# Conditional Generation of Periodic Signals with Fourier-Based Decoder

arXiv: https://arxiv.org/abs/2110.12365 · HTML: https://mlsanity.com/paper/2110.12365/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 39 references that are in the map.
- First posted on arXiv 24 Oct 2021.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Conditional Time Series Forecasting with Convolutional Neural Networks](https://mlsanity.com/paper/1703.04691/) (2017)
- [Neural Networks Fail to Learn Periodic Functions and How to Fix It](https://mlsanity.com/paper/2006.08195/) (2020)
- [T-CGAN: Conditional Generative Adversarial Network for Data Augmentation in Noisy Time Series with Irregular Sampling](https://mlsanity.com/paper/1811.08295/) (2018)
- [Fourier Neural Networks: A Comparative Study](https://mlsanity.com/paper/1902.03011/) (2019)

## Built on by (most cited first, 6 of 6)

- [Confronting Ambiguity in 6D Object Pose Estimation via Score-Based Diffusion on SE(3)](https://mlsanity.com/paper/2305.15873/) (2023)
- [FAN: Fourier Analysis Networks](https://mlsanity.com/paper/2410.02675/) (2024)
- [Deep Generative Models for Physiological Signals: A Systematic Literature Review](https://mlsanity.com/paper/2307.06162/) (2023)
- [Periodic Extrapolative Generalisation in Neural Networks](https://mlsanity.com/paper/2209.10280/) (2022)
- [Imputation of Missing Data in Smooth Pursuit Eye Movements Using a Self-Attention-based Deep Learning Approach](https://mlsanity.com/paper/2506.00545/) (2025)
- [Towards High-Fidelity Gaussian Splatting with Queried-Convolution Neural Networks](https://mlsanity.com/paper/2512.12898/) (2025)

## Abstract (arXiv)

Periodic signals play an important role in daily lives. Although conventional sequential models have shown remarkable success in various fields, they still come short in modeling periodicity; they either collapse, diverge or ignore details. In this paper, we introduce a novel framework inspired by Fourier series to generate periodic signals. We first decompose the given signals into multiple sines and cosines and then conditionally generate periodic signals with the output components. We have shown our model efficacy on three tasks: reconstruction, imputation and conditional generation. Our model outperforms baselines in all tasks and shows more stable and refined results.