# Ordinal Pooling

arXiv: https://arxiv.org/abs/2109.01561 · HTML: https://mlsanity.com/paper/2109.01561/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 23 references that are in the map.
- First posted on arXiv 3 Sep 2021.

## Builds on (most cited first, 13 of 13)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [Network In Network](https://mlsanity.com/paper/1312.4400/) (2013)
- [Seed, Expand and Constrain: Three Principles for Weakly-Supervised Image Segmentation](https://mlsanity.com/paper/1603.06098/) (2016)
- [Stochastic Pooling for Regularization of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1301.3557/) (2013)
- [Fractional Max-Pooling](https://mlsanity.com/paper/1412.6071/) (2014)
- [Learned-Norm Pooling for Deep Feedforward and Recurrent Neural Networks](https://mlsanity.com/paper/1311.1780/) (2013)
- [Minimum Energy Quantized Neural Networks](https://mlsanity.com/paper/1711.00215/) (2017)
- [S3Pool: Pooling with Stochastic Spatial Sampling](https://mlsanity.com/paper/1611.05138/) (2016)

## Abstract (arXiv)

In the framework of convolutional neural networks, downsampling is often performed with an average-pooling, where all the activations are treated equally, or with a max-pooling operation that only retains an element with maximum activation while discarding the others. Both of these operations are restrictive and have previously been shown to be sub-optimal. To address this issue, a novel pooling scheme, named ordinal pooling, is introduced in this work. Ordinal pooling rearranges all the elements of a pooling region in a sequence and assigns a different weight to each element based upon its order in the sequence. These weights are used to compute the pooling operation as a weighted sum of the rearranged elements of the pooling region. They are learned via a standard gradient-based training, allowing to learn a behavior anywhere in the spectrum of average-pooling to max-pooling in a differentiable manner. Our experiments suggest that it is advantageous for the networks to perform different types of pooling operations within a pooling layer and that a hybrid behavior between average- and max-pooling is often beneficial. More importantly, they also demonstrate that ordinal pooling leads to consistent improvements in the accuracy over average- or max-pooling operations while speeding up the training and alleviating the issue of the choice of the pooling operations and activation functions to be used in the networks. In particular, ordinal pooling mainly helps on lightweight or quantized deep learning architectures, as typically considered e.g. for embedded applications.