# Frequency Regularization: Restricting Information Redundancy of Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2304.07973 · HTML: https://mlsanity.com/paper/2304.07973/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 52 references that are in the map.
- First posted on arXiv 17 Apr 2023.

## Builds on (most cited first, 30 of 30)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [HRank: Filter Pruning using High-Rank Feature Map](https://mlsanity.com/paper/2002.10179/) (2020)
- [Dynamic Network Surgery for Efficient DNNs](https://mlsanity.com/paper/1608.04493/) (2016)
- [DepGraph: Towards Any Structural Pruning](https://mlsanity.com/paper/2301.12900/) (2023)
- [Learning in the Frequency Domain](https://mlsanity.com/paper/2002.12416/) (2020)
- [Spectral Representations for Convolutional Neural Networks](https://mlsanity.com/paper/1506.03767/) (2015)
- [Frequency-driven Imperceptible Adversarial Attack on Semantic Similarity](https://mlsanity.com/paper/2203.05151/) (2022)
- [TernausNet: U-Net with VGG11 Encoder Pre-Trained on ImageNet for Image Segmentation](https://mlsanity.com/paper/1801.05746/) (2018)
- [Exploring Frequency Adversarial Attacks for Face Forgery Detection](https://mlsanity.com/paper/2203.15674/) (2022)
- [CHEX: CHannel EXploration for CNN Model Compression](https://mlsanity.com/paper/2203.15794/) (2022)
- [Compressing Convolutional Neural Networks](https://mlsanity.com/paper/1506.04449/) (2015)
- [Domain Generalization via Frequency-domain-based Feature Disentanglement and Interaction](https://mlsanity.com/paper/2201.08029/) (2022)
- [DuetFace: Collaborative Privacy-Preserving Face Recognition via Channel Splitting in the Frequency Domain](https://mlsanity.com/paper/2207.07340/) (2022)
- [Object Detection Networks on Convolutional Feature Maps](https://mlsanity.com/paper/1504.06066/) (2015)
- [Band-limited Training and Inference for Convolutional Neural Networks](https://mlsanity.com/paper/1911.09287/) (2019)
- [LC-FDNet: Learned Lossless Image Compression with Frequency Decomposition Network](https://mlsanity.com/paper/2112.06417/) (2021)
- [Rethinking FUN: Frequency-Domain Utilization Networks](https://mlsanity.com/paper/2012.03357/) (2020)
- [EZCrop: Energy-Zoned Channels for Robust Output Pruning](https://mlsanity.com/paper/2105.03679/) (2021)
- [Frequency learning for structured CNN filters with Gaussian fractional derivatives](https://mlsanity.com/paper/2111.06660/) (2021)
- [DCT-Conv: Coding filters in convolutional networks with Discrete Cosine Transform](https://mlsanity.com/paper/2001.08517/) (2020)
- [Transform-Based Feature Map Compression for CNN Inference](https://mlsanity.com/paper/2106.12850/) (2021)
- [Memory-Efficient CNN Accelerator Based on Interlayer Feature Map Compression](https://mlsanity.com/paper/2110.06155/) (2021)
- [Learning-Based Video Coding with Joint Deep Compression and Enhancement](https://mlsanity.com/paper/2111.14474/) (2021)
- [CompConv: A Compact Convolution Module for Efficient Feature Learning](https://mlsanity.com/paper/2106.10486/) (2021)
- [Hybrid Cosine Based Convolutional Neural Networks](https://mlsanity.com/paper/1904.01987/) (2019)
- [Dense Pruning of Pointwise Convolutions in the Frequency Domain](https://mlsanity.com/paper/2109.07707/) (2021)

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

- [Compressed Image Captioning using CNN-based Encoder-Decoder Framework](https://mlsanity.com/paper/2404.18062/) (2024)

## Abstract (arXiv)

Convolutional neural networks have demonstrated impressive results in many computer vision tasks. However, the increasing size of these networks raises concerns about the information overload resulting from the large number of network parameters. In this paper, we propose Frequency Regularization to restrict the non-zero elements of the network parameters in the frequency domain. The proposed approach operates at the tensor level, and can be applied to almost all network architectures. Specifically, the tensors of parameters are maintained in the frequency domain, where high frequency components can be eliminated by zigzag setting tensor elements to zero. Then, the inverse discrete cosine transform (IDCT) is used to reconstruct the spatial tensors for matrix operations during network training. Since high frequency components of images are known to be less critical, a large proportion of these parameters can be set to zero when networks are trained with the proposed frequency regularization. Comprehensive evaluations on various state-of-the-art network architectures, including LeNet, Alexnet, VGG, Resnet, ViT, UNet, GAN, and VAE, demonstrate the effectiveness of the proposed frequency regularization. For a very small accuracy decrease (less than 2%), a LeNet5 with 0.4M parameters can be represented by only 776 float16 numbers (over 1100× reduction), and a UNet with 34M parameters can be represented by only 759 float16 numbers (over 80000× reduction). In particular, the original size of the UNet model is 366MB, we reduce it to 4.5kb.