# Improving Variational Autoencoder using Random Fourier Transformation: An Aviation Safety Anomaly Detection Case-Study

arXiv: https://arxiv.org/abs/2601.01016 · HTML: https://mlsanity.com/paper/2601.01016/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 27 references that are in the map.
- First posted on arXiv 3 Jan 2026.

## Builds on (most cited first, 12 of 12)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [Overview frequency principle/spectral bias in deep learning](https://mlsanity.com/paper/2201.07395/) (2022)
- [Theory of the Frequency Principle for General Deep Neural Networks](https://mlsanity.com/paper/1906.09235/) (2019)
- [Rethinking Positional Encoding](https://mlsanity.com/paper/2107.02561/) (2021)
- [Reproducing Activation Function for Deep Learning](https://mlsanity.com/paper/2101.04844/) (2021)
- [Fourier-basis Functions to Bridge Augmentation Gap: Rethinking Frequency Augmentation in Image Classification](https://mlsanity.com/paper/2403.01944/) (2024)
- [Improved Positional Encoding for Implicit Neural Representation based Compact Data Representation](https://mlsanity.com/paper/2311.06059/) (2023)

## Built on by (most cited first, 1 of 1)

- [Neural Operator-Based Surrogate Model for CFD:Helical Coil Steam Generator in Small Modular Reactor](https://mlsanity.com/paper/2605.30277/) (2026)

## Abstract (arXiv)

In this study, we focus on the training process and inference improvements of deep neural networks (DNNs), specifically Autoencoders (AEs) and Variational Autoencoders (VAEs), using Random Fourier Transformation (RFT). We further explore the role of RFT in model training behavior using Frequency Principle (F-Principle) analysis and show that models with RFT turn to learn low frequency and high frequency at the same time, whereas conventional DNNs start from low frequency and gradually learn (if successful) high-frequency features. We focus on reconstruction-based anomaly detection using autoencoder and variational autoencoder and investigate the RFT's role. We also introduced a trainable variant of RFT that uses the existing computation graph to train the expansion of RFT instead of it being random. We showcase our findings with two low-dimensional synthetic datasets for data representation, and an aviation safety dataset, called Dashlink, for high-dimensional reconstruction-based anomaly detection. The results indicate the superiority of models with Fourier transformation compared to the conventional counterpart and remain inconclusive regarding the benefits of using trainable Fourier transformation in contrast to the Random variant.