# Fractional Max-Pooling

arXiv: https://arxiv.org/abs/1412.6071 · HTML: https://mlsanity.com/paper/1412.6071/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2014.

## Built on by (most cited first, 30 of 35)

- [Resolution learning in deep convolutional networks using scale-space theory](https://mlsanity.com/paper/2106.03412/) (2021)
- [Learning strides in convolutional neural networks](https://mlsanity.com/paper/2202.01653/) (2022)
- [A Survey of Automated Data Augmentation Algorithms for Deep Learning-based Image Classification Tasks](https://mlsanity.com/paper/2206.06544/) (2022)
- [LocalDrop: A Hybrid Regularization for Deep Neural Networks](https://mlsanity.com/paper/2103.00719/) (2021)
- [Survey: Exploiting Data Redundancy for Optimization of Deep Learning](https://mlsanity.com/paper/2208.13363/) (2022)
- [A General Framework for Robust G-Invariance in G-Equivariant Networks](https://mlsanity.com/paper/2310.18564/) (2023)
- [Meta-learning of Pooling Layers for Character Recognition](https://mlsanity.com/paper/2103.09528/) (2021)
- [Strengthening the Training of Convolutional Neural Networks By Using Walsh Matrix](https://mlsanity.com/paper/2104.00035/) (2021)
- [A Layer-wise Adversarial-aware Quantization Optimization for Improving Robustness](https://mlsanity.com/paper/2110.12308/) (2021)
- [Comparison Analysis of Traditional Machine Learning and Deep Learning Techniques for Data and Image Classification](https://mlsanity.com/paper/2204.05983/) (2022)
- [Will there be a construction? Predicting road constructions based on heterogeneous spatiotemporal data](https://mlsanity.com/paper/2209.06813/) (2022)
- [Rethinking Token Reduction for Large Vision-Language Models](https://mlsanity.com/paper/2603.21701/) (2026)
- [LogAvgExp Provides a Principled and Performant Global Pooling Operator](https://mlsanity.com/paper/2111.01742/) (2021)
- [Fuzzy Pooling](https://mlsanity.com/paper/2202.08372/) (2022)
- [FedAVO: Improving Communication Efficiency in Federated Learning with African Vultures Optimizer](https://mlsanity.com/paper/2305.01154/) (2023)
- [Maximal function pooling with applications](https://mlsanity.com/paper/2103.01292/) (2021)
- [DNN Quantization with Attention](https://mlsanity.com/paper/2103.13322/) (2021)
- [Frequency Pooling: Shift-Equivalent and Anti-Aliasing Downsampling](https://mlsanity.com/paper/2109.11839/) (2021)
- [An application of Pixel Interval Down-sampling (PID) for dense tiny microorganism counting on environmental microorganism images](https://mlsanity.com/paper/2204.01341/) (2022)
- [Differentiable Self-Adaptive Learning Rate](https://mlsanity.com/paper/2210.10290/) (2022)
- [A Structurally Regularized Convolutional Neural Network for Image Classification using Wavelet-based SubBand Decomposition](https://mlsanity.com/paper/2103.01823/) (2021)
- [Deep Learning Based Analysis of Prostate Cancer from MP-MRI](https://mlsanity.com/paper/2106.01835/) (2021)
- [Ordinal Pooling](https://mlsanity.com/paper/2109.01561/) (2021)
- [Unsupervised MKL in Multi-layer Kernel Machines](https://mlsanity.com/paper/2111.13769/) (2021)
- [Dilated Continuous Random Field for Semantic Segmentation](https://mlsanity.com/paper/2202.00162/) (2022)
- [Fully Convolutional Fractional Scaling](https://mlsanity.com/paper/2203.10670/) (2022)
- [Deep Multi-Branch CNN Architecture for Early Alzheimer's Detection from Brain MRIs](https://mlsanity.com/paper/2210.12331/) (2022)
- [Scale-Space Hypernetworks for Efficient Biomedical Imaging](https://mlsanity.com/paper/2304.05448/) (2023)
- [ADASR: An Adversarial Auto-Augmentation Framework for Hyperspectral and Multispectral Data Fusion](https://mlsanity.com/paper/2310.07255/) (2023)
- [Dual-View Pyramid Pooling in Deep Neural Networks for Improved Medical Image Classification and Confidence Calibration](https://mlsanity.com/paper/2408.02906/) (2024)

## Abstract (arXiv)

Convolutional networks almost always incorporate some form of spatial pooling, and very often it is alpha times alpha max-pooling with alpha=2. Max-pooling act on the hidden layers of the network, reducing their size by an integer multiplicative factor alpha. The amazing by-product of discarding 75% of your data is that you build into the network a degree of invariance with respect to translations and elastic distortions. However, if you simply alternate convolutional layers with max-pooling layers, performance is limited due to the rapid reduction in spatial size, and the disjoint nature of the pooling regions. We have formulated a fractional version of max-pooling where alpha is allowed to take non-integer values. Our version of max-pooling is stochastic as there are lots of different ways of constructing suitable pooling regions. We find that our form of fractional max-pooling reduces overfitting on a variety of datasets: for instance, we improve on the state-of-the art for CIFAR-100 without even using dropout.