN: Fourier Analysis Networks](https://mlsanity.com/paper/2410.02675/) (2024)
- [Variational Bayes Deep Operator Network: A data-driven Bayesian solver for parametric differential equations](https://mlsanity.com/paper/2206.05655/) (2022)
- [Conditional Generation of Periodic Signals with Fourier-Based Decoder](https://mlsanity.com/paper/2110.12365/) (2021)
- [Periodic Extrapolative Generalisation in Neural Networks](https://mlsanity.com/paper/2209.10280/) (2022)
- [Reasoning is Periodicity? Improving Large Language Models Through Effective Periodicity Modeling](https://mlsanity.com/paper/2502.21309/) (2025)
- [Quaternion-Hadamard Network: A Novel Defense Against Adversarial Attacks with a New Dataset](https://mlsanity.com/paper/2502.10452/) (2025)
- [OS-net: Orbitally Stable Neural Networks](https://mlsanity.com/paper/2309.14822/) (2023)
- [SigWavNet: Learning Multiresolution Signal Wavelet Network for Speech Emotion Recognition](https://mlsanity.com/paper/2502.00310/) (2025)
- [Fourier Learning Machines: Nonharmonic Fourier-Based Neural Networks for Scientific Machine Learning](https://mlsanity.com/paper/2509.08759/) (2025)

## Abstract (arXiv)

We review neural network architectures which were motivated by Fourier series and integrals and which are referred to as Fourier neural networks. These networks are empirically evaluated in synthetic and real-world tasks. Neither of them outperforms the standard neural network with sigmoid activation function in the real-world tasks. All neural networks, both Fourier and the standard one, empirically demonstrate lower approximation error than the truncated Fourier series when it comes to an approximation of a known function of multiple variables.