# Frequency Pooling: Shift-Equivalent and Anti-Aliasing Downsampling

arXiv: https://arxiv.org/abs/2109.11839 · HTML: https://mlsanity.com/paper/2109.11839/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 28 references that are in the map.
- First posted on arXiv 24 Sep 2021.

## Builds on (most cited first, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Spatial Pyramid Pooling in Deep Convolutional Networks for Visual Recognition](https://mlsanity.com/paper/1406.4729/) (2014)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Making Convolutional Networks Shift-Invariant Again](https://mlsanity.com/paper/1904.11486/) (2019)
- [Semi-Supervised Learning with Ladder Networks](https://mlsanity.com/paper/1507.02672/) (2015)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Why do deep convolutional networks generalize so poorly to small image transformations?](https://mlsanity.com/paper/1805.12177/) (2018)
- [Comparative Study of CNN and RNN for Natural Language Processing](https://mlsanity.com/paper/1702.01923/) (2017)
- [Exploring the Landscape of Spatial Robustness](https://mlsanity.com/paper/1712.02779/) (2017)
- [Generalizing Pooling Functions in Convolutional Neural Networks: Mixed, Gated, and Tree](https://mlsanity.com/paper/1509.08985/) (2015)
- [Fractional Max-Pooling](https://mlsanity.com/paper/1412.6071/) (2014)

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

- [Group Downsampling with Equivariant Anti-aliasing](https://mlsanity.com/paper/2504.17258/) (2025)

## Abstract (arXiv)

Convolution utilizes a shift-equivalent prior of images, thus leading to great success in image processing tasks. However, commonly used poolings in convolutional neural networks (CNNs), such as max-pooling, average-pooling, and strided-convolution, are not shift-equivalent. Thus, the shift-equivalence of CNNs is destroyed when convolutions and poolings are stacked. Moreover, anti-aliasing is another essential property of poolings from the perspective of signal processing. However, recent poolings are neither shift-equivalent nor anti-aliasing. To address this issue, we propose a new pooling method that is shift-equivalent and anti-aliasing, named frequency pooling. Frequency pooling first transforms the features into the frequency domain, and then removes the frequency components beyond the Nyquist frequency. Finally, it transforms the features back to the spatial domain. We prove that frequency pooling is shift-equivalent and anti-aliasing based on the property of Fourier transform and Nyquist frequency. Experiments on image classification show that frequency pooling improves accuracy and robustness with respect to the shifts of CNNs.