# Learning Convolutional Neural Networks in the Frequency Domain

arXiv: https://arxiv.org/abs/2204.06718 · HTML: https://mlsanity.com/paper/2204.06718/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 38 references that are in the map.
- First posted on arXiv 14 Apr 2022.

## Builds on (most cited first, 15 of 15)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [High Frequency Component Helps Explain the Generalization of Convolutional Neural Networks](https://mlsanity.com/paper/1905.13545/) (2019)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Training behavior of deep neural network in frequency domain](https://mlsanity.com/paper/1807.01251/) (2018)
- [Fast Algorithms for Convolutional Neural Networks](https://mlsanity.com/paper/1509.09308/) (2015)
- [Fast Training of Convolutional Networks through FFTs](https://mlsanity.com/paper/1312.5851/) (2013)
- [Spectral Representations for Convolutional Neural Networks](https://mlsanity.com/paper/1506.03767/) (2015)
- [Fast Convolutional Nets With fbfft: A GPU Performance Evaluation](https://mlsanity.com/paper/1412.7580/) (2014)
- [On Complex Valued Convolutional Neural Networks](https://mlsanity.com/paper/1602.09046/) (2016)
- [FALCON: A Fourier Transform Based Approach for Fast and Secure Convolutional Neural Network Predictions](https://mlsanity.com/paper/1811.08257/) (2018)
- [Image classification in frequency domain with 2SReLU: a second harmonics superposition activation function](https://mlsanity.com/paper/2006.10853/) (2020)
- [Rethinking FUN: Frequency-Domain Utilization Networks](https://mlsanity.com/paper/2012.03357/) (2020)

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

- [As large as it gets: Learning infinitely large Filters via Neural Implicit Functions in the Fourier Domain](https://mlsanity.com/paper/2307.10001/) (2023)

## Abstract (arXiv)

Convolutional neural network (CNN) has achieved impressive success in computer vision during the past few decades. The image convolution operation helps CNNs to get good performance on image-related tasks. However, the image convolution has high computation complexity and hard to be implemented. This paper proposes the CEMNet, which can be trained in the frequency domain. The most important motivation of this research is that we can use the straightforward element-wise multiplication operation to replace the image convolution in the frequency domain based on the Cross-Correlation Theorem, which obviously reduces the computation complexity. We further introduce a Weight Fixation mechanism to alleviate the problem of over-fitting, and analyze the working behavior of Batch Normalization, Leaky ReLU, and Dropout in the frequency domain to design their counterparts for CEMNet. Also, to deal with complex inputs brought by Discrete Fourier Transform, we design a two-branches network structure for CEMNet. Experimental results imply that CEMNet achieves good performance on MNIST and CIFAR-10 databases.