# Learnable Discrete Wavelet Pooling (LDW-Pooling) For Convolutional Networks

arXiv: https://arxiv.org/abs/2109.06638 · HTML: https://mlsanity.com/paper/2109.06638/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 23 references that are in the map.
- First posted on arXiv 13 Sep 2021.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [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)
- [Spectral Representations for Convolutional Neural Networks](https://mlsanity.com/paper/1506.03767/) (2015)
- [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)
- [Scaling the Scattering Transform: Deep Hybrid Networks](https://mlsanity.com/paper/1703.08961/) (2017)
- [LIP: Local Importance-based Pooling](https://mlsanity.com/paper/1908.04156/) (2019)
- [Wavelet Convolutional Neural Networks](https://mlsanity.com/paper/1805.08620/) (2018)
- [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)
- [LiftPool: Bidirectional ConvNet Pooling](https://mlsanity.com/paper/2104.00996/) (2021)

## Built on by (most cited first, 3 of 3)

- [From Coarse to Fine: Learnable Discrete Wavelet Transforms for Efficient 3D Gaussian Splatting](https://mlsanity.com/paper/2506.23042/) (2025)
- [Multiscale Low-Frequency Memory Network for Improved Feature Extraction in Convolutional Neural Networks](https://mlsanity.com/paper/2403.08157/) (2024)
- [Spectral Rectification for Parameter-Efficient Adaptation of Foundation Models in Colonoscopy Depth Estimation](https://mlsanity.com/paper/2603.15374/) (2026)

## Abstract (arXiv)

Pooling is a simple but essential layer in modern deep CNN architectures for feature aggregation and extraction. Typical CNN design focuses on the conv layers and activation functions, while leaving the pooling layers with fewer options. We introduce the Learning Discrete Wavelet Pooling (LDW-Pooling) that can be applied universally to replace standard pooling operations to better extract features with improved accuracy and efficiency. Motivated from the wavelet theory, we adopt the low-pass (L) and high-pass (H) filters horizontally and vertically for pooling on a 2D feature map. Feature signals are decomposed into four (LL, LH, HL, HH) subbands to retain features better and avoid information dropping. The wavelet transform ensures features after pooling can be fully preserved and recovered. We next adopt an energy-based attention learning to fine-select crucial and representative features. LDW-Pooling is effective and efficient when compared with other state-of-the-art pooling techniques such as WaveletPooling and LiftPooling. Extensive experimental validation shows that LDW-Pooling can be applied to a wide range of standard CNN architectures and consistently outperform standard (max, mean, mixed, and stochastic) pooling operations.