Fourier Neural Networks: A Comparative Study
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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.
Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). First posted on arXiv 8 Feb 2019.
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Citing papers per year: 2021: 3; 2022: 3; 2023: 1; 2024: 3; 2025: 4.
14 papers.
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- 2022A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstructioncited by 150
- 2024Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalizationcited by 37
- 2021Fully Learnable Deep Wavelet Transform for Unsupervised Monitoring of High-Frequency Time Seriescited by 29
- 2021Periodic Activation Functions Induce Stationaritycited by 21
- 2024SineKAN: Kolmogorov-Arnold Networks Using Sinusoidal Activation Functionscited by 15
- 2024FAN: Fourier Analysis Networkscited by 12
- 2022Variational Bayes Deep Operator Network: A data-driven Bayesian solver for parametric differential equationscited by 11
- 2021Conditional Generation of Periodic Signals with Fourier-Based Decodercited by 6
- 2022Periodic Extrapolative Generalisation in Neural Networkscited by 3
- 2025Quaternion-Hadamard Network: A Novel Defense Against Adversarial Attacks with a New Datasetcited by 1
- 2025Reasoning is Periodicity? Improving Large Language Models Through Effective Periodicity Modelingcited by 1
- 2023OS-net: Orbitally Stable Neural Networkscited by 0
- 2025Fourier Learning Machines: Nonharmonic Fourier-Based Neural Networks for Scientific Machine Learning10 Sep 2025
- 2025Reasoning is Periodicity? Improving Large Language Models Through Effective Periodicity Modeling28 Feb 2025
- 2025Quaternion-Hadamard Network: A Novel Defense Against Adversarial Attacks with a New Dataset12 Feb 2025
- 2025SigWavNet: Learning Multiresolution Signal Wavelet Network for Speech Emotion Recognition1 Feb 2025
- 2024Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization23 Dec 2024
- 2024FAN: Fourier Analysis Networks3 Oct 2024
- 2024SineKAN: Kolmogorov-Arnold Networks Using Sinusoidal Activation Functions4 Jul 2024
- 2023OS-net: Orbitally Stable Neural Networks26 Sep 2023
- 2022A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction26 Nov 2022
- 2022Periodic Extrapolative Generalisation in Neural Networks21 Sep 2022
- 2022Variational Bayes Deep Operator Network: A data-driven Bayesian solver for parametric differential equations12 Jun 2022
- 2021Periodic Activation Functions Induce Stationarity26 Oct 2021
- 2024Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalizationcited by 37
- 2021Fully Learnable Deep Wavelet Transform for Unsupervised Monitoring of High-Frequency Time Seriescited by 29
- 2021Periodic Activation Functions Induce Stationaritycited by 21
- 2024SineKAN: Kolmogorov-Arnold Networks Using Sinusoidal Activation Functionscited by 15
- 2024FAN: Fourier Analysis Networkscited by 12
- 2022Variational Bayes Deep Operator Network: A data-driven Bayesian solver for parametric differential equationscited by 11
- 2021Conditional Generation of Periodic Signals with Fourier-Based Decodercited by 6
- 2022Periodic Extrapolative Generalisation in Neural Networkscited by 3
- 2025Quaternion-Hadamard Network: A Novel Defense Against Adversarial Attacks with a New Datasetcited by 1
- 2023OS-net: Orbitally Stable Neural Networkscited by 0
- 2025SigWavNet: Learning Multiresolution Signal Wavelet Network for Speech Emotion Recognitioncited by 0
- 2025Fourier Learning Machines: Nonharmonic Fourier-Based Neural Networks for Scientific Machine Learningcited by 0
- 2025Fourier Learning Machines: Nonharmonic Fourier-Based Neural Networks for Scientific Machine Learning10 Sep 2025
- 2025Quaternion-Hadamard Network: A Novel Defense Against Adversarial Attacks with a New Dataset12 Feb 2025
- 2025SigWavNet: Learning Multiresolution Signal Wavelet Network for Speech Emotion Recognition1 Feb 2025
- 2024Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization23 Dec 2024
- 2024FAN: Fourier Analysis Networks3 Oct 2024
- 2024SineKAN: Kolmogorov-Arnold Networks Using Sinusoidal Activation Functions4 Jul 2024
- 2023OS-net: Orbitally Stable Neural Networks26 Sep 2023
- 2022Periodic Extrapolative Generalisation in Neural Networks21 Sep 2022
- 2022Variational Bayes Deep Operator Network: A data-driven Bayesian solver for parametric differential equations12 Jun 2022
- 2021Periodic Activation Functions Induce Stationarity26 Oct 2021
- 2021Conditional Generation of Periodic Signals with Fourier-Based Decoder24 Oct 2021
- 2021Fully Learnable Deep Wavelet Transform for Unsupervised Monitoring of High-Frequency Time Series3 May 2021