# LiftPool: Bidirectional ConvNet Pooling

arXiv: https://arxiv.org/abs/2104.00996 · HTML: https://mlsanity.com/paper/2104.00996/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 42 references that are in the map.
- First posted on arXiv 2 Apr 2021.

## Builds on (most cited first, 22 of 22)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation](https://mlsanity.com/paper/1511.00561/) (2015)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [Making Convolutional Networks Shift-Invariant Again](https://mlsanity.com/paper/1904.11486/) (2019)
- [i-RevNet: Deep Invertible Networks](https://mlsanity.com/paper/1802.07088/) (2018)
- [Benchmarking Neural Network Robustness to Common Corruptions and Surface Variations](https://mlsanity.com/paper/1807.01697/) (2018)
- [Spectral Representations for Convolutional Neural Networks](https://mlsanity.com/paper/1506.03767/) (2015)
- [Semi-Supervised Learning with Normalizing Flows](https://mlsanity.com/paper/1912.13025/) (2019)
- [Stochastic Pooling for Regularization of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1301.3557/) (2013)
- [Generalizing Pooling Functions in Convolutional Neural Networks: Mixed, Gated, and Tree](https://mlsanity.com/paper/1509.08985/) (2015)
- [Pixelated Semantic Colorization](https://mlsanity.com/paper/1901.10889/) (2019)
- [Detail-Preserving Pooling in Deep Networks](https://mlsanity.com/paper/1804.04076/) (2018)
- [S3Pool: Pooling with Stochastic Spatial Sampling](https://mlsanity.com/paper/1611.05138/) (2016)
- [Deep Adaptive Wavelet Network](https://mlsanity.com/paper/1912.05035/) (2019)
- [Semi-Conditional Normalizing Flows for Semi-Supervised Learning](https://mlsanity.com/paper/1905.00505/) (2019)

## Built on by (most cited first, 11 of 11)

- [AdaPool: Exponential Adaptive Pooling for Information-Retaining Downsampling](https://mlsanity.com/paper/2111.00772/) (2021)
- [Temporal Lift Pooling for Continuous Sign Language Recognition](https://mlsanity.com/paper/2207.08734/) (2022)
- [Learnable Discrete Wavelet Pooling (LDW-Pooling) For Convolutional Networks](https://mlsanity.com/paper/2109.06638/) (2021)
- [NOAH: Learning Pairwise Object Category Attentions for Image Classification](https://mlsanity.com/paper/2402.02377/) (2024)
- [Hierarchical Spherical CNNs with Lifting-based Adaptive Wavelets for Pooling and Unpooling](https://mlsanity.com/paper/2205.15571/) (2022)
- [Progressive Meta-Pooling Learning for Lightweight Image Classification Model](https://mlsanity.com/paper/2301.10038/) (2023)
- [Local and Global Context-and-Object-part-Aware Superpixel-based Data Augmentation for Deep Visual Recognition](https://mlsanity.com/paper/2512.00130/) (2025)
- [A Novel Dual-pooling Attention Module for UAV Vehicle Re-identification](https://mlsanity.com/paper/2306.14104/) (2023)
- [Dual-View Pyramid Pooling in Deep Neural Networks for Improved Medical Image Classification and Confidence Calibration](https://mlsanity.com/paper/2408.02906/) (2024)
- [Redefining the Down-Sampling Scheme of U-Net for Precision Biomedical Image Segmentation](https://mlsanity.com/paper/2602.19412/) (2026)
- [Task-Relevant Null-Space Residuals for Non-Injective Neural Mappings](https://mlsanity.com/paper/2609.37272/) (2026)

## Abstract (arXiv)

Pooling is a critical operation in convolutional neural networks for increasing receptive fields and improving robustness to input variations. Most existing pooling operations downsample the feature maps, which is a lossy process. Moreover, they are not invertible: upsampling a downscaled feature map can not recover the lost information in the downsampling. By adopting the philosophy of the classical Lifting Scheme from signal processing, we propose LiftPool for bidirectional pooling layers, including LiftDownPool and LiftUpPool. LiftDownPool decomposes a feature map into various downsized sub-bands, each of which contains information with different frequencies. As the pooling function in LiftDownPool is perfectly invertible, by performing LiftDownPool backward, a corresponding up-pooling layer LiftUpPool is able to generate a refined upsampled feature map using the detail sub-bands, which is useful for image-to-image translation challenges. Experiments show the proposed methods achieve better results on image classification and semantic segmentation, using various backbones. Moreover, LiftDownPool offers better robustness to input corruptions and perturbations.